Risky Business

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Title: Risky Business A Case for Cat-Bonds in Florida's Insurance Crisis
Physical Description: Book
Language: English
Creator: Kling, David A.
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2009
Publication Date: 2009


Subjects / Keywords: Cat-Bond
Bond Catastrophe
Risk Management
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation


Abstract: Following Hurricane Andrew in the mid 1990's insurers invented a new kind of bond to provide coverage for improbable, costly, catastrophes. Known as "cat-bonds" investors bought these bonds before a catastrophe ever happened. In return they received a high coupon-rate. However, if a catastrophe "triggered" the bond, then the investor would lose the bond's principal, which instead would pay the insurer's losses. This thesis accomplishes three objectives with regards to these bonds. First, I demonstrate these bonds' potential effectiveness and efficiency in financing the Florida Hurricane Catastrophe Fund's current coverage shortfall. Second, I demonstrate the attractiveness of cat-bonds to investors through modeling their low correlation with other asset classes over the last five years. Third I show how this low-correlation property broke down in 2008. I use the events of the 2008 financial crisis to build an explanatory model of this singular behavior.
Statement of Responsibility: by David A. Kling
Thesis: Thesis (B.A.) -- New College of Florida, 2009
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Strobel, Frederick

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2009 K6
System ID: NCFE004130:00001

Permanent Link:

Material Information

Title: Risky Business A Case for Cat-Bonds in Florida's Insurance Crisis
Physical Description: Book
Language: English
Creator: Kling, David A.
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2009
Publication Date: 2009


Subjects / Keywords: Cat-Bond
Bond Catastrophe
Risk Management
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation


Abstract: Following Hurricane Andrew in the mid 1990's insurers invented a new kind of bond to provide coverage for improbable, costly, catastrophes. Known as "cat-bonds" investors bought these bonds before a catastrophe ever happened. In return they received a high coupon-rate. However, if a catastrophe "triggered" the bond, then the investor would lose the bond's principal, which instead would pay the insurer's losses. This thesis accomplishes three objectives with regards to these bonds. First, I demonstrate these bonds' potential effectiveness and efficiency in financing the Florida Hurricane Catastrophe Fund's current coverage shortfall. Second, I demonstrate the attractiveness of cat-bonds to investors through modeling their low correlation with other asset classes over the last five years. Third I show how this low-correlation property broke down in 2008. I use the events of the 2008 financial crisis to build an explanatory model of this singular behavior.
Statement of Responsibility: by David A. Kling
Thesis: Thesis (B.A.) -- New College of Florida, 2009
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Strobel, Frederick

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2009 K6
System ID: NCFE004130:00001

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RISKY BUSINESS: A CASE FOR CAT-BONDS IN FLORIDAS INSURANCE CRISIS By David A. Kling A Thesis Submitted to the Division of Social Sciences New College of Florida in partial fulfillment of the requirements for the degree Bachelor of the Arts Under the Sponsorship of Dr. Fred Strobel Sarasota, FL April, 2009


RISKY BUSINESS: A CASE FOR CAT-BONDS IN FLORIDAS INSURANCE CRISIS David Kling New College of Florida, 2009 ABSTRACT Following Hurricane Andrew in the m id 1990s insurers invented a new kind of bond to provide coverage for improbable, costly, catastrophes. Known as cat-bonds investors bought these bonds before a catastroph e ever happened. In return they received a high coupon-rate. However, if a catastr ophe triggered the bond, then the investor would lose the bonds principal, which in stead would pay the insurers losses. This thesis accomplishes three objectives with regards to these bonds. First, I demonstrate these bonds potential effectiveness and efficiency in financing the Florida Hurricane Catastrophe Funds current covera ge shortfall. Second, I demonstrate the attractiveness of cat-bonds to investors th rough modeling their low correlation with other asset classes over the last fi ve years. Third I show how this low-correlation property broke down in 2008. I use the events of the 2008 financial crisis to build an explanatory model of this singular behavior. Dr. Fred Strobel Division of Economics ii


Table of Contents Abstract.............................................................................. Error! Bookmark not defined. ii Table of Contents.............................................................................................................. ii Introduction: Floridas Herculean Task.........................................................................1 Chapter 1: Floridas Catastrophes on the Gulf and In the Insurance Market...........3 1.1 Introduction............................................................................................................... 3 1.2 The Structure of Catastrophe Risk Management......................................................4 1.2 Hurricanes in Florida................................................................................................8 1.4 Impact of Hurricane Andrew on the Insurance Market..........................................11 1.4.1 Putting on the brakes: Moratoriums and Phase-outs........................................12 1.4.2 Providing Insurers a Shelter fr om the Storm: The Cat Fund...........................13 1.4.3 Expanded Public Insurance: Citizens Prototypes............................................14 1.5 Effects of Hurricane Katrina on Insurance.............................................................17 1.6 Floridas 2007 Insurance Legislation......................................................................18 1.7 Cost Benefit Analysis of Alternativ e Risk Transfer in the Cat Fund.....................21 1.7.1 The Failure of the Law of Large Numbers......................................................24 1.7.2 Additional Concerns Regarding Risk Transfer................................................26 1.8 Policy Actions in 2008: The Financ ial Crisis and the Buffett Deal........................28 1.9 Policy Recommendations Using Cat-Bonds...........................................................30 1.10 Conclusions...........................................................................................................36 Chapter 2: The Function and Place of Cat-Bonds in Risk Management..................38 2.1 Introduction.............................................................................................................38 2.2The Structure of a Typical Cat-Bond.......................................................................38 2.3 History of Cat-Bonds..............................................................................................42 2.4 Hurricane Katrinas effect on the cat-bond market.................................................45 2.5 Cat-Bond Triggers..................................................................................................47 2.6 Pricing Cat-Bonds...................................................................................................53 2.7 Optimal Allocation of Cat-Bonds w ithin an Insurers Portfolio.............................61 2.8 Conclusions.............................................................................................................64 Chatpter 3: Cat-Bonds and Market Risk.....................................................................66 3.1 Introduction.............................................................................................................66 3.2 Zero correlation evidence.......................................................................................66 3.3 The Swiss Re Cat-Bond Indices.............................................................................72 3.4 Analysis I: Regression analysis of the Swiss Re U.S. Wind Index 2004-2009......75 3.4.1 Baseline Results in Period (1)..........................................................................79 3.4.2 Experimental Results in Period (2)..................................................................79 3.4.3 Five-Year Analysis in Period (3).....................................................................81 3.5 Cat-Bonds and Counterparty Credit Risk...............................................................82 3.6 Analysis II: Specific Impact of Lehmans Collapse on the Cat-Market.................85 3.6.1 The Model for Analysis II................................................................................87 3.6.2 Selecting the Persistency of the Dumm ies for Ike and Lehmans Collapse....90 3.6.3 Results from Analysis II..................................................................................92 3.7 Adaptations in New-Bond Issues............................................................................94 3.8 Conclusions.............................................................................................................95 iii


iv Conclusion: 2009 and Beyond........................................................................................97 Appendix 1: Analysis I Tables.......................................................................................99 Appendix 2: Analysis II Tables....................................................................................100 References..................................................................................................................... .102


Introduction: Floridas Herculean Task. The ancient Greeks tell of a nine-headed dragon named the Hydra. Whenever a hero attempted to cut off one of the Hydras heads, the beast merely sprouted two new heads and ate its opponent. At last, Hercules was able to slay the hydra by burning each neck after slicing off the Hydras heads. In their own herculean task, Florida policymakers have tried to segregate hurricane risk through its partition into Citizens and the Florida Hurricane Catastrophe Fund, the states public insurance entities. The crisis has responded by sprouting two new heads: a weakened private market and a potential $25 billion short-fall in collateral. Public institutions are an important weapon in the insurance crisis. However, Florida needs the torch of reinsurance to effectively sever hurricane risk and prevent its reappearance. Among the most creative reinsu rance products to emerge in the last twenty years are cat-bonds. Insurers can sell these bonds before a hurricane to collateralize their obligations to policy holders. In return cat-investors rece ive a healthy interest rate. However, if a hurricane trigge rs the cat-bond, the investor lo ses his entire principal, which goes instead to pay insured losses. Insurers have generally used these bonds to provide capital for the least pr obable events, i.e. the highest levels of loss. This makes cat-bond triggers extremely rare. Only one such bond has been tr iggered since their invention. Since hurricane-related losses ar e independent of other capital markets, proponents often claim that cat-bonds have a zero-correlation with the market, making them an attractive hedge with in an investment portfolio. In this thesis I demonstrate that catast rophe bonds are an effective and efficient means of reinsurance when compared to alte rnatives products available to the Florida 1


Hurricane Catastrophe F und. I further provide evidence of cat-bonds low-correlation with other asset classes. This reinforces their attractiveness to investors. I finally demonstrate the effect of the 2008 financ ial crisis on these bonds and outline the challenges ahead for this developing market. Chapter 1 outlines the crisis facing Flor ida policy makers and shows how catbonds could be helpful in desi gning a sustainable solution for high-risk coverage layers. Specifically, I find that a thre e-year plan using cat-bonds is both more efficient and effective at transferring risk than a plan using only post-storm bonding contracts. Chapter 2 discusses the structure, history and academ ic literature surrounding cat-bonds in greater detail. Chapter 3 provides two empirical analyses of cat-bond trading in the secondary market. Analysis I demonstrates the low corre lation of cat-bonds with other assets from 2004 to 2009 using an ordinary least squares re gression model. However, the model also shows that cat-bonds had significant correlation with other assets in 2008. I attempt to explain the causes behind this recent co-moveme nt with other asset classes in Analysis II. Analysis II uses dummy variab les for Hurricane Ike and the collapse of Lehman Brothers to flesh-out the story underlyi ng this increased correlation. 2


Chapter 1: Floridas Catastro phes on the Gulf and In the Insurance Market 1.1 Introduction Floridas risk of economic disaster is enormous. Its present and future wealth depends greatly on the viability of its real -estate market and yet every year these properties face the possibility of destruction through Hurricane winds. Of the other fifty states, perhaps only California with its active fa ult-lines shares in this degree of incessant, and potentially crippling, danger. To make matters worse this same real-estate market requires a robust insurance infrastructure to continue. This infrastructure is buckling under the weight of expected losses in th e Florida market and current reinsurance mechanisms are not appropriate ly transferring the risk. Policymakers find themselves torn between the choice of either smothering the real-est ate market with high insurancepremiums or jading private insurers by legislating impotent strategies. As yet a satisfactory solution to thes e issues has not emerged. Although cat-bonds have transferred risk in Floridas private insurance market for more than a decade, to date Floridas extens ive public insurance organizations have not used these products. Floridas policymakers ha ve not used cat-bonds to transfer risk, purportedly due to the inability of current rates to support purchasing reinsurance of any kind. Floridas burden of catastrophic risk will not disappear, however, and these instruments may prove useful in the future as policy and market regimes change. This chapter serves to situate th e broader discussion of catastr ophic risk management within Floridas geographic and polit ical environment. An examination of the key storms, 3


stakeholders and legislation in the Florida in suran ce crisis provides the motivation for a more in-depth analysis of cat-bonds themselv es in the following chapters. This chapter will present the issues and costs associated w ith cat-bonds as they currently face Florida. 1.2 The Structure of Catastrophe Risk Management The m assive losses caused by a major catastrophe present a unique financial problem to property owners. Indeed, the prob lem exceeds the resources of an individual owner or even an individual insurer. The economic risks are so great that a whole network of stakeholders must take part in the spreading of that risk. While both public and private institutions participate in this pr ocess, an idealized model of private risk management and its stakeholders will first be summarized. The private stakeholders in catastrophe risk management naturally references those obligated to pay for ensuing damage. This includes not only the property owners themselves, but also a network of private in dividuals and institutions willing to purchase part of their risk. Grossi a nd Kunreuther describe this network as a pyramid, wherein each layer sells a portion of their risk to th e layer directly above. Thus at the bottom of the pyramid are the property owners themselv es. These individuals may then sell their risk to primary insurers. These insurers may th en sell, or cede, a portion of their risk to reinsurers who may, in turn, sell a portion of their risk to investors in the capital markets.1 1 Grossi, 8. 4


Capital Markets Reinsurers Primary Insurers Property Owners Figure 1.1 Risk Management Structure Property ow ners, both residential and commercial, bear the brunt of a catastrophes risk. They face pe rsonal loss as well as physical danger in the case of residential homeowners. They may reduce thei r risk by strengthening their homes wind resistance or by purchasing homeowners insu rance. Commercial property owners face the further loss of earnings if the hurricane should interrupt their ope rations through physical damage or loss of infrastructure. They thus tend to take a more pr oactive approach than residential owners in the risk management process.2 Lending institutions like banks usually require property owners to purchase insurance before offering a mortgage since wind damage threatens the ability for a bui lding to produce income for the lenders. Property owners also remain responsible for their deductibles. The next stake-holders in the risk management process are primary insurers, who provide the first layer of risk coverage after the deductable. An insurer balances its risk portfolio, or book of business, much like an in vestor in the capital market would balance 2 Grossi, 9. 5


his portfolio. Many investors re duce the r isk of loss in thei r portfolios by investing in a variety of asset classes, such as stocks, bonds, and real estate. This makes it more likely that the failure of one asset cl ass will not dangerously threaten the portfolio as a whole. In a similar way, insurers want to spread the risk of natural catastrophes through diversifying geographically, avoi ding concentration in a particular area. They can reduce their risk either by limiting the number of po licies in a given area or by charging higher premiums in disaster prone regions to mitigate possible losses. Much like insurance companies, reinsurers do not want to conc entrate their risk. To reduce their concentration, reinsurers often purchase ri sk for uncorrelated disasters over a broad range of areas. For instance a reinsurer could purchase one companys earthquake risk in Japan and a different co mpanys hurricane risk in Texas and a third companys fire risk in Pennsylvania. This ma kes it less likely that a single disaster could completely drain the reinsurer financially. It also makes it more probable that the reinsurer can continue enough prem iums from the other regions to finance a large disaster in one. Much like a homeowner in search of a mortgage, most insurers must purchase a certain amount of reinsurance in order to ap pease insurance regulat ors and to maintain their financial rating.3 Essential for the purposes of this paper is an understanding of the risk management stakeholders in the capital mark ets. These include the hedge fund managers and institutional investors interested in purch asing insurance linked securities as well as the investment banks who assist in main taining these securi ties. Also known as alternative risk transfer inst ruments, these insurance linke d securities have taken many 3 Grossi, 10. 6


for ms in the past two decades. The most su ccessful of these innovations have been catbonds. While not direct stake-holder s, rating agencies, insurance regulators and naturaldisaster modeling companies serve as custodian s of the risk management process. These parties ensure that all stake holders benefit from accurate information and standardized practices. Insurance commissioners evaluate insurers on their solvency and their rates. Solvency regulations are meant to ensure that insurance companies keep enough capital available to pay for a disaster. The rate regu lations are meant to ensure that insurers conduct business with policy hold ers in a fair and equitabl e manner. This includes the rates charged to customers as well as the beha vior of insurance salespeople. In all states this includes a license bureau which controls who may legally underwrite policies. Commissioners evaluate reinsurers on solvency regulations only.4 Rating agencies in the capital markets al so provide a crucial role. Agencies like Standard and Poors, Fitch and Moodys evalua te the bonding capabilities of insurers as well as their corporate strength. These institu tions also asses individual cat-bonds. Rating agencies thus evaluate both insurance companies and bonds for their benefits to customers. A poor rating impacts the rates such companies and bonds can charge. Modeling agencies provide computer estimat es of an insurers risk. The software used by these companies evaluates the number and strength of properties in a region and then generates catastrophe simulations to model the probable losses for a particular insurer. The software may estimate as many as ten thousand years of hypothetical hurricane paths in reaching its decision. While a perfect mo del may be unattainable, the 4 Grossi, 11-12. 7


software has improved immensely in its precision in the last two decad es. Insurers rely on these models in setting rates. The three ma jor modeling agencies are Risk Management Solutions (RMS), AIR Worldwide (AIR), and HAZUS, an agency of the Federal government. The risk management pyramid can be thought of as a roadmap for this thesis trajectory. This thesis will follow the risk management pyramid in Florida from the ground up. Policyholders concerns in hurricane s will first be considered, followed by those of insurers and re insurers. The thesis will conclude with the concerns of investors in the capital market. Ultimately, the reactions and concerns of each of these stakeholders contribute to the success of cat-bonds in transferring risk. 1.2 Hurricanes in Florida. Millionaires flocked to F lor ida in the 1920s seek ing a glamorous coastal lifestyle. This led to a boom in the real-estate ma rket, inflated by rampant speculation. In 1925, Miami had been the fastest growing city in America with over $60 million in new construction. In the early hours of September 18, 1926 a storm of unprecedented fury made landfall in Miami, reaching sp eeds of 138 miles an hour. Now classified as a category 4 storm, the hurricanes eye passed directly thro ugh Miami. Its winds buf feted the city for a full twelve hours before crossing the peni nsula through the evergl ades and landing once again in Pensacola on September 20 for a s econd attack. Damages were estimated at between $112 million and $159 million with the Red Cross reporting 373 dead, 6,381 injured, 43,000 homeless and 811 missing.5 5 Barnes, 110, 112, 121, 126. 8


The Great Miam i Hurricane killed the Fl orida real-estate boom. Land prices declined by ten-fold in many places. New construction was left unfinished. Although the great financial crash of 1929 was three years away, for Florida, the descent into the depression had already begun.6 The National Hurricane Center estimates that if the 1926 Great Miami Hurricane had instead struck in 2006 given current population and wealth, it would cause approximately $165 billion in economic damages in 2006-adjusted dollars.7 Although the 1926 hurricane has nearly passed out of living memory, many Floridians still remember Hurricane Andrew vividly. Those who do not still live under the Andrews influence, adhering to regulations and policies provoked by this catastrophe. On August 24, 1992 Andrew ma de landfall in South Dade County, sustaining speeds of 145 miles per hour a nd reaching speeds of 175 mph, a category 5 storm. Andrew trailed a swath of destruc tion the size of Chica go, nearly destroying 80,000 homes and damaging a further 52,000. The in flation adjusted costs would total $48 billion and 100,000 people would leave the county permanently.8 Both the 1926 hurricane and Andrew had grave physical and political consequences for Florida. However, alt hough the bulk of Hurricane Katrinas economic losses were in Louisiana, this storm, too, ha s had massive implicati ons for Floridas risk environment. Katrina made landfall in Louisiana on August 29, 2005 passing near New Orleans and logging speeds of 125 miles an hour, a category 3 storm. The storm surge, however, would prove as destructive as th e winds. New Orleanss levees broke; Oil production halted in the gulf. The costliest storm in history, the National Hurricane 6 Barnes, 126. 7 Blake et al, 9. 8 Barnes, 265, 276, 284. Blake et all, 9. 9


Center estim ates Katrina caused $84 billion in economic losses. It was also the third deadliest storm in U.S. history causing 1500 deaths.9 According to the National Hurricane Cent er, 113 of the total 279 hurricanes to strike the U.S. in the last 150 years struck Florida. This 40.5 percen t share of storms in the data-set spanning 1851-2006 could well be higher due to low population-levels in Florida before 1900. Of these 279 U.S. storms, Florida had two of the three category 5 hurricanes, six of the eighteen category 4 hurricanes and 29 of the 75 category 3 hurricanes. This means Florida had 38.5 percen t of these dangerous-category storms. This was a far greater share than any other state, the closest runner-up being Texas with 19.8 percent of the upper-level storms. The cente r notes that on average seven hurricanes strike the United States every four years, or nearly two per year, with two major hurricanes making landfall every three years. A study of hurricane cycles in 20 year periods further revealed that Florida was a prominent target in every cycle.10 This persistence in storm behavior has translated, and will continue to translate, into enormous costs for Florida. All five of th e costliest storms in U.S. history hit Florida: Katrina, Andrew, Wilma, Charley and Ivan. Four of these occurred in the last five years, each causing economic damages in excess of $15 billion using a 2006 deflator. No matter the speculations of accelerating hurricane patter ns, economic losses certainly appear to be accelerating as storms strike ever more populous coastlines.11 An equally chilling report from the cente r shows Floridas futu re through its past. Running historic hurricane paths assuming 2006 population and wealth, Katrina drops to third-place among the costliest storms. The Great Miami Hurricane tops the list. Two 9 Blake et all, 7 and 9. 10 Blake et al, 17 and 18. 11 Blake et al, 8 and 9. 10


other Florida storm s before 1950 make the t op ten, indicating the increase in population and wealth redistribution in the last half-century.12 1.4 Impact of Hurricane Andrew on the Insurance Market No hurricane had a greater effect on Flor ida s public policy and its insurance market than Andrew. Following the devasta tion of 1992, a string of special legislation sessions made a desperate attempt to hold the market together. New regulations and organizations rapidly emerged. These altered prices, fees and portf olio composition for insurers and polic yholders alike. Just prior to Andrew Florida had the fi fth largest insurance market of all the states, with a five percent share of all pr operty casualty premiums. Andrew caused an immediate move among these insurers to reduce their Florida exposure. The Property Claim Service (PCS) estimated insured losses from Andrew to be $15.5 billion. By early 1993 a total of 39 insurers no tified the Florida Department of Insurance that they intended to cancel 844,433 policie s in the Florida market.13 Andrew initiated a paradigm shift among th ese insurers as new models revealed current exposure to be untenable for individu al companies. This new understanding of the potential scale of losses cast current rates into doubt. Primary insurers feared the loss of profits and unfavorable credit ratings. With balance sheets already in arrears, the high cost of reinsurance made even risk transfer difficult. Some companies chose to withdraw from the Florida market altogether. Even worse, Andrew caused nine primary insurers to become insolvent. Eight of the nine companies were based in Florida. E ach had suffered significa nt decreases in their 12 Blake et al, 8 and 9. 13 Lecomte, 105-106. 11


surpluse s, or the capital available to pay claims. The companies together held surpluses of $37 million. Their defaults ex acerbated the shortages of the remaining companies, who were forced to make up the balance. The Florida Insurance Guarantee Asso ciation (FIGA) in accordance with 1970 state legislation assessed these insurers by 2 percent of gross annual premiums, the maximum legal amount. Indeed the legislature doubled the legal assessment from 1 to 2 percent soon after Andrew when it became appa rent that the FIGA would need to finance unprecedented levels of claims. The assessmen t generated $70 million and caused a tenth company to become insolvent. Needing $430 m illion to finance unpaid claims, the FIGA received further power to asse s insurers an additional 2 per cent annually for ten years in order to finance up to $500 billion in ta x-free bonds. The bonds, issued as municipal bonds through the city of Homest ead, were retired early in 1997.14 1.4.1 Putting on the brakes: Moratoriums and Phase-outs In addition to the expanded powers of the FIGA, the state gov ernment issued a series of moratoriums on withdrawals for in surance companies. The Florida Insurance Commissioner issued a ninety-day moratori um in November after the storm. Under Florida law, the Commissioner retained full executive authority in insurance matters. Insurers had to give ninety days notice befo re withdrawing and had to prove that their absence would not negatively affect the insurance market. The Department of Insurance placed a further moratorium in May of 1993 on canceling or not renewing residential policies for ninety days. The Legislature extended this moratorium an additional three months. 14 Lecomte, 107-108 12


At the m oratoriums expiration in November 1993 the legislature regrouped for a special legislative session which would dr astically altar the te nor of the states relationship to the insurance i ndustry. Only slightly weaker than the moratorium, they issued a phase-out bill which restricted cancelations and non-rene wals to ten percent annually in a given county a nd five percent state-wide. A lthough originally mandated for three years, this legisla tion was extended until 1999.15 Legislators found themselves in the relati vely new position of being at odds with the private Insurance industry. Writing contemporaneously, Lecomte and Gahagan note: While the moratorium serves as a barrier to market exit, it is also a barrier to market entry. Insurers not doing bu siness in Florida are reluctant to enter because they are concerned that the may not be able to exit if business circumstances change. More significantly, the moratorium contributes to the reluctance of insu rers already writing in the state to increase their market share.16 Higher market shares meant both higher potential assessments as well as increased levels of unmovable risk. Companies had to wei gh the costs and rewards of expanding their book of business. 1.4.2 Providing Insurers a Shelter fr om the Storm: The Cat Fund During the same special legislative se ssion in November 1993, the legislature established the Florida Hurricane Catastr ophe Fund (FHCF). The motivation for the fund was to facilitate the continued renewal of policies through providing public reinsurance. This was to expand capacity offered by private reinsurers. The FHCF would collect premiums from insurers in proportion to each insurers exposure, considering factors of location, deductable, and cons truction type. It would supplement these premiums through 15 Lecomte, 110-111. 16 Lecomte, 111. 13


post-storm bonds financed through a maxi mum four percent assessment on insurer premiums. The tax-exempt status of the fund would also aid insurers by keeping a portion of available cash off their balance sheets. Th is would reduce insure rs taxes on reserves during years of low-hurricane activity.17 As originally conceived, the FHCF was not responsible for paying more than the sum of its assets and borrowi ng capacity in the event of a hur ricane. Insurers could expect to recoup the amount of thei r actual premium paid to the FHCF times a coverage multiple. The coverage multiple would be calculat ed as the total capacity of the FHCF for that year divided by the total premiums collected. For instance, in 1997 the fund had $1.97 billion in cash and a bonding capacity of $6 billion for a to tal capacity of $7.97 billion. The total premiums paid into th e fund that year were $471 million yielding a coverage multiple of 16.9. Thus an insurer could expect a minimum reimbursement of $16.90 for every dollar paid into the fund. If some insurers did not utilize this minimum, others might receive a larger share.18 1.4.3 Expanded Public Insurance: Citizens Prototypes The special legislative session in Dece m ber 1992 directly af ter Andrew also addressed the insurance crisis at its root. Although an existing organization, the Florida Windstorm Underwriting Asso ciation (FWUA), had provide d residential hurricane policies to risk-prone coasta l areas since 1970, the general contraction in the Florida insurance market motivated a more wide -spread program. The legislature thus established the Florida Residential Property and Casualty Jo int Underwriting Association (FRPCJUA). They designed this program to work in parallel to the FWUA but with a 17 Lecomte, 112-113. 18 Lecomte, 112-113. 14


broader geographic m andate. Also, while th e FWUA had a focused goal of providing wind coverage, the FRPCJUA could act as a holistic insurer, offering multi-peril policies. In regions already eligible for FWUA coverage, the FRPCUJUA sold these multi-peril contracts without the wind clause. Togeth er these organizations formed Floridas residual insurance market. They acted as primary insurers to those unable to find coverage in the voluntary market. 19 The two organizations wo uld later merge to form Citizens Property Insurance in 2002. Legislators and regulators alike held ear ly concerns that these public insurers would offer below market rates. This w ould undercut the private market and could actually reduce overall capacity. Indeed, the rates initially charged by the FRPCJUA were lower than the market, ostensibly to entice ne w participants in the fledgling organization. This state of affairs did not last long. Indeed, from 1993 to 1998 premium quotes for the FRPCJUA increased a total of 90 pe rcent for homeowner policies and 67 percent for mobile homes. In 1995, the legislature set new price floors for the FRPCJUAs rates. For houses, the associations average rate coul d be no lower than the lowest rate quoted by the ten largest private insurers. For mob ile homes, the minimum rate would be the lowest rate quoted by the five largest pr ivate insurers. This standard was to be recalculated for each county. By 1998 the FR PCJUA had the highest average rates for each of Floridas 67 counties.20 Similarly, after Hurricanes Opal a nd Erin the FWUA realized it needed significantly higher rates. These storms led to assessments of $84 million and $33 million respectively upon the private market. After these deficits the FWUA reviewed its 19 Lecomte, 113-114. 20 Lecomte, 115. 15


portfolio and decided they need ed to m ore than double their rates. They estimated this figure to be an average increase of 124 percen t. Realizing that an immediate increase of this magnitude would not be tolerable for policy holders, they pe titioned the insurance commissioner to raise rates gradually to this rate.21 The FRPCJUA seldom rejected a policy application. The private market financed both the associations operating costs and th e collateral for its coverage. The FRPCJUA levied an annual assessment on all private insurers based on market share, as defined by the gross premiums collected in the previ ous year. The association could charge the higher of two optional maximum rates: either 10 percent of the associ ations deficit or 10 percent of the sum of premiums written in the states private mark et. Moreover, if the regular assessments could not finance the a ssociations deficit then the FRPCJUA could levy an additional emergency assessment at the same maximum rate.22 Thus a company could face a maximum assessment of either 20 percent of total markets business or 20 percent of the deficit. Thus the immediate political response to A ndrew resulted in greater restrictions on private insurers as well as increased reinsura nce for these insure rs through the FHCF or Cat Fund. Moreover, th e immediate formation of the FRPCJUA provided last-resort coverage to interior and coasta l areas alike at above-market prices. Above all, the states ability to finance these new institutions through levying assessments, or taxes, on insurers and policyholders greatly increased. 21 Lecomte, 120. 22 Lecomte, 116-117. 16


1.5 Effects of Hurricane Katrina on Insurance By 2005 huge steps had been taken in ra te policies and bonding capabilities since Andrew. In 2002 the Legislature consolidated the office of the Insurance Commissioners into that of the Florida CFO. The Legisl ature further consolidated the FRPCJUA and FWUA into a single entity: Citizens Insura nce Corporation. These consolidations had netted further efficiencies in policy-maki ng and execution. Moreover, the Cat Fund now had extensive power in issuing tax-free bonds equivalent to municipal bonds. However, the months following Katrina in 2005 saw Florida once again scrambling to find enough coverage for policyholders as primary insure rs reevaluated their books of business. The problem was particularly pronounced for commercial insurance in Florida. A 2006 Florida Office of Insurance Regulation surv ey of the commercial insurance market found that 17 percent of commercial property owners could not obtain coverage at any price. In addition, 39 percent found they could only find rates they considered unreasonable with only 19 pe rcent reporting the availability of reasonable prices. Those currently holding commercial polices freq uently experienced rate-hikes. Of these, approximately 29 percent reporte d that their rates had quadr upled. Another 9 percent saw rates at least double.23 In all, eight major storms had hit Flor ida in a 15 month window of time between 2004 and 2005. This was four times the expected national average according to the National Hurricane Center. Thus even if Fl orida had escaped the brunt of Katrinas wrath, significant concerns remained regard ing Floridas vulnerability. The FHCF had spent nearly $7 billion in this period and entered 2006 w ith a deficit. Naturally, 23 Dixon et al, 1-2. 17


hom eowners received assessments for 2005 in addition to the assessments received in 2004. 24 Citizens, too, faced deficits and had begun levying the necessary assessments on its policyholders. The Legislature responded by shoring up Citizens with $715 million in an effort to reduce assessments from 11 pe rcent to 2.5 percent. The Legislature also mandated that Citizens take a more rigor ous underwriting process for high risk properties. This included limiting coverage of homes with over $1 million in replacement costs. Citizens would also begin assessing high-risk accounts based on a 70-year probable maximum losses (PML) in 2007, an 85-year PML in 2008 and an 100-year PML in 2009.25 These changes would bring Citizens business model much closer to those of private insurers. This legislation would carry the state for six months before the sweeping policy changes of the 2007 sp ecial legislative session. 1.6 Floridas 2007 Insurance Legislation As 2006 progressed, it b ecame apparent that not only commercial and residential property owners were having difficulties fi nding coverage. Primary insurers faced a severe shortage in available reinsurance. Rein surance prices spiked just as they had after Andrew. Rate on line ratios increased across the board from anywhere between 18 and 40 percent.26 By early 2007 it was clear that the first three levels of the risk-management pyramid were shaking. Andrew had prompted the creation of an extensive public insurance infrastructure, but the 2006 reinsurance shor tage would prompt its tr ansformation. In a special 24 Reddick, 1. 25 Riddick, 2. 26 Reinsurance for Natural and Man-Made Catastrophes, 18. 18


legislative session early in 2007, the legislat ure passed new mandates for the FHCF to drastica lly increase its risk portfolio. The bill reads: Because of temporary disruptions in th e market for catastrophic reinsurance, many property insurers were unable to pr ocure reinsurance for the 2006 hurricane season with an attachment point below th e insurers respective Florida Hurricane Catastrophe Fund attachment points.The reinsurance market problems were responsible, at least in pa rt, for substantial premium increases to many consumers and increases in the number of polic ies issued by the Citizens Insurance Corporation.27 The bill attempted to solve this predicament by instituting Temporary Emergency Additional Coverage Options (TEACO). Th ese would allow primary insurers to purchase additional reinsurance coverage in FHCF above and beyond the required amount during the three year period from June 2007 through May 2009. This concept evolved into a furthe r increase in availabl e coverage known as Temporary Increased in Coverage Limits (TICL), under which insure rs could buy a collective $12 billion of coverage in addition to the mandato ry $15.85 billion already under contract.28 The bill further advised the State Board of Administration (SBA), the board in charge of the FHCF, to investigate purchasi ng third-party insurance or alternative risk transfer products in the capital markets. The bill gave the SBA authority to contract with any of these options which woul d maximize the funds capacity: The board may procure reinsurance from reinsurers acceptable to the Office of the Insurance Regulation for the purpose of maximizing the fund and may enter into capital market transactions, incl uding, but not limited to industry loss warranties, catastrophe bonds, side-car arrangements, or financial contracts permissible for the boards usage consis tent with prudent management of the fund.29 27 CS/HB 1A, Engrossed 1/c, 16.a and 16.b. 28 The Florida Senate: Interim Project Report 2008-104, 1. 29 CS/HB 1A, Engrossed 1/c, 7.a. 19


This represented a significant deviation fr om the SBAs hitherto conservative bonding strategies which had always dealt almost ex clusively in post-stor m principal-guaranteed notes. A brief experiment in pre-storm princi pal-guaranteed notes had failed to attract sufficient investor interest. The new TICL legislation proved to o successful for its own good. Primary insurers flocked to the new, below-market pr iced reinsurance. By November of 2007, the Florida Senate committee charged with evaluating the special sessions effect reported sobering news. The new TICL legislation had not solved the reinsu rance shortage, but only concentrated it in the hands of the st ate. Just like the primary insurers who had purchased TICL contracts, the SBA now f ound that it could not purchase reinsurance under its current rate regime. As stated earlier, In the event of a catast rophe, any shortfall in the FHCF must be eliminated through issuing bonds. To fi nance such bonds, the State Board of Administration would levy emergency assessmen ts on most Florida property and casualty insurance policies. These assessments are cap ped at an annual six percent of premium rate to finance damage from a single year. However, if multiple years of damage require financing, then the SBA may not levy more than ten percent of the premium in total. The senate report noted that in 2007 th e FHCF could have potentially owed $27.85 billion to insurers. The fund would ha ve had to finance $25.75 billion of this figure through bonds in the event of a major hurricane. The report elaborated that a bond issue this size was unprecedented and that the demand for such bonds might not exist in that quantity. A bond issue of that magnitude would require thir ty years of annual assessments at five percent of premiums. If two years of severe hurricanes occurred 20


insurers would expect the FHCF to pa y a m aximum of $56 billion. The bond issue required for this sum would imply a ten pe rcent annual assessment for thirty years.30 Once the level of TICL contracts became generally known, the 2007 legislation became notorious in the reinsurance industr y. Black marks were given to the Florida market in general. This was compounded by what Don Brown, chair of the Florida House Committee on Insurance called the potential fo r the largest tax increase in Florida history should the full assessment amount be levied.31 1.7 Cost Benefit Analysis of Alterna tive Risk Transfer in th e Cat Fund As suggested by the 2007 special session le gislation, the FHCF investigated risk transfer strategies for the 2007 hurricane s eason. Their analysis revealed a possible $6 billion of risk transfer through three methods: traditiona l reinsurance, cat-bonds and industry loss warranties. The analysis considered the av ailable capacity each option would generate, the associated premium and the rate on line. The rate on line refers to the ratio of the premium to the coverage. The results are summarized in table 1.1. Traditional reinsurance would offer the highest amount of coverage but at also commanded the highest rate on line at 12 percen t. Cat-bonds had the lowest rate on line at 9 percent, providing a possi ble $1 billion. Warranties fell in between these two options offering $1 billion at 10 percent. In aggregat e the $6 billion would cost 11.2 percent rate on line for a total premium of $670 million. 30 The Florida Senate: Interim Project Report 2008-104, 1. 31 Report to Speaker of the House, 1. 21


Table 1.1: Summary of Risk Transfer Options in 2007 Reinsurance CatBond Industry Loss Warranties Total Risk Transfer Capacity $4 billion $1 billion $1 billion $6 billion Premium $480 million $90 million $100 million $670 billion Rate on Line 12% 9% 10% $11.2 billion As stated in the interim project report to the Florida Senate: The basic effect of this purchase would be to transfer a low probability risk of a large liability, in exchange for an increased risk of a much smaller liability. 32 The amount of cash the FHCF would receive from these tr ansfers in the event of a hurricane differed significantly based on the lo ss size. For low to moderate loss levels, every dollar spent towards the high risk transf er would widen the pot ential shortfall by one dollar. This is because the transfers insured only thos e losses above about $22 billion. Thus for smaller storms the risk transfers attachment points, or deductibles, would not be reached. However, at high levels of loss, i.e. those above $22 billion, every dollar spent on the transfer would yield $8.95. More over, this would significantly improve the FHCFs task of issuing post-catastrop he bonds, decreasing th e $25.75 billion required sale to $19.75 billion. Again, the FHCF was particularly interest ed in transferring th e top half of the TICL, that is the top $6 billion in risk fo r which the FHCF was responsible. This means that the fund would need to pay almost $22 bi llion before the risk transfer would net benefits. The fund estimated that a storm would need to cause total ground-up losses of $31.3 billion to achieve insured losses of this order. Such storms are expected to occur once every 52 years, which translates to a 1.92 percent chance annually. 32 The Florida Senate: Interim Project Report 2008-104, 11-12. 22


Paying the $ 670 million for risk transfer would decrease the funds cash, thereby increasing the probability of a capital shortfa ll for smaller storms from 24.7 percent to 27.5 percent. As already discussed, a stor m of $27.5 billion in size would require Floridians to pay an annual 4.98 percent on premium assessments for thirty years. Transferring the top $6 billi on in capacity would reduce th is percentage to 3.94 percent annually for thirty years. This would sa ve $350 million annually or $10.87 billion over 30 years. 33 Considered as a stream of payments and assuming interest rates of 3 percent these savings would have a present value of roughly $6.86 billion at the hurricanes occurrence. Unfortunately, the FHCF charges much lower rates to acquire risk then these estimated rates to transfer it. In 2007 for this top layer of $6 billion the FHCF received a 1.85 percent rate on line premium or $111 million. This comes far below the $670 million needed to transfer the risk. This significant spread between the market rate and current rate should indicate that the FHCF rates are actuarially unsound. Indeed the FHCF is mandated to charge the actuaria lly indicated premiums for its risk. By convention, the fund has interpre ted this clause to mean premiums that coincide with expected annual losses plus expenses. Models indicate this average annual loss to be approximately $1.2 billion. Thus, ironical ly, although FHCFs 2007 $1.33 billion income covered more than its expected annual loss es, paying the $670 million to transfer the top twenty percent of its risk would leave onl y $538 million to cover the expected loss of $1.2 billion, well below its own actuarial objective.34 33 The Florida Senate: Interim Project Report 2008-104, 12. 34 The Florida Senate: Interim Project Report 2008-104, 12. 23


Since pr ivate reinsurers were charging mu ltiples of expected losses in the months after Katrina, one can well understand the enthusiasm among primary insurers for the FHCF coverage offered at essentially par valu e of expected losses. Expected losses are a workhorse of actuarial valuation. However, considering only expected annual losses would leave funds woefully shor t if a 1-in-100-year storm were to occur before its full 100 years of tenure. This could be described as the failure of the Law of Large Numbers. 1.7.1 The Failure of the Law of Large Numbers Insurance markets often capitalize on the Law of Large Numbers. This law states that if a series of independe nt events follows a common prob ability distribution, then the variance of the series about its expected value decreases as the number of events increases. For insurance companies the events are insured policies each of which has a given probability to cause the company lo sses. Thus according to the Law of Large Numbers, insurance companies can predict the average loss per claim with increasing accuracy as the number of insured events in creases. This assumes, however, that the insured events remain independent of each other and that each event has the same probability to incur a given level of loss. Empirically, Automobile insurance follows the Law of Large Numbers. Each automobile policy is largely independent from the others. Moreover, the predictability of automobile accidents implies that the probability of losses follows a similarly predictable distribution. A simple numerical example will serve to demonstrate the laws function in pricing risk. Consider a set of identical au tomobiles driven by drivers with identical profiles. Each car costs $20,000 to replace and each driver has a 1/500 annual chance of 24


totaling his car. If each driver h as only one accident a year then a full-replacement policy would have an expected a nnual loss of $20,000 (1/500) = $40. The accuracy of this estimate depends on the variance of the expected annual loss: 2 L = [ Lp (1 p) ] / n where 2 L is the variance of the expected annual loss for a single event, L is the size of the loss for the single event, p is the annual probability of that loss, and n is the total number of policies issued.35 If the company issues only a single policy, then the variance would be [$20,000 (1/500) (499/500)] / 1 = $39.92. However, if the company issues a thousand such policies, i.e. n = 1000, then the variance becomes approximately four cents. Thus a higher number of policies would improve a companys accuracy in estimating annual risk. The company can then co llect premiums from this set of drivers slightly above each ones estimated average annu al loss and be reasonably sure of turning a profit. This is an insurers ideal scenario. Unfortunately, catastrophic events li ke hurricanes, earthquakes, floods or wildfires break down this tidy business model. In these cases a si ngle catastrophe causes insured losses across an entire region and individual policie s can no longer be considered independent. Instead, companies must consider not the variance of an individual loss, but rather the variance of the aggregate losses associated with a catastrophic event. This variance is much more chal lenging to accurately predict.36 Observed in this fashion, the FHCF seem s like a Ponzi Scheme. It takes in rockbottom premiums and is supposed to provide coverage for an enormous event thirteen times its holdings. 35 Insurability Conditions, 24. 36 Insurability Conditions, 25. 25


1.7.2 Additional Concerns Regarding Risk Transfer In addition to these pricing concerns, th e Florida Senate report also raises the question of whether an FHCF risk transfer would be counterproductive. The FHCF was created to expand reinsurance capacity in the Florida market. In 2007 the legislature decided to use the FHCF to re duce residential insurance prem iums, in effect substituting capacity rather than expanding it. Risk transf er might run contrary to both these goals. The transfer might reduce capacity at othe r insurers as well as raise costs for policyholders in order to reduce the spread in the rates on lines.37 While an important consideration, this concern does not take into account the already es tablished pattern of reinsurers spreading, or cedi ng, risk through peers in the re insurance market or through the capital markets. This concern would be partially alleviated if it could be dem onstrated that the FHCF could buy risk transfer in bulk at a lo wer rate than the comb ined efforts of the private market. Reinsurance prices do differ based on the quality of the primary insurers risk. If an insurers risk of loss is less than modeled losses or if the insurer is particularly adept at managing claims then the insurer w ould get a better reinsurance rate. Insurers may also receive better rates from a parent company if that company also deals in reinsurance. Unlike these private reinsurers underwriting process, the FHCF charges the same rate to all primary insurers. Likewise, the FHCF would receive a flat rate for each of its risk transfer products. While it was estimated this rate would be somewhere in the middle of the spectrum of market rates, it was not determined whether this rate would be 37 The Florida Senate: Interim Project Report 2008-104, 11. 26


less than the aggregated rates offered to Flor ida private insurers fo r the sam e amount of transfer.38 In an interview with cat -bond fund manager John Seo, Seo predicted that there would be significant investor in terest if the FHCF were to issue at least $1 billion in Cat Bonds. He noted that while the market wa s just beginning to grow, the FHCF would have the potential to, materially spur the ma rket, due to its ability to place such an order. Moreover, Seo advised that an FHCF bond issue would have a much better chance at using an indemnity trigger rather than an index trigger due to its role in reinsuring every insurer in the state. This would elim inate the problem of basis risk, so often a drawback for other insurers.39 The difference between these triggers and the importance of basis risk will be considered at length in chapter 2 of this thesis. The Senate Interim Project Report concludes that if rates are not raised to cover the risk transfer, such a transfer would not be an actuarially sound option in the long term. Policy arguments could be made that such a transfer would be beneficial for specific objectives, such as the additional TICL capacity offered in 2007, 2008 and 2009. A transfer in this case would increase the FHCFs ability to meet its post-storm bonding obligations. However, as a ge neral long-term strategy the drain on cash reserves would raise the risk of funding gaps for smaller storms. Long term risk transfer plans might also send a negative message regarding the State s financial confidence in the FHCF as a reinsurer. Furthermore, raising the rates in order to transfer the risk would only net an efficiency gain if the FHCF could get a lower rate than possible in the private market. 38 The Florida Senate: Interim Project Report 2008-104, 13. 39 The Florida Senate: Interim Project Report 2008-104, 13. 27


Such a rate hike would also negate the recen t goal of using the FHCF to lower residential premiums.40 It is important to keep in mind Seos idea that the cat-bond ma rket is still so young that such a bond issue would actually generate demand. The FHCFs bulk purchase would speed markets growth faster than the private market could. There is a definite question of whether th e private market would act in cohesion to transfer the risk. If the risk needs to be transferred, there could be an adde d benefit of one organization doing it, if the response of the private market is to flee or to ignore the option to transfer their risk. Moreover, I propose that the state should have done the bond issue at 9 percenton-line rates. In 2007 annual income for the FHCF was $1.33 billion and expected losses were $1.2 billion. The $130 million surplus could easily have covered the $90 million fee for a $1 billion CAT bond issue. Additi onally, the typical CA T bond provides three years of coverage. This would have covered all three years of the TICL. Thus the $90 million fee would only have impacted the 2007 FHCF balance sheet regardless of the next two years income or the bonding environment in 2008 and 2009. This added advantage should not be underest imated in light of the cr edit crunch of 2008 which has continued into early 2009. 1.8 Policy Actions in 2008: The Financial Crisis and the Buffett Deal Needless to say, the FHCF did not pursue any of Senate Reports risk -transfer options in 2007 or in the following year of 2008. During this period, anxiety increased throughout the industry as it became more apparent that the TICL had been a shell game, 40 The Florida Senate: Interim Project Report 2008-104, 14. 28


transferring the risk from one cup to another, but without the collateral to actually take the r isk off the table. The Florida House of Representatives Committee on Insurance examined expert testimony in the spring of 2008 which formalized the bleak suspicions of the November 2007 Senate Report The study bemoaned the shift in us ing Citizens as a tool to reduce rates rather than to expand coverage. In 2005 Citizens charged the highest rates in the industry and had 810,000 polices. At the end of that year after the comparatively minimal impact of Katrina on Florida, Citizens still had a deficit of $888,000. However, as of April, 2008, Citizens charged the lowest rates in the industry and had increased its number of polices by 62 percent to 1.3 million policies. The result was that a repeat of the storm paths of 2004 and 2005 would result in a $4 billion shortfall in Citizens. Higher losses were, of course, possibl e and would naturally result in assessments, or hurricane taxes. 41 Moreover, 40 percent of the FHCFs funds were dedicated to reinsuring Citizens. The deficiencies in the FHCF thus amplified Citizens likelihood of a deficit. This made it more probable that many claims would go unpaid for a long time in the event of a storm. An independent actuary confirmed testim ony that Citizens new rates were unsound, particularly in its high-risk policies. 42 John Forney of Raymond James, the financ ial advisor to Citi zens and the FHCF, testified that $10 billion was th e largest bond issue ever comple ted after a storm. This put the potential $25.75 billion bonding task in pers pective. When asked how the sub-prime market conditions of early 2008 would compare to the market conditions following a 41 Rubio, 2 and 6. 42 Rubio, 2 and 6. 29


catastroph ic storm Forney responded that There would be unprecedented market conditions. It would revolve around a shadow banking system, a broken-down system where short-term borrowing would be difficult, if not impossible.43 Market conditions continue d to deteriorate through 2008 which led the FHCF to take a desperate contract three months af ter Forneys testimony. Eschewing the three options cited in the 2007 Senate Report, the FHCF purchased a $4 billion line of credit from Warren Buffetts Berkshire Hathaway company on July 3, 2008. For $224 million, Buffett promised to purchase $4 billion of 30year tax-free bonds at a 6.5 percent coupon. Buffett would only have to purchase the bonds if insured losses exceeded $25 billion for the FHCF, whose exposure had risen to $29 bi llion. Dennis McKee of the State Board of Administration commented th at this was essentially a put-option to buy bonds.44 The deal did not provide any coverage in itself, but rather guaranteed liquidity in the 2008 credit crunch. Rather than reducing possible assessments, the Buffett deal secured the privilege of paying such assessmen ts at all. Indeed, when faced with the possibility of attempting the largest catastrophe bonding in histor y in the worst credit market in memory, this privilege should not be taken for granted. 1.9 Policy Recommendations Using Cat-Bonds I provide a series of tables to evaluate the efficiency and effectiven ess of the Buffett deal. One can consider the issues surrounding the FHCF expanded financing tasks after the 2007 special legisl ative session as a case study. The problem that faced the FHCF was to finance the top levels of lo ss over a three-year period in which it found itself over-exposed. The amount in question was $4 billion for a single year. 43 Rubio, 5 and 6. 44 Reuters, accessed at on April 14, 2009. 30


For m y analysis I first assumed a market in which the FHCF could choose either cat-bonds or the Buffett deal to finance the full $4 billion of coverage. I also assumed that the Fund would exercise these strategies in a ll three years. Both th e Buffett deal and the cat-bond would require storms of the same magnit ude in order to be t riggered, that is in order for the FHCF to access the promised capita l. I examined the relative costs of these methods given a single triggering storm in either first, second or thir d year, as well as the costs if no triggering storm occu rred during the th ree-year period. For the Buffett deal I used a 5.6 percent a nnual cost to secure the line of credit. This corresponds with the act ual rate Berkshire Hathaway charged the FHCF for the 2008 storm season. If this put option was triggered I calculated the ensuing thirty-year costs using this same deals 6.5 percent annual rate. For the cat-bond I assumed a 9 percent annual cost as outlined in the 2007 Senate Report. Table 1.2: Total Costs of Buffett D eal Given a Single Storms Occurrence Buffett Cost Year 1 Storm Year 2 Storm Year 3 Storm No Storm cumulative cost of line 224 448 672 672 Additional 30 year costs 11,800 11,800 11,800 0 Total Costs $12,024 $12,248 $12,472 $672 All figures in thousands Table 1.3: Present Value Costs of Buffett Deal Given a Single Storm Buffett Cost Year 1 Storm Year 2 Storm Year 3 Storm No Storm cumulative cost of line 224 448 672 672 PV 30-year costs 6,750 6,750 6,750 0 Total PV Costs $6,974 $7,198 $7,422 $672 Assuming Market Rate of 3 percent 31


Table 1.4 T otal Costs of $4 billion Cat-Bond Deal Given a Single Storm Cat-Bond Cost Year 1 Storm Year 2 Storm Year 3 Storm No Storm cumulative cost of line 360 720 1080 1080 Additional 30-year costs 0 0 0 0 Total Costs $360 $720 $1,080 $1,080 The clear conclusion from this analysis is that if a triggering storm occurs in any of the three years, then cat-bonds are th e better choice. Inde ed cat-bonds provide enormous savings over the Buffett deal if a storm actually occurs, whereas the Buffett deal provides relatively minor savings if a storm does not. I summarize these respective savings in the following tables. Tables 1.5 and 1.6 show the amount saved by choosing cat-bonds if a triggering storm occurs while Table 1.7 shows the amount saved by choosing the Buffett deal if a storm does not. Table 1.5: Cat-Bonds Total Advantage if Storm Occurs Year 1 Storm Year 2 Storm Year 3 Storm Cat-Bond $11,664 $11,528 $11,392 Table 1.6: Cat-Bonds Present Va lue Advantage if Storm Occurs Year 1 Storm Year 2 Storm Year 3 Storm Cat-Bond $6,614 $6,478 $6,342 Table 1.7: Buffett Deal Advant age if Storm Does Not Occur No Storm Year 1 No Storm Year 2 No Storm Year 3 Buffett Deal $136 $272 $408 Clearly, a cat-bond has a multi-billion dolla r advantage over a Buffett deal if a storm occurs, but the Buffett deal has less than a half-billion dollar advantage if a storm does not occur. Why is this? The cat-bond provides the advantage of being fully 32


collateralized; there are no addi tional costs outside of the an nual $360 million fee. Thus if a triggering storm occurs, the FHCF can claim the full $4 billion without additional payment. In contrast, the Buffett-style bonding putoption requires the FHCF to issue $4 billion in municipal bonds at 6.5 percent for thirty years. This translates to thirty annual coupons payments of $260 million from the FHCF to Berkshire Hathaway. This would be a total cost of $7.8 billion in addition to the retu rn of the $4 billion of principal at the end of 30 years. One could alternatively look at the present value of the Buffett deal costs. This acknowledges value of the time the FHCF impl icitly purchases in this deal. It also summarizes the stream of payments to Berksh ire Hathaway into a single, immediate cost to the state of Florida after a storms occurrence. If a market interest rate of 3 percent is assumed, these coupon payments have a pres ent value of $5.1 billion. Moreover, the present value of the $4 billion in principal repaid to Buffett would be $1.65 billion. One could thus think of the imme diate costs for Florida in addition to the $224 million annual fee already paid as $6.75 billion. Thus the FHCF would implicitly be paying a 69 percent premium for the additional time to pay off its $4 billion loan. Cat-bonds alone, however, cannot currentl y finance the full $4 billion loss according to the estimates in the Senate Report. Indeed, while John Se o implied that an issue over $1 billion would be possible, it must be noted that a $1 billion issue would be the largest single catbond issue to date. The market at its peak in 2008 had a total volume of $15 billion and a new issue volume peak in 2007 of $7.7 billion.45 45 Swiss Re: Insurance-Linked Securities Update 2 and 3. 33


Hence I next exam ine the case in which the FHCF issues a $1 billion cat-bond and takes a Buffett-deal put-option for the remaining $3 billion of coverage. I assume the same rates. This translates to an annual fee of $90 million for the cat-bond in order to cover the coupon payment and an annual fee of $168 million to secure Buffett deal for a total annual payment of $258 million. Moreover, if a triggering storm occurs, then the FHCF only has to issue $3 billion in bonds to Berkshire, th ereby reducing the necessary post-storm annual coupon payments to $195 milli on. In addition to thirty years of these payments the FHCF would have to repay onl y $3 billion in principal at maturity. Table 1.8: Total Costs of Combi ned Strategy if Storm Occurs Combined Cost Year 1 Storm Year 2 Storm Year 3 Storm No Storm cumulative cost of line 258 516 774 774 Additional 30 year costs 9,850 9,850 9,850 0 Total Costs $10,108 $10,366 $10,624 $774 Table 1.9: Present Value Costs of Co mbined Strategy if Storm Occurs Combined Cost Year 1 Storm Year 2 Storm Year 3 Storm No Storm cummulative cost of line 258 516 774 774 Additional 30 year costs 5472 5472 5472 0 Total Costs $5,730 $5,988 $6,246 $774 As would be expected, the combined strategy provides a middle ground between the two previous options. However, the overarching conclusion is that using the smaller cat-bond still saves nearly $2 billion if a st orm occurs over the Buffett-deal-only option found in Table 1.2, while this cat-bond woul d only cost approximately $100 million extra if a storm does not occur. Even if present values are examined, the cat-bond combo still has at least a $1 billion adva ntage over the Buffett deals present value in Table 1.3. These findings are summarized as follows: 34


Table 1.10: Total Advantage of Combined Strategy over Buffett Deal Year 1 Storm Year 2 Storm Year 3 Storm No Storm Combo $1,916 $1,882 $1,848 -$102 Table 1.11: Present Value Advantage of Combined Strategy over Buffett Deal Year 1 Storm Year 2 Storm Year 3 Storm No Storm Combo $1,244 $1,210 $1,176 -$102 The conclusions in this case take into account the current developmental stage of the cat-bond market. However, a more robust market with increased liquidity, a real possibility at current growth rates, would fu rther expand the FHCFs opportunity set as in the initial case in which the full $4 billion is financed thr ough cat-bonds. There is thus a positive externality in expanding this market The cat-bond market remains something of a mystery to many investors, thereby limiting th is markets size and capacity. However, a large successful issue by a public insurer like the FHCF would set an important precedent in this market and increase its visibility in viability among investors. All of this could potentially contribute to the cat-markets a cceptance into the mainst ream market. This, in turn, would increase the capacity available fo r public and private reinsurers alike. The positive effect of this externality has not yet been quantified. To conclude this section of policy re commendations, it appears that given the available information, the FHCF did make the best choice for a single year of coverage. A single cat-bonds rates, while competitive with other reinsurance products, cannot compete with a one-year 5.6 percent rate on line. That is, as long as a storm does not occur. 35


Indeed, my analysis shows that if the FHCF does not believe a triggering storm will occur in three year period, then the Buffe tt deal is the most cost-effective proposal. However, if the FHCF believes that a trigge ring storm will occur in the three-year period, then a cat-bond is the best option. I would recommend a combined strategy which would incorporate the maximum amount of cat-bond coverage available and ma ke up the difference with a Buffett deal. This would result in over a billion dollars in savings over the Buffett deal should a storm occur and only cost $100 million more if a storm did not occur. 1.10 Conclusions Hurrican es will remain a long-term problem for Floridas insurers and its riskmanagement stakeholders. These include the FHCF, the Legislature, Citizens Corporation, private insure rs and reinsurers, the cap ital markets and Floridians themselves. As such, this long-term problem requires long-term solutions. Hurricane Andrew completely altered the insurance indus try as Florida grappled to keep insurers in state and property owners insured. Katrina caused spikes in reinsurance prices which trickled down to the rest of the insurance market, motivating the legislature lower key rates in a special 2007 le gislative session. This session essentially changed the mission of Citizens to that of lowe ring the market rate instead of providing additional coverage above that rate. Th e 2007 session also raised the amount of reinsurance that insurers could purchase from the FHCF for 2007, 2008, and 2009. The FHCF did not have the money to collate ralize this additional risk. Its ability to bond over $25 billion in post-storm bonds re mained uncertain. In response the FHCF 36


paid W arren Buffetts Berkshire Hathaway $224 million for a one-year promise to buy the last $4 billion of tax -free 30-year bonds in 2008. Unlike the Buffett-Deal cat-bonds bonds pr ovide actual coverage for a storm by pulling in funds from outside investors. The Buffett-Deal comes with the additional costs of years of financing the full $4 billion at 6.5 percent over 30 years, costs that will come form Florida insurers and homeowners. Using the same rates reported to the Flor ida Legislature, I demonstrate that the Buffett deal only provides savi ngs if a triggering storm does not occur. I show that a strategy using both cat-bonds and a Buffett d eal cost only $100 million more than the straight Buffett deal if no storm occurred. Howe ver, if a triggering storm did occur, then cat-bond would save Florida over a billion dollars. Clearly cat-bonds deserve a detailed examination by Floridas stakeholders in the risk management process. This thesis will con tinue in the next chapter with a review of the history and theory underlying some of the key academic and practical issues of catbonds. 37


Chapter 2: The Function and Place of Cat-Bonds in Risk Management. 2.1 Introduction The previous chapter established the mo tivation for exploring cat-bonds within the context of Floridas insurance policy. Private insu rers and reinsurers are already using these instruments to manage wind risk in the Florida market and the instruments have become a fixture in conversations among Florid a politicians. This ch apter will review the history and structure of this kind of bond as well as the challenges facing the asset-class as a whole. The scholarly literature su rrounding cat-bonds has focused principally on three such challenges. First, much discu ssion has focused on which trigger for a cat-bond is appropriate in a particular circumstance. Secondly, studies have debated over the fair price of these bonds. Thirdly, studies have disc ussed the optimal allocation of such assets, both on an insurers balance sheet as well as w ithin an investors por tfolio. This chapter will address each of these topics after firs t examining the origin and anatomy of the bonds themselves. 2.2The Structure of a Typical Cat-Bond The typical cat-bond is actu ally a complex contract between a series of stakeholders. First, a prim ary insurer contracts with a reinsurance company for a given catastrophe, coverage level, a nd region. The reinsurance company then forms a Special Purpose Vehicle (SPV). The SPV functions legally as its ow n firm with the lifespan of the bonds maturity. At maturity the SPV is di ssolved. Due to this close tie between bond and SPV the industry refers to different cat -bonds by the name of their SPV. The sole purpose of this SPV is to monitor and maintain the funds under its management. Similarly, the funds themselves may only be used to pay losses from a specified event. 38


The reinsu rer then collects principal from investors, the majority of whom are large institutional portfolio managers. This principal is deposited with the SPV. The SPV does not remain completely dormant. It is re sponsible to investors to pay a riskless rate, usually LIBOR, plus a spread. It also must make sure that sufficient funds remain under management so that the primary insurers contract is completely collateralized. The assets must also be liquid enough to quickly provide the principal in the event of a catastrophe. To these ends, the SPV places its principal in to highly-rated fixed-income investments in order to maintain value. The SPV then hedges itself by entering into a total-return swap with a counterparty, generally a larg e investment bank or commercial bank. The total-return swap allows the SPV to exchange the risk and returns of its inve stments for a regular payment from the counterparty. Again, this pa yment from the counterparty to the SPV is generally LIBOR plus a spread. In essence, the counterparty rents th e assets on the SPVs balance sheet without needing to report them on its own. The counterparty receives th e returns on the SPVs investments. However, it is also responsible to make up losses below pa r value. The counterpartys agreement to make up losses in the principal and to pa y a fixed coupon to the SPV thereby further insurers that the SPV will meet its obliga tions to the reinsurer and to bond-holders. Thus the stakeholders in a cat-bond are the primary insurer, the reinsurer, institutional investors, the SPV and the tota l-return swap counterparty. A cash flow proceeds through the stakeholders as follows The SPV makes returns on its investments which it pays to the swap counterparty. In return the counterparty pays the SPV its LIBOR-based periodic payment. The coupon pa id by the counterparty may be less than 39


the coupon owed to the bond holders. However, th e prim ary insurer or the reinsurer pays the SPV the balance owed on the coupon spread.46 A good example to illustrate this is CAT-Mex Ltd. The Mexican government, acting as a primary insurer, contracted with a reinsurance company that had expertise in the cat-bond market: Swiss Re Swiss Re then implemente d the cat-bond through creating the SPV, CAT-Mex Ltd. Now, as the sponsor ing reinsurer, Swi ss Re made regular payments into this SPV in order to supply the spread above LIBOR. Once the counterparty and sponsors regular payments have been collected, the SPV then pays the full coupon amount to the bond holders. If the bond is triggered then the flow stops and the SPV pays its holdi ngs to the primary insurer. Although some bonds have protected tranches, in general both the coupon and the princi pal are forfeit. If the bond remains untriggered then the investors receive their principal at maturity. For a full example, consider the cash flow of the cat-bond Mystic Re II as diagrammed in figure 2.1. Cummins notes that in 2007, the year of the highest number of bonds, most catbonds in the market had crystall ized around this basic structure.47 In the past some bonds contained principal protected tranches as in the pre-event bonds offered by the Florida Hurricane Catastrophe Fund. Such tranches pr otect the principal by simply extending the maturity date until the principal must be re paid. However, these have become rarer as they do not provide as mu ch capital for the issuer.48 46 Ganapati et al, 279. (Found in Handbook of Structured Financial Products ) 47 CAT Bonds and Other Risk-Linked State of the Market and Recent Developments, 14. 48 The Convergence of Insurance and Financial Markets, 41. 40


Figure 2.1 Cat-Bond Cash Flow 4 Trust Fund: Contains AAA bonds, Treasuries. Total Return Swap Co unterparty: i.e. Goldman Sachs 5 6 3 7 2 Institutional Investors and Hedge Funds : i.e. John Seos Fermat Captial Reinsurer: The Cat-Bond Sponsor i.e. Swiss Re Special Purpose Vehicle: The Cat-Bond i.e. Mystic Re II Trigger 8 Trigger 1 Normal cash flow Trigger cash flow Key Primary Insurer: i.e. Liberty Mutual 1.) Primary Insurer pays premiums to the Reinsurer to transfer risk from policy holders. 2.) Institutional investors give principal to the SPV, thus buying the cat-bonds. 3.) The SPV places this principal in a Trust Fund of highly-rated b onds and treasuries. 4.) The SPV gives the returns (if any) from the Trust Fund to the Total Return Swap Counterparty. 5.) The Counterparty pays the Trust Fund LIBOR. It also replenishes the fund if its principal has dipped below par value. 6.) The Trust Fund pays LIBOR into the SPV. 7.) The Reinsurer pays the spread above LIBOR of the cat-bond coupon to the SPV. 8.) The SPV pays the Investor the co mbined coupon of LIBOR plus the spread. It also returns the entire principal at maturity if the bond is not triggered. Trigger:If the bond is triggered, then the entire principal from the Trust Fund is paid into the SPV and transferred to the Reinsurer, who then can m eet its reimburse the Primary Insurers losses. 41


2.3 History of Cat-Bonds As naturally follows from the previous chapter, Hurrican e Andrew resulted in a paradigm shift for the insura nce industry. This new paradi gm motivated a series of financial innovations as insure rs sought new products to be tter manage catastrophic risk. Specifically, various stakeholders realized the benefits of raising cap ital before a major events occurrence. A variety of such instruments developed more or less in parallel in the mid-1990s before cat-bonds became the instrument of choice. Immediately following Andrew in 1992 th e Chicago Board of Trade introduced catastrophe futures, complete with put and ca ll options on these futures contracts. In 1997 the Bermuda Commodities Exchange offered a similar market for catastrophe options. These contracts wagered on the level of the Property Claims Services (PCS) aggregate catastrophe loss index. Both contract markets were discontinued s oon after their incepti ons due to lack of interest. Ideally, insurers coul d have purchased a futures cont ract to hedge losses in the event of a catastrophe. However insurers objected to the und erdevelopment of the market and the possibility of counter-p arty credit risk. Furthermore, the basis risk of using the PCS aggregate index as the future s mechanism concerned insurers. 49 Basis risk refers to the possibility that the aggregate loss inde x would have low correlation with individual losses. The futures would thus be an ineffective hedge. This first innovation, however, was not th e only attempt to securitize catastrophic 49 CAT Bonds and Other Risk-Linked Securities: State of the Market, Cummins 2. 42


risk. In 1995 Nationwide Insurance issued $400 million of ten-year Act of God bonds, more formally known as contingent notes. These bonds were invested in ten-year treasuries and paid 2.2 percent above the tr easury rate as a coupon. Nationwide reserved the right to call the entire principal amount to at its discre tion before the bonds matured. However, Nationwide would immediately substi tute the old bonds for new ones, with an interest rate of 9.22 percent. Over the ne w bonds life, Nationwide would replenish the original principal amoun t. Thus the contingent notes basi cally paid investors for the right to a one-time, immediate loan at a high interest rate. The structure of this loan mitigated, but did not reduce, Nationwides catastrophe exposure since it was still responsible to pay b ack the principal. Investors thus still saw a significant risk of default on Nationw ides part should a catastrophe hit.50 The attractive 9.22 percent coupons would then be moot. Only a few such bonds were ever issued in the private market, though the Florida Hurricane Ca tastrophe Fund issued an extendible note similar to the contingent note in 2006.51 Unlike both cat futures and contingent not es, cat-bonds have gr own steadily since their inception in 1994. Hannover Re issued the fi rst cat-bond in that year to raise $85 million. The following two years each saw a single cat-bond issue as insurers experimented with the instrument. Among th e important early issues was a 1997 USAA residential insurance bond deal, which fina nced a hurricane-linked loss along the Gulf and Atlantic states within one year. This prominent national issue was crucial to building the early viability of the asset class. Four addition al new cat-bonds entered the market in 1997. The assets 50 CAT Bonds and Other Risk-Linked Securities: State of the Market, Cummins 3. 51 Raimes, 1. 43


continued to gain traction after this positive growth. Ten new bonds were issued in 1999, with new issuances spiking in 2000 and 2007 to 20 and 27 new bonds respectively.52 The number of outstanding bonds al so grew over this ten year period, indicating an increase in multi-year maturity dates. In 1999 the total market size for cat-bonds was approximately $1.1 billion. By 2007 this figure had grown to $14 billion. Over the same period the composition of bond-holders altered dramatically. While in 1999, insurers or reinsurers held 55 percent of cat-bonds, by 2007 this percentage had decreased to 7 percent. This essentially reversed market share with catbond funds, which increased their holdings from 5 percent to 55 per cent of the market over the same eight year period. Hedge funds also tripled their hol dings in cat-bonds to 17 percent of the market and money managers retained a substantial portion of the bonds.53 The cat-bond market thus drastically expanded its investor bond over the previous ten years, indicating moti on towards the mainstream market. The major issuers of cat-bonds also divers ified during this period with new issuers entering the market. The stalwarts of the indus try remained large European and American insurers and reinsurers. In pa rticular, the Swiss-based Swiss Re as well as German-based insurers Allianz and Munich Re were leader s in new-issues, as were Nationwide, USAA and Allstate as U.S.-based companies. Howe ver, as of January 2009, over forty different sponsors had outstanding bonds in the market-place. Although the bulk of sponsors have been private reinsurers and insurers there have been isolated examples of other t ypes of sponsor. The property owner for Tokyo Disneyland, Oriental Land Co mpany, issued a bond directly, without a financial 52 Guy Carpenter: The Catastrophe Bond Market at Year-End 2007 14. 53 Yago and Reiter, 15. 44


interm ediary, in 1999.54 The California Earthquake Authority issued $100 million in twoyear cat-bonds through Swiss Re in 2001.55 This bond, Western Capital Ltd., is a good example of a state-run public insurance company using catbonds to secure a line of financing. A larger example of such a public insurance issuance was CAT-Mex Ltd. Swiss Re designed this bond as part of a larger contract fo r the Mexican Natural Disaster Fund in 2006. The bonds provided $160 million dollars of earthquake coverage if triggered by specified Richter scale readings.56 2.4 Hurricane Katrinas effect on the cat-bond market Hurrican e Katrina marked an important milestone in the history of cat-bond development. The storm initiated the first to tal-loss of principal for a cat-bond on public record. The storm thus acted as a kind of litmus test for the bonds hitherto unproven claims of efficacy in risk management. Zurich Financial, a Swissbased insurance firm had issued KAMP Re 2005 Ltd., just months before Katrina in July of 2005. KAMP re was designed to provide multi-peril coverage, but Katrina was sufficient to trigger the full amount of the bonds $190 million in principal. The bond used an indemnity trigge r, which directly linked the principals use to the losses of Zurich Financial. Suffice to say, this proved to be an excellent wager for this firm. Initial reactions to KAMP Res triggeri ng were mixed. Just as cat-bonds ability to hedge insurer shortfalls had remained hypot hetical, so too had th e potential losses for investors. However, Guy Carpenter, one of th e largest reinsurers in the U.S., remained optimistic in that years annua l summary of the cat-bond market: 54 Cat Bonds and Other Risk-Linked Securities: State of the Market, Cummins 4. 55 Business Wire, February, 15 2001. 56 Cat Bonds and Other Risk-Linked Securities: State of the Market, Cummins 15. 45


However, provided that the KAMP Re pr incipal payout process goes sm oothly, the establishment of a precedent in whic h a catastrophe bond contract functioned as designed i.e., with minimal confus ion and legal wrangling over terminology and transactions mechanics could serv e to reduce the overall uncertainty associated with the marketplace and ther efore increase both in vestor and sponsor demand for these instruments.57 It might seem overly bullish to infer th at Kamp Res liquidation would actually stimulate investor interest, especially from the perspective of a reinsurer like Guy Carpenter. However from the investors si de, funds specializing in cat-bonds made similar comments. In his interview with Mich ael Lewis, John Seo said, The important thing is that the money wasnt lost in an unearned manner.Thats all my clients need to know. He further commented, I would be embarrassed if we had a big event and our loss wasnt commensurate with it. It would mean that we di dnt serve society. We failed society.58 If nothing else, the numbers speak for themselves. Both 2006 and 2007 saw record years of new issuances in cat-bonds. Moreover the secondary market as a whole grew 29 percent during the two years after Katr ina as measured by the level of the Swiss Re Cat Bond Performance Index.59 Investors, thus, did show strong interest both in new and outstanding bonds in the aftermath of Ka trina. Ultimately, the reliability of KAMP Re during Katrina eliminated a lingering uncer tainty about the asset-class as a whole Ironically the natural cata strophe of Katrina would pr ove far less detrimental to the cat-bond market than the financial catastrophes of 2008. However, this reality resonates with Seos own comments that inve stors can remain content as long as losses 57 Guy Carpenter: The Catastrophe Market at Year-End 2005, 4. 58 Lewis, 12. 59 Data source: Swiss Re. 46


follow the expected pattern. Investors were fully prepared to loose m oney due to hurricanes. This was not the case for the 2008 cr isis. I will defer discussing the effects of the financial crisis in detail until chapter 3, where those events will bear directly on my empirical analysis. 2.5 Cat-Bond Triggers The debate over which type of trigger s hould access a cat-bond s principal strikes at the v ery heart of the tensions within the market. All stake-holders share interest in the stability and smooth operation of the SPV, so it is little wonder that much consensus has been achieved in the general structure of cat -bonds. However, the trigger choice quickly brings out the distinctions be tween investor and insurer, th e former desiring the funds to remain safely in the fund and the latter needing the bond to payout when needed. A perfectly safe bond from an investment sta ndpoint would be a point less exercise for the insurer, whereas a hair-trigger for the bond w ould make the risk to investors untenable. For every bond a compromise must be reached, and different triggers appear to work in different circumstances. The trigger debate also engages in a much older convers ation within the insurance industry: the balance between moral hazard and basis risk. Moral hazard is the danger that reported losses will be gr eater than actual losses in order to exceed the deductable amount, or attachment point. Moral hazard exis ts at every level of the risk-transfer process between all the stakehol ders. A property owner could in flate his losses in order to receive funds from the primary insurer. Th e primary insurer coul d be too cavalier in recognizing losses in order acce ss its reinsurance. A reinsurer could similarly be overly generous with its customers in order to tr igger a cat-bond. Moral hazard could also enter 47


into th e underwriting process in which an insurer or reinsurer writes more risk than is actuarially sound, knowing that an extra layer of coverage wi ll cover excessive losses. Basis risk emphasizes the opposite concer n. Rather than worrying about if lossevaluation techniques are too re laxed, basis risk refers to loss-evaluation metrics being too severe. The tendency in basis risk is to underestimate the true amount of damages. A cat-bond trigger with severe basi s risk refers to a trigger wh ose activation is uncorrelated to the actual losses experienced by the spons or. Naturally, insurers are most concerned with basis risk while investors are most concerned with moral hazard. There are three basic types of triggers : parametric, index-linked, and indemnity triggers. Cummins also identifies a fourth type of bond, which is a combination of the three basic triggers.60 Each has a different profile of pr os and cons for the stakeholders involved. The mixture of moral hazard versus basis risk will also differ depending on the type of bond. The most intuitive trigger is the indemnity trigger. This trigger is directly tied to the losses incurred by the s ponsor. KAMP Re held an indemnity trigger and was activated immediately after Zu rich Financial confirms that its losses have reached its attachment point. The opportunity for mora l-hazard remains greatest for the indemnity trigger but the probability of basis risk is the lowest. This stems from the comparative amount of freedom the sponsor has in dictating its loss level. An index-linked trigger reduces the moralhazard inherent in indemnity triggers by acting as a kind of average i ndemnity trigger for an entire market of insurers. If an insurer makes up a small part of the market, then it will not be able to manipulate the level, or index, of aggregate losses to trigge r a bond. The most prominent indices used are 60 CAT Bonds and Other Risk-Linked Securities: State of the market, Cummins 7. 48


those com piled and maintained by the Propert y Claims Service (PCS), which track the aggregate losses within the en tire insurance industry due to specific catastrophes. The indices can be broken into regions. Thus, a bond with a trigger tied to the PCS for a tristate area would not trigger unt il insurers in those three st ates collectively recorded a certain amount of losses due to an event. The 1997 USAA bond used state-wide PCS triggers. Naturally, in averaging a companys losses with the losses of its peers, basisrisk increases. Individual losses become less correlated to the triggering mechanism. Theoretically, basis risk thus also exists for an index over-estimating losses, though this has not been a primary concern in professional or academic literature. A parametric trigger is the quickest to act and the least prone to moral hazard. This trigger is activated by the objectiv e measurement of the catastrophe itself. Earthquake bonds with a parametric trigger, like CAT-Mex Ltd, would be activated by a Richter scale reading in a speci fied region. Parametric trigge rs for hurricane bonds can be activated by wind-speed, barometric pressure or category of storm (i.e. category 4 or 5 etc.). Clearly these types of bonds can very quickly become activat ed while the bonds in an indemnity or index-linked bond must wait for damages to be filed and losses confirmed. Doherty and Richter suggest an interesti ng hybrid trigger in their paper Moral Hazard, Basis Risk, and Gap Insurance. They applaud the reductions in moral hazard of index-triggers over indemnity triggers, but th ey offer additional tools for dealing with basis risk in such bonds. They consider the gap between losses and index-linked payouts: G = L I (2.1) 49


Where L is the tota l losses and I is an index correlated to L and is the hedge ratio of the cat-bond contract. The hedge ratio is the fr action of losses whic h has been insured through the index-linked bond. Thus the bonds potential payout will be I and G will be the coverage gap. Doherty and Richter suggest that insurers be able to directly insure G using an indemnity contract with a hedge ratio of The new expected payout for a bond would be: P= I + (L I) (2.2) where P is the payout. Clearly a of unity would mean full c overage for the loss. The indemnity contract on G once again allows pot ential moral hazard. In fact an indemnity bond could be thought of as the special case in which = 0. A pure index bond, in contrast, would be the special case in which =0. Interestingly however, the authors find that even when is less than unity, the ab ility to manipulate both and instead of simply one or the other, as in the special cas es, expands the opportunity set of the insurer, potentially netting an efficiency gain. Manipulating both hedges also allows a greater range of mixtures between moral hazard a nd basis risk to better fit the insurers preference structure.61 Of particular interest to Floridas hurricane cove rage crisis is a paper by Cummins, Lalonde and Phillips which exam ines the effectiveness of index-linked triggers in the 1998 Florida insurance market The papers specific motivation is the short-lived Chicago Board of Trade cat-futures market, wh ich offered short and long positions in the PCS index. The authors show that basis-risk fears surrounding this market were partially unfounded. Their findi ngs have implications, however, for all index-linked securities, including cat-bonds. 61 Doherty and Richter, 9, 14-16. 50


The paper offers a com prehensive empirical study of the true extent of basis risk in indexed triggers. Anxiety in the insurance indu stry over these triggers remained high, though little rigorous evidence existed. The authors data set includes 225 Florida insurers, accounting for 93 per cent of Floridas insured resi dential property. The authors use hurricane modeling software provided by Applied Insurance Research (AIR) to simulate hurricanes on these properties. A statewide loss-index is then calculated as are four additional intrastate indices for Florida regions: a Panhandle, Gulf Coast, North Atlantic and South Atlantic i ndex. These index-based losses ar e then correlated with each individual insurers losses in order to measure each firms basis risk under differing intensities of hurricane. The AIR computer mo del is a prevalent tool in the insurance industry for simulating catastrophic losses. The authors use this model to simulate10,000 years of potential hurri canes on the data set.62 After studying both the effectiveness and the efficiency of index-based hedging strategies for losses over $1 billion, the authors find that the regional, intrastate indices do not cause significant basis risk for most fi rms. For an expenditu re of 15 percent of expected losses, the variance of net losses decreases by 40 percent for state-wide index hedges, 58 percent for regional index hedges and 62 percent for a perfect, indemnity, hedge. The top three quartiles of insurers by size all saw similarly strong results for regional-index hedges, with th e bottom quartile registering much weaker results. For the top two quartiles, however, regi onal indices proved nearly as effective as indemnity contracts. The regional hedge was found to be 95 percent as effective as the indemnity hedge for 76 of the 255 insurers and 90 percen t as effective for 143 insurers. Even the 62 Cummins, Lalonde and Phillips, 79. 51


statewide index-hedge proved to be 90 percen t e ffective for 36 insurers. However, for 105 firms the statewide hedge wa s only 50 percent effective. The public policy implications of the pape r are that indices could be effectively used as triggers for the majority of the Fl orida market. Using a re gional index, 70 percent of the data-set could be hedged with 95 pe rcent efficiency and 92 percent could be hedged with 90 percent efficiency. For a stat ewide index 36 percent of insurers could hedge with 95 percent efficiency and 55 percent could hedge with 90 percent efficiency.63 If policymakers wanted to avoid si gnificant moral hazard, index-based triggers could be used effectively in Flor ida for larger companies, without incurring significant basis risk, particularly regional hedges. The study thus confirmed basis fears for smaller companies but opened the discussion for index he dges for 75 percent of Florida risk firms in 1998. Parametric triggers have obvious adva ntages in speed over both index and indemnity contracts. This eliminates the hass le, and often litigation, over disputed claims slowing down a necessary trigger. However, Brandts and Laux argue that parametric triggers have the additional advantage of keeping traditional reinsurance prices competitive for insurers. Their study integrates cat-bonds into another key discussion in insurance literature: adverse selection. In essence adverse selection describes an insurance portfolios tendency to become more risky over time. An insurer wi ll experience adverse selection because the people who have the highest demand for insu rance are often the customers with the highest risk profiles. Though insurers try to screen for unacceptable risks, adverse selection may still occur because of asymme tric information between two parties. A 63 Cummins, Lalonde and Phillips, 93-98. 52


custom er may know information which makes hi m a poor risk, but the insurer may not be able to legally obtain or us e this information. Similarly, reinsurers experience adverse selection in their portfolios co mprised of private insurers. Th e asymmetry arises from the fact that reinsurers do not know insurers outside their por tfolio as well as they know insurers inside their portfolio. This asy mmetry between insiders and outsiders is a disincentive for reinsurers to bid aggressively to obtain ou tside contracts. This reduction in competition allows reinsurers to charge an information rent to its inside customers since external reinsurance contracts are scarce. Moreover, information asymmetries between familiar and unfamiliar customers cause reinsurers to charge higher premiums. This cross-subsidization means low-risk insure rs unfairly defray costs for high-risk ones. Because parametric triggers are complete ly independent of special information, Brandts and Laux argue that parametric -trigger cat-bonds form an upper bound on reinsurance prices. These bonds form a kind of objective thir d-party in the reinsurance party, always willing to offer reinsurance on fixed terms and thus widening the competition in the reinsurance market. Th e authors propose that this upper bound is particularly important for low-risk insurers These valuable customers will not tolerate being charged cross-subsidization premiums above the fee for a parametric cat-bond. Reinsurers will thus keep their prices below th is threshold level in order to retain their best risks. The authors thus argue that pa rametric cat-bonds serve the market through availability alone, even if their use remains rare.64 2.6 Pricing Cat-Bonds Historically cat-bonds have offered high spreads above LIBOR com pared to other corporates with the same ra ting. The structure of cat-bonds means that these high spreads 64 Brandts and Laux, 1-4 and 23. 53


equate to high costs for insurers. This has provoked m uch discussion among experts. Why, if the ratings are accurate, should thes e bonds require excessive premiums? Earlier in the markets history pricing seemed to be uncompetitive with traditional reinsurance as well. Debate has centered on identifying pricing considerations as structural, psychological or both. Although recent eviden ce suggests that some of these pricing issues may have subsided, measuring catastr ophic risk remains an imperfect science. Indeed, traditional reinsuran ce itself has been the subject of debate with regards to catastrophe pricing for decades. Appropriate pricing for cat-bonds will thus remain an important question as the market ad apts to each new catastrophe. Writing in 1999, Bantwal and Kunreuther s A Cat Bond Premium Puzzle? offers a seminal comment on the early deviancy in cat-bond prices. Re call that the market itself had gained traction for only two years by this point. As of the papers publication the authors note that spreads over LIBOR were nearly four times those of comparable corporate bonds rated Ba2 through B3. At the same time, the Sharpe ratios of the catbonds were far superior to cor porate Sharpe ratios. In most cases the corporate historical default probabilities were also higher than the probability that the cat-bonds would be triggered. For instance, the average probability of attachment, or trigger, for the cat-bonds studied was 1.81 percent. This fell directly be tween the probability of default for Ba2 and Ba3 corporates at 0.6 percent and 2.7 percent, respectively. Yet cat-bonds had an average spread of 5.08 percent over LIBOR while Ba 2 and Ba3 were 1.1 percent and 1.36 percent above LIBOR respectively. At the same time the average Sharpe ratio for cat-bonds was 0.57 while Ba2 corporates had a ratio of 0.25 and Ba3 corporates had a ratio of 0.02. 65 65 Bantwal and Kunreuther, 23. 54


Bantwal and Kunreuther note that investor s would need to be highly risk adverse not to choose cat-bonds at their contem porary rates. They cite a study by Moore in which Moore finds a coefficient of relative risk aversion (CRAA) on the order of thirty.66 Bantwal and Kunreuther explain this coefficien t as similar to having the option to flip a coin to determine ones consumption. If th e toss is heads then one receives $100,000. If the coin comes up tails then one receives $50,000. The alternativ e is to take $51,209 up front. A CRAA of 30 implies that one would be indifferent between the coin toss and the up front payment. This does not make intuitive sense. Thus the authors look for ways to adapt the simple risk-aversion argument for high cat-bond spreads.67 Among their explanations, Kunreuther and Bantwal offer the interesting distinction between risk aversion and ambiguity aversion. The authors argue that ambiguity aversion causes a statistically signi ficant pricing effect. Essentially, investors use their own knowledge as a frame of refe rence. They thus require a premium for making a bet in an area in which they perceive themselves to be unfamiliar.68 In a 1995 study, Kunreuther had demonstrated the statistically si gnificant effect of ambiguity on the pricing strategies used by tr aditional reinsurers. Th e study, administered to nearly 900 underwriters, as ked them to assign a pure pr emium to a series of lowprobability events. The study found significant difference in the premiums assigned to events with equal probability of occurrence but differing certainty as to this probabilitys accuracy. They performed the same test for events with the same probability of occurrence but where the peri l was unnamed and found simila rly higher premiums. The unknown peril and the unknown proba bility variance were used to simulate ambiguity. 66 Moore, 35. 67 Bantwal and Kunreuther, 5. 68 Bantwal and Kunreuther, 15. 55


The prem iums reinsurance underwriters asked for were between 1.43 and 1.77 times nonambiguous risk. This confirmed psychological literature but contradi cted a conventional utility functions prediction.69 Kunreuther and Bantwal use this study to infer a possible ambiguity problem in the cat-bond market, this time for investor behavior. If investors hold the same preferences as underwriters, e xperts at valuing ris k, then they would require similar spreads over LIBOR for cat-bonds.70 This formalizes the pithy Warren Buffett aphorism: dont invest in what you dont understand. It moreover explains why, initially, many investors in cat-bonds were re insurance companies, for whom catastrophic risk was less ambiguous. The problem of pricing cat-bonds did not evaporate, but it did change. After 2001 the infamous spreads began to decline. Cumm ins examines secondary market data of catbonds to gauge yields for the market. He notes that cat-bond premiums were approximately 6 times expected losses for th e market in 2001 but declined to 2.1 times expected losses by first quarter 2005. Expected losses rose gently during this period, suggesting that costs in general for ca t-bonds were decreasing. Moreover, spreads between yields on cat-bonds and Merrill Lync h-rated BB corporates also decreased to comparable levels between 2001 and 2005. Howe ver, Katrina caused a spike in yields peaking at 3.7 times expected losses and di verging from BB cor porates. While higher than the previous two years, this was far below the spreads seen before 2001. Cummins argues that this spike, while significant, was in-line with similar price movements in traditional rein surance. Although no systematic dataset currently exists on aggregate reinsurance prices, Cummins crea tes a proxy using unpublished data from Guy 69 Ambiguity and the underwriter decision making process, 340 and 344. 70 Bantwal and Kunreuther, 6 and 28. 56


Carpenter. He defines a ratio of rate on lin e (ROL) divided by loss on line (LOL). The ROL refers to the reinsurance prem ium divided by the policy limit and the LOL refers to the expected loss divided by the policy limit. Th e ratio of the ROL to the LOL serves as an analogue for the ratio of yield to expected loss for cat-bonds. The data-set consists of the reinsurance contracts issued by Guy Carpenter to its clients in 2005 and 2006. The reinsurance contracts most compar able to cat-bonds are those covering extreme, improbable events, i.e. those contract s with a low LOL. For LOLs of 1 percent, 2 percent, and 3 percent, the ROL to LOL ra tios for national primar y insurers were 5.9, 3.6, and 2.9 respectively in 2005. After Hurricane Katrina these ratios leaped to 12.9, 7.1 and 5.2 for national customers in 2006. These compare to cat-bond ratios of yield over expected loss of 2.7 in 2005 and 3.3 in 2006. T hus, according to Cummins metric, catbonds actually kept pace with the reinsuran ce market, offering competitive, if not superior, prices after Katrina.71 Although, cat-bond prices may be more in co ncert with traditional reinsurance, the question of why the reinsu rance market as a whole s hould spike in prices after Katrina remains. The spread between compar able corporates and cat-bonds immediately following Katrina also raises an interesting que stion. A variety of explanations have been offered, including an analysis by Froot of th e reinsurance price-movement and a study by Dieckmann modeling the spread from corporates. Froot views the reinsurance price move ment as a supply shock to available capital aggravated by structural issues in the industry. The co rporate structure of reinsurance companies and the presence of sh areholders demands that such companies maintain high grades with respected rating agencies such as Standard and Poor or 71 Cat Bonds and Other Risk-linked Securities: State of the Market, Cummins 19-21. 57


Moodys. T hese rating agencies require that reinsurance agencies spread their risk geographically. Thus firms are often liable for an even amount of capital in Europe, Australia, the United States and Japan. However, since risk is not evenly spread between these three geographic regions this results in perennial capital shortages in the U.S. reinsurance industry, where rein surance needs are highest, an d commiserate surpluses in the European, Japanese and Australian markets, where the needs are less. These shortfalls in the U.S. could well explain the disconnect in reinsurance prices after Katrina. Froot asserts that reinsurance prices for U.S. wind contracts increased four-fold from 2005 to 2006 following the 2005 storm cycle.72 However, prices also doubled for U.S. earthquake during the same period, despite no significant increase in expected losses from earthquake catastrophe. Froot cries foul, argu ing that the general undercapitalization of U.S. rein surance means that a catastro phe spike in one area results in prices rising across the board. The cross e ffect occurs even though there has been no change in the underlying pr obabilities of earthquakes. Froot further notes that this market failu re is more aligned with a supply shock than a demand shock. By mapping the quantity of risk transfer versus its price he finds a strongly negative correlation, a pattern of decreasing quant ity and increasing emerges. This behavior more typifies a supply s hock than a demand shock, which would show increasing quantity with increasing price. T hus Froot argues that major catastrophes jolt the capital-strapped reinsuran ce industry with a supply s hock which then produce cross effects in prices for unrelated forms of risk. Again, Froot holds reinsurers corporate ob ligations responsible for the inefficient geographic diversification at th e heart of this supply shock. He argues further that this 72 Froot calculates price as the ratio of the premium to the expected loss in a contract. 58


insistence on geographic diversification, while effective, ignores the already significant diversification possible between different kinds of peril and with the b roader capital market. He writes, Naturally, because U.S. hurricane and earthquake losses are uncorrelated with financial market returns and not just losses from perils abroad investor diversification of these expos ures should be relatively cheap and easy to provide. These exposures are automatically diversif ied in the context of far larger and broader investor portfolios.73 Dieckmann comments on the spread between corporates and cat-bond prices in the secondary market between 2005 and 2006. Dieckmann chooses this narrow time-span with the goal of examining Hurricane Katrinas effect on catpricing. He begins his study by observing three stylized facts about the cat-bond industry through secondary market data. First he finds that cat-bonds have a sp read between two to three times expected losses. Second he finds the term-structure, that is the cost of borro wing with respect to maturity, to be moderately upward sloping. Th irdly, he finds that investors require a greater yield for bonds with indemnity triggers versus those with para metric triggers. He further observes that Hurricane Katrina caused an 18 percent upward s hock in the price of wind bonds, as measured by the growth in yields over LIBOR. Dieckmann then creates a dynamic equilibrium model that mimics these st ylized facts. In cont rast to Bantwal and Kunreuther or Froot (2001), who hypothesize psychological or fricti onal reasons for the pricing discrepancy, Dieckmann s model instead uses a fric tionless market but with a certain degree of systematic, or undiversifiable, risk.74 In establishing his stylized facts, Dieckmann performs univariate tests on his data73 The Intermediation of Financial Risks, 285-286. 74 Dieckmann, 1-4. 59


set; he shows an average yield spread of 4.3 tim es expected losses with a 3.8 median multiple. This is in line with Froot s (2008) findings in the same period.75 Using multivariate regression analysis Dieckmann further found that indemnity trigger bonds averaged 6.3 times expected losses when compar ed to other parametric or indexed triggers at 3.9 times losses. This e quated to an average 100 basis point spread between the trigger groups. Dieckmann cons iders this as evidence supporting Doherty and Richter (2002) and Froot (2001), who posit moral hazard concerns as the underlying cause of the indemnity spread. Confirming financial intuition, Dieckmann al so found that the expected losses and the time to maturity for the bonds were also significant determinates of yield spreads. Each month closer to maturity the bonds displayed an average decrease in spreads between 1.87 and 2.38 bps. This confirms a mo derately upward-sloping term structure. 76 Perhaps most significant for this study is its examination of Hurricane Katrinas effect on pricing cat-risk. Dieckmann uses a dummy variable in a multivariate regression to test pre and post Katrina significance in premium levels. This analysis reveals that Katrina caused immediate increases in CA T bond spreads from 2.36 times expected losses to 2.78, an 18 percen t price shock. Intriguingl y, Dieckmann found that nonwindstorm bonds experienced even greater s hocks after Katrina, increasing by 0.89 times expected losses.77 This apparent co-movement in spreads following a major catastrophe suggests a systematic risk to Dieckmann. Instead of e xplaining Katrinas price shock in terms of investors adjusting their expect ations or comprehension of windstorm risk, he argues 75 Dieckmann, 9. 76 Dieckmann, 10. 77 Dieckmann, 12. 60


that the econom ic impact itself of Katrinasized catastrophes causes the spread. The direct economic costs of Katrina were betw een 100 and 200 billion dollars, or between one and two percent of U.S. consumption. The storm also destroyed 10% of U.S. domestic oil capacity. Thus, Dieckmann argues, one must consider an events effect on not just one sector of risk, but on an entire portfolio of di fferent risks. Such an event increases the cost of capital across the board for a portfolio and thus impacts all other kinds of risk.78 Dieckmanns equilibrium model assumes i nvestors whose investing behavior is based on their surplus consumption level. By introducing a -1% shock to consumption in the model, Dieckmann was able to replicate bo th the spike in wind risk prices and the commensurately higher increase in non-wind pr ices. These increases were 17 percent and 19 percent respectively, well in line with the 18 percent shoc k after Katrina. Dieckmann explains that the generalized 1 percent shock br ings the investor closer to his subsistence level, causing future risks to be more expensive.79 2.7 Optimal Allocation of Cat-Bonds within an Insurers Po rtfolio. Nell and Richter (2004) examine the adva ntages in using cat-bonds to improve risk allocation. They choose to confine their study to bonds using an industry-loss index trigger or a parametric trigger. They consider a primary insurer confronted with a potential catastrophe that th reatens its portfolio. The firm can purchase a reinsurance contract as well as cat-bond coverage. The st udy optimizes a utility function to find the optimal combination of these two options given the level of basis risk in the index-linked cat-bonds. Since the study is in terested in the ap propriate combination of both kinds of 78 Dieckmann, 22. 79 Dieckmann, 14 and 21. 61


coverage, the authors identify and elim inat e cases in which the cat-bonds trigger is independent of actual losses making it a usel ess hedge. They also eliminate cases in which the bonds issuing cost is prohibit ively expensive. The remaining bonds under consideration are thus both useful and affordable implying a non-zero demand.80 They first derive a Pareto-optimal solution for a reinsurance-only situation in order to model these instances of bond deficiency and to serve as a benchmark for the succeeding combinations. Holding this benchmark amount of reinsurance example as constant, they then introduce effective cat-bonds into the deci sion to study the change in the structure of coverage allocation. The bond has a fixed payout. They optimize over a range of loss levels given a probability f unction that describes th e likelihood of a bonds trigger.81 Not surprisingly, they find that reinsu rance holds a comparative advantage over cat-bonds for small losses, confirming the fact that small losses would not activate the index-linked trigger. The model does, however, show a structural change towards using a cat-bond for high expected losses.82 This first example held th e reinsurance level constant and optimized the amount of additional coverage bought in the form of bonds. In their second example, Nell and Richter optimize the firms utility if the reinsu rance level is allowed to float. They find that in cases of large expected losses the firm will substitute bond coverage for reinsurance coverage. At such expected losse s the firm potentially allocates less income to reinsurance than in the benchmark example.83 80 Nell and Richter, 189-191. 81 Nell and Richter, 191. 82 Nell and Richter, 193. 83 Nell and Richter, 194-195. 62


Richter also m entions the advantages of cat-bond allocation regarding the moral hazard and basis risk trade-off already discussed in detail in section 2.4. This study finds that in every circumstance cat-bonds netted efficiency gain s for a reinsurer assuming no transaction costs.84 Finally, Harrington and Niehaus cite current tax-laws as arguments for allocating cat-bonds to portfolio. They fi nd that corporate income tax actively discourages insurers from hol ding adequate capital for cata strophe coverage. Since this capital is not considered a business expense it counts as taxable profit. Harrington and Niehaus use an equilibrium price model to show the optimal price of supplying catastrophic insurance for 25, 50, 75 and 100 bill ion dollars of coverage. They examine corporate tax regimes ranging from 15% to 35%.85 They also look at the mitigating effects of investors in insurance companies re quiring a lower rate of return on equity or insurers investing 100% of the equity in tax exempt bonds.86 However, taxes persistently cost a signifi cant percentage of the present value of expected claims in this bracket. Supplying coverage in the 25-50 billion dollar bracket cost 49% to 183% of the presen t value of the expected cost s, with the base-line model predicting 115%. This implies that taxes on equity could increase costs of providing catastrophe coverage from anywhere between half to more than double the market cost. Harrington and Niehaus further note th at financing catastr ophic loss through conventional subordinated debt instead of equity, while reducing taxes, would not necessarily solve the problem. Namely, in th e event of a catastr ophe, the insurer would 84 Doherty and Richter, 22. 85 Harrington and Niehaus ,374-379. 86 Note that tax-exempt bonds contain an implicit tax rate in the spread between tax-exempt and taxable returns. 63


have to draw heavily on such bonds princi pal. This would result in a credit downgrade on the assets and a black m ark on the companys franchise.87 In contrast, cat-bonds intent ionally build in the princi pals potential default. Harrington and Niehaus thus advo cate these bonds as a way to avoid the pitfalls of both equity and conventional debt. They note, however, that the principal from a cat bond avoids taxes only through its placement in an off-shore special purpose vehicle. This cumbersome necessity further contributes to the difficulties in financing high risk thresholds.88 2.8 Conclusions Cat-bonds have emerged from the initial burst of innovation after Andrew as the dominant alternative risk transfer vehicle. The instruments maintained their popularity with insurers and investors alike even afte r the crucible of Hurricane Katrina and the ensuing trigger of KAMP Re. Cat-bonds have th ree basic types of such triggers: indexlinked, parametric and indemnity. Each of these has advantages and disadvantages. Among the most crucial considerations in choos ing such a trigger is the balance between basis risk and moral hazard. Academic literature has been remarkably positive in its assessments of cat-bonds potential. Studies analyzing allocation have f ound cat-bonds to be an efficient member of an idealized insurers risk-transfer opti ons. These generalized findings confirm the specific calculations put forth in Chapter 1 of this thesis regarding the FHCFs options for risk transfer. Other papers have crusaded fo r the rights of cat-bond issuers to fair pricing. However, this concern seems to have subsided as recent rates have more comparable 87 Harrington and Niehaus, 382. 88 Harrington and Niehaus, 383. 64


spreads to traditional reinsurance. In deed, the cost-benefit analysis presented to the Florida Senate in November 2007 (Tab le 1.1) confirms this observation. This chapter has discussed the opportuniti es and challenges in cat-bond allocation for insurers. Chapter 3 will continue this discussion from the investors stand-point, thereby shifting focus from insurers to the capstone of the risk-management pyramid: the capital markets. 65


Chatpter 3: Cat-Bonds and Market Risk 3.1 Introduction Cat-bond proponents frequently cite these bonds low correlation with other investments. Such a claim, if true, would ma ke cat-bonds a useful addition to a portfolio. Although initial studies have conf irmed this claim, events in the financial crisis of 2008 exposed even the cat-market to systemic risk. In this chapter I provide an updated regression analysis of cat-bond co-movement with other asset classes using secondary market data from 2004 through first-quarter 2009. I find that while the cat-bond market performed relatively well during the recent bear market of 2008 and 2009, coefficients between cat-bonds and other assets were significantly higher than in previous periods. The exposure to market risk through Lehman Brothers collapse and the ensuing failure of several cat-bonds no doubt impacted the market as a whole. The overall strong performance of cat-bonds during 2008 and l ong-term low correlations, however, cannot be discounted. I thus conclude with my assessment of the industrys prospects. 3.2 Zero correlation evidence Among the most important assertions in the cat-bond market is its claim of zero beta or zero correlation with other asset classes. This property, if true, would make cat-bonds a valuable hedge in managing a conventional portfolio of stocks and bonds. The claim makes intuitive sense. There is certainly no causal relationship between movements in the market and movements in weather patterns. Securities linked to hurricane behavior should thus share this low correlation with the wider market. Although often cited, rigorous analysis of th is claim remains relatively scarce. As discussed in Chapter 2, basis risk exists be tween hurricane activity and cat-bond triggers. 66


This im plies that the bonds themselves may not be perfectly correlated to storm activity. This complicates conclusive as sertions of low correlation for the bonds, even if the claim holds true for storms. The natural solution would be to study the performance of the bonds themselves. Historically, however, prici ng data has been scarce for the cat-bond market as a whole, making analysis of aggreg ate behavior difficult. Researchers must use creativity in devising acceptable metrics for market behavior in order to provide evidence for this common belief. In their seminal paper Litzenberger, Beaglehole and Reynolds produce the first formal evidence for catastrophe insurance li nked securities low co rrelation with other asset classes. The authors also demonstrat e insurance linked securities beneficial inclusion in a model portfolio. This paper is particularly remarkable given the early date of its composition. Written only a few years af ter Hurricane Andrew and the advent of such assets, the authors did not have the be nefit of extensive data sets. However they resourcefully note that the value of these asse ts should be inversely correlated to the loss ratios reported in an index for property insu rance. They thus use the most comprehensive such index, the Property Claims Services (P CS) index, as a proxy for pricing information from March 1955 to December 1994.89 Over this period they calculated a Pear son correlation coefficient of 0.058 for these loss ratios with return s on the S&P 500 and 0.105 between the loss ratios and a government bond index. Both of these coefficien ts were statistically insignificant. In contrast, the correlation coefficient betw een the S&P 500 and the government bonds was found to be 0.278 during this time span.90 89 Assessing Catastrophe-Linked Secu rities as a New Asset Class, 79. 90 Assessing Catastrophe-Linked Secu rities as a New Asset Class, 83. 67


Using a Black-Litterm an model portfolio analysis to determine asset allocation, they find that an investor with an S&P 500 index portfolio could optimally assign one percent of the portfolio to cat-linked assets if the asset offered at least eleven basis points above the short-term interest rate. They advocate two percent if the asset offers 22 basis points above this rate. For a bond portfolio they found that a one percent cat-allocation would be optimal given an excess return of three bps. A five bp spread would prompt a two percent allocation. For an equally weighted stock a nd bond portfolio they found 13 bps to be necessary for a one percent allo cation and 27 bps for a two percent allocation. The authors note that observed returns ar ound 794 bps for contemporaneous Cat-bonds thus made them particularly attractive as of their writing.91 Although the obvious shortcoming in this methodology is the lack of perfect correlation between the PCS index and the performance of Cat-bonds, it remains an adequate proxy for index-triggered bonds, many of which use the PCS itself as their trigger. Using the benefit of improved data, Cummins and Weiss design a multivariate regression model to evaluate th e zero beta claims of insu rance linked securities. They use the relatively new Swiss Re U.S. Wind CAT Bond Total Return Index as a proxy for the hurricane-linked bonds and choose comparab le bond and equity indices as regressors: Log(IILS,t/IILS,t-1) = + 1 log(IBI,t/IBI,t-1) + 2 log(ISP,t/I SP,t-1) + 3 log (RBaa,t) + (3.1) Where, IILS,t = Swiss Re wind total return index in period t IBI,t = Merrill Lynch U.S. BBB bond index price in period t ISP,t = S&P 500 price in period t RBaa,t = Moodys U.S. Baa corpor ate bond yield in period t. 91 Assessing Catastrophe-Linked Secur ities as a New Asset Class, 83-84. 68


Their m odel transforms raw index data into yields through a log difference transformation. This makes the time series data stationary. They sample weekly data from the period June 6, 2005 to January 30, 2008.92 Cummins and Weiss results demonstrat e that cat-bond betas for other asset classes, while not zero, are quite low. For both the Merril l Lynch and Moodys bond indices the coefficients were found to be statis tically insignificant. The coefficient for the S&P 500 was found to be statistically significant for an alpha of 0.05, however the coefficient remained quite low at 0.03. The model thus provides evidence that the bond and equity markets indeed have minimal explanatory power for hurricane-linked catprices. The study found even more favorable results when they used the yield on the Swiss Re BB Rated CAT Bond Total Return index as the dependent variable. The majority of the bonds in this index also pr ovide U.S. wind coverage, but the members of this index are all rated BB or higher. For this index none of the explanatory regressors were statistically signifi cant at an alpha of 0.01.93 This is the most rigorous study of the zero-beta claim to date. The observed data and explanatory methodology are not as pr ovisional as in the classic Litzenberger study. The data set includes hurricane Katrin as negative impact on the CAT indices as well as the early stages of the recent meltdown in the capital markets beginning in late 2007. An industry study by Guy Carpenters re search department finds similarly encouraging evidence of cat-bonds low market risk. The study calcu lates a correlation 92 Convergence of Insurance and Financial Markets, 47. 93 Convergence of Insurance and Financial Markets, Table 4. 69


m atrix of returns from January 2002 to September 2007 on the Swiss Re BB Cat Performance Index versus six other asset cla sses: a correlation of 0.03 between the Swiss Re total return aggregate index, confirming th e intuition of a very low correlation with equities. The correlation between the cat index was 0.11 for the three month LIBOR and 0.02 with gold. They found slightly higher correla tions with debt-based assets, finding a 0.22 correlation with Baa corporate bond yi elds, a 0.33 correlation with the Lehman Brothers Mortgage Backed securities index yields and a 0.22 correlation with the Lehman Bothers Government Bond Index yields.94 Cummins comments that the total returns for Cat-bonds will be naturally linked to debt indices since returns for these assets all include coupon payments. As stated, cat-bonds typica lly define their coupon payments as LIBOR plus a spread. 95 This study is frequently cited in both academic and professionally literature. However, while these correlations for cat-bonds are attractive, claims that these correlations demonstrate cat-bond superiority to the other cl asses deserve scrutiny. In no 94 ILS Comes of Age: Structured Products on the Horizon, 5. 95 ILS Comes of Age, 5. 70


case were cat-bond coefficients the lowest for a particular asset class. Moreover, The S&P 500, gold and LIB OR all had average corre lations near zero for the basket as a whole. In some sense, this merely restates the observation above that debt-based assets have a natural correlation with each other. Thus, while individua lly interesting, the correlation matrix is not as effective in providing a metric for any assets correlation with the market as a whole, offering at best onl y a rough approximation of aggregate market behavior. It is perhaps more relevant to compare only debt-based correlations to the S&P 500, but this too raises questions. Curiously, the touted 0.03 coefficient for cat-bonds versus the S&P 500 was identical to the 0.03 coefficient for BBB corporates versus the S&P 500. Both these coefficients were high er than the -0.39 coe fficient found between the government bond index and the S&P 500. This evidence, again, complicates assertions of cat-bond co rrelation superiority. Thus at first glance, doubt emerges as to cat-bonds superiority to its peers. However, looking at the average correlations of the four debt securities reveals supportive evidence for cat-bonds competitive edge. When mortgage-backed securities are excluded from the data, cat-bonds have the same average coefficient as the government index with rest of the basket at approximately 0.14. This is attractive when compared to the average coefficient of 0.22 for BBB corporates, and demonstrates that cat-bonds are at least as eff ective as long term government bonds on average at hedging other risks. When mortgage-backed securities are included, the average coefficient is even more attractive at 0.17 when compar ed to a 0.26 average for government bonds and 0.31 for both mortgage and corporate debt. Thus ultimately, insofar as correlation 71


com parison is a useful metric, cat-bond yields do appear to offer an edge in hedging across asset classes when compared with other debt securities. Again, this analysis of the correlatio n matrix can only approximate aggregate market behavior. Cummins and Weiss regr ession analysis provides a much more theoretically sound assessment of cat-bonds holistic hedging capabilities. Both studies make use of Swiss Re Cat Indices to study cat-bond performance, but neither data-set extends through the full effects of the 2008 financial crisis and its aftermath. In order to investigate the zero-correla tion claims during this critical period through a regression model based on the Cummins Weiss methodology. I will proceed first with a more formal introdu ction to the Swiss Re dataset. 3.3 The Swiss Re Cat-Bond Indices Swiss Re created the Swiss Re US W i nd Cat bond Performance Index in the fall of 2007. The index tracks the aggregate re turns on cat-bonds which provide hurricane coverage. Three additional indices were also created to track th e insurance-linked bond market. These included an earthquake bond in dex, an index of cat-bonds rated BB or higher, and a total cat-bond ma rket index. I will restrict my study to the Swiss Re US Wind Index so as to provide the most focused analysis possible as relevant to Floridas hurricane insurance dilemma. The indices begin their pri ce histories in January 2002 w ith an collec tive total of twenty bonds. This figure climbed to 104 by August 2008, dropping to 93 by years end 2008 due to a high number of maturities. In January 2009 the Wind Index contained 22 outstanding bonds.96 96 Insurance-linked securities market update, 6. 72


The W ind Index contains only single peril bonds in U.S. dollars. Thus bonds that insure multiple kinds of catastrophes, such as both earthquakes and hurricanes, would not be included in this index. As of August 2008, 82 percent of the bonds in the Wind Index were rated BB by Standard and Poors and 17 percent were rated B, together accounting for 99 percent of the index.97 These ratings place the Wind Index at the top of the noninvestment grade bond spectrum. This rating re flects the built-in risk of losing the bonds principal. Eighty percent of the Wind Index s bonds used an industry-index trigger and 17 percent used an indemnity trigger, together accounting for 97 percent of the market.98 It is instructive to observe the methodology that Swiss Re uses in calculating its cat bond indices. The process is a good primer in how to view index data. First, the Swiss Re Distribution team collects bid indications for the bonds every Friday at the close of the market. This gives the pricing and c oupon information necessary to calculate the market value of each bond: MVk,t = Ak,t-1 + Pk,t-1 where, MVk,t is the market value of the kth bond during weekly period t Ak,t-1 is the bonds accrued interest up to the previous period and Pk,t-1 is the price from the previous period.99 The price return is then calculated for each bond by dividing the change in price during period t by the market value in period t: PRk,t = (Pk,t Pk,t-1)/MVk,t 97 Swiss Re Cat Bond Indices, 5. 98 Swiss Re Cat Bond Indices, 5. 99 Accrued interest is the portion of the bonds coupon owed between coupon dates. Thus on the day of a coupon payment the accrued interest is zero. After si x months for an annual coupon, the accrued interest would be half the normal coupon payment. By conven tion, the accrued interest payment is incorporated into a bonds market value to reward the seller for the full amount of time he or she has held the bond. 73


A similar calculation is made for accrued interest returns on each bond: ARk,t = Ak,t /MVk,t Where ARk,t is the accrued interest return. Since by definition the accrued interest rate represents all accumulated in terest since the previous coupon, no difference from the accrued interest in the previous period is necessary. The sum of the price return and accrued interest return gives the individual bonds total return: TRk,t = PRk,t + ARk,t where TRk,t is the total return on weekly period t, for bond k. Since the index incorporat es the returns on many bonds, it uses a weighted sum to represent the aggregate returns of these bonds in each period. The weight takes into account each bonds underlying principal, that is its notional amount, as well as its price. The weights are defined as: Wk,t = (Nk,t-1 Pk,t-1 )/( Ni,t-1 Pi,t-1) where Wk,t is the weight of bond k during period t. Note that the sum of all the weights is one. This methodology, adopted in 2008, deviates from a previous methodology which considered only prices in the weight cal culation. This could be deceptive since an increasing price would give a bond higher and higher weights, while a decreasing price would give a bond lower and lower weights. Th e indices thus did not accurately reflect the scope of Hurricane Katrinas impact on the bond market. Specifically, the multi-peril bond KAMP re was partially triggered in 2005 due to hurricane Katrina, which resulted in a price decrease for this bond. The lower pr ice translated to a lower weight in the 74


Swiss Re BB Cat Bond Perform ance index, of which the bond was a member. The new methodology has mitigated the prior underweighting of this bond. Weights taking into account the outstanding principal make sure that price changes shock the index in proportion to the bonds size. The final calculation for the total return for the index in period t is simply the sum of each of the individual bonds total return s multiplied by their respective weights: It = TRi,t Wi,t where It is the index level in period t.100 3.4 Analysis I: Regression analysis of the Swiss Re U.S. Wind Index 2004-2009 A visual inspection of the performance in the level of the Wind Index next to the Dow Jones Corporate Bond Index and the S&P 500 from 2004 to first quarter 2009 revealed outstanding returns. This is r eadily observed in figure 3.1. From April 2004 through February 2009 the Wind Index had annu alized returns of 10 percent, a very healthy performance. Moreover, the Wi nd Index held par value through 2008s tumultuous market with much more volatile be havior in corporates and equities. Figure 3.2 demonstrates this. From January 2008 through February 2009 the Wind index returned 2 percent, no small accomplishment in that periods tough market. This led me to hypothesize that these bonds would have sim ilarly low-correlation during the financial crisis as found in previous periods by Cu mmins and Weiss. To test this hypothesis I proceed with a structural regression analysis. 100 Swiss Re Cat Bond Indices, 1 and 8. 75


Figure 3.1: Relative Index Performance 2004 First Quarter 2009 0.6 0.8 1.0 1.2 1.4 1.6 20042005 2006 2007 2008 Swiss Re Wind Index Dow Corporates S&P 500 Figure 3.2: Relative Index Performance 2008 First Quarter 2009 0.5 0.6 0.7 0.8 0.9 1.0 1.1 2008Q1 2008Q2 2008Q3 2008Q4 2009Q1 Swiss Re Wind Index S&P 500 Dow Corporate 76


While m y regression model follows the structure of Cummi ns and Weiss in equation (3.1), I replace thei r use of the Merrill Lynch U.S. BBB rated bond index with the Dow Jones Corporate Bond Index. Although th is choice sacrifices the focused rating encoded in the Merrill Lynch data, the Dow Jones Corporate index is a better proxy for the corporate bond market as a whole in the U.S. Moreover, the Moodys U.S. Baa Corporate Bond Yield parameter preserves th e advantage of ratings comparability. All data is weekly and calculated by the weeks closing price. As in Cummins and Weiss I take the log differences of the indices to compare growth-rates instead of levels between the time -series. This serves the regression analysis by transforming the raw price into a stationary series. Stationarity essentially means that a series is mean reverting. This property is a key requirement for non-spurious regressions. I further follow Cummins and Weiss in taki ng the log of the Moodys Baa Yield data, though this data is already in yield form. Th is facilitates equitable comparison between all four series and eases comparison betw een my findings and those of Cummins and Weiss. My regression is defined as follows: log( Wt/Wt-1) = 0 + 1 log( Dt/Dt-1) + 2 log( St/St-1) + 3 log ( Mt) + ut (3.2) where Wt = Swiss Re Wind Total Return I ndex price level in period t Dt = Dow Jones Corporate Bond Index price level in period t St = S&P 500 closing price level in period t Mt = Moodys Seasoned U.S. Baa Corporate Bond Yield in period t101 101 Time series data for the Swiss Re Wind Total Return Index data is from Swiss Re Capital Markets Corp. S&P 500 data is from Commodity Systems Inc. Dow Jones Corporate Bond Index data is from Dow Jones and Company. Moodys Seasoned U.S. Baa Corporate Bond Yield data is from the Federal Reserve Economic Database. 77


ut = stochastic white-noise term. I use robust standard errors th roughout in order to correct fo r heteroskedasticity, that is auto-correlation in the stochastic term. Th e model relates the Swiss Re Wind Index to other asset classes and there by observes these classes expl anatory power in different time periods. The degree of signi ficance in the parameters will thus clarify the amount of systematic, market-based risk in hurricane cat-bonds. I organize my study into three distinct tim e periods: a baseline period to calibrate the model, an experimental period to test recent behavior and a long-term period to cover both. The baseline period, her eafter called period (1), us es weekly data covering approximately three years from Janua ry 6, 2005 through May 30, 2008. Cummins and Weiss use an identical period in their model. Hence, this choice of baseline facilitates comparison between my model and the Cummins Weiss model and also offers a frame of reference for the experimental period. The experimental period, he reafter called period (2), contains the same number of 178 week ly observations as in the Cummins Weiss model, but updates the time frame to c over January 7, 2005 through February 20, 2009 to evaluate the cat indexs recen t behavior, particularly during the 2008 financial crisis. The long-term period, hereafter called period (3), covers nearly five years from April 9, 2004 through February 20, 2009. Period (3) thus cove rs both the experimental and baseline periods, extending the scope of the Cummins Weiss study by a year on either side. This allows a more comprehensive evaluation of the zero-correlation claim and a broader conclusion of the indexs performance. 78


3.4.1 Baseline Results in Period (1) In period (1) I find very similar results to Weiss and Cummins. The results are summarized in table A.1.1, found in Appendix I. Using an alpha of 0.05, the F (3,173) statistic with a p-value of 0.39 was not found to be statisti cally significant. There was thus not significant evidence to reject th e null hypothesis that at least one of the parameters would have explanatory value. Th is indicates that the model as a whole did not have a great deal of e xplanatory power for the cat i ndexs growth rate. Moreover, during this time-frame none of the para meters had a statistically significant t -score, with p-values ranging from 0.13 to 0.54. Furthermore, coefficients remained very low, all less than 0.02 for the Dow Corporate Index parameter. The adjusted R-squared value of zero further confirmed the low explanatory value of the model. In comparison, recall that the Cummins Weiss Model during th is period found a statistically significant parameter at the 0.05 level for the S&P 500, albeit with a low coefficient of 0.03. The adjusted R-squared fo r the model was also quite low at 0.01. My change in the model by introducing the Dow Corporate Index thus reduced the models explanatory power below even the Cummins Weiss study. This is thus even stronger evidence of cat-bonds low correlation. The Dow Corporates basket of ratings is more diverse than in the Merrill Lynch BBB i ndex, which no doubt contributed to this difference. Nevertheless, my baseline period confirms the results in the Cummins Weiss study that the model has low explanatory power from June 2005 through May 2008. 3.4.2 Experimental Results in Period (2) The experimental results calculated in period (2) differ greatly from the baseline. The results may be found in table A.1.2. For an alpha of 0.05, the models F (3,173) statistic is clearly significan t with a p-value of zero. Th e null hypothesis that the model 79


has no explanatory value m ust thus be reject ed. Indeed, each paramete r had a statistically significant t-statistic for an alpha of 0.05. Although coefficients remained low, they at least doubled in every case, with the Dow Co rporates coefficient increasing seven-fold. The adjusted R-squared saw a marked increa se from zero to 0.26. This new adjusted Rsquared, with a p-value less than 0.005, is statistically significant according to a chisquare distribution with four degrees of freedom. This clearly indicated the presence of a relationship between the modeled parame ters and the cat-indexs growth-rate. These findings counter my initial hypothesis that the cat-index would continue to show low shared-movement with other asset classes in the experimental period. Indeed, market risk appears to have been signif icant during this period. Given this new information, I suspect that the 2008 financial crisis impacted the movement of the index. To test this new hypothesis I br oke the experimental period into two segments in hopes of isolating this new behavior in the regression. The first segm ent, hereafter period (2.a), covers the 118 observations from September 30, 2005 through December 28, 2007. The second segment, hereafter period (2.b), cove rs the 60 observations from January 4, 2008 through February 20, 2009. I expected to find that period (2.b), the smaller segment, would account for the majority of the increased correlation between th e asset classes. I also expected that period (2.a) would more closely resemble the baseli ne period. After testing regressions for both these segments I found these suppositions to be accurate. Tables A.1.3 and A.1.4 in Appendix I summarize these findings. In period (2.a) the model as a whole was not found to be statisti cally significant, with a F (3,113) p-value of 0.27. There was thus not sufficient ev idence to conclude that 80


the m odel held significant explanatory valu e during this segment. The coefficients remained low; all were below 0.04. However, the S&P 500 parameter, with p=0.05, was just found to be significant for an alpha of 0.05. The other parameters remain well out of range of significance. In period (2.b), the model was found to be highly significant, with an F (3,56) pvalue of zero. Interestingly, in this shorter period, onl y the Dow Corporate index parameter was found to be statistically signi ficant at the 0.05 level, with a p-value of 0.01. The S&P 500 parameter, however, actually decreased in significance with p=0.15. The coefficient for the Dow Corporate was also relatively high at 0.18, while other betas remained low. The R-squared for the model was 0.37. This was higher than the in the total experimental period, and clearly st atistically significant with p<0.005 for the relevant Chi-Square distribution. Taken together, period (2.a) and period (2.b) provide more information on the highly significant t-scores for the total period (2). The first segment shows some explanation in the S&P 500 regressor while the second segm ent shows strong explanation in the Dow Corporate regressor. Thus while neither regressor was significant in both segments, the combined period (2) registers both the S&P 500 and the Dow Corporate as significant. 3.4.3 Five-Year Analysis in Period (3) I concluded my analysis by exam ining the full data-set at my disposal. In this long-term period covering five years of data the regressions behavior returns to the intuitively low correlations hypothesized. Ther e was not sufficient evidence to assume that the model as a whole ha d statistical significance for an alpha of 0.05 due to a F (3, 81


251) p-value of 0.28. All t-statisti cs for the parameters were al so well out of the range of significance, indicating that none of the param eters individually held explanatory value for the cat indexs yield. Intere stingly, the Dow Corporate indexs coefficient was higher than that found in the baseline analysis, with a value of 0.11. My model thus finds that cat-bonds were at least moderately correlated to marketrisk during the experimental period. Furt her analysis reveal s a relatively strong relationship with corporate de bt in 2008. The long-term anal ysis confirms previouslyheld intuitions of a weak relationship between cat-bonds and the broader market. The baseline analysis is in line with Cummin s and Weiss findings and provides further evidence of cat-bond independence during the Ka trina period. The overall conclusion is that, while not perfect, cat-bonds have show n resilience over the last five years, producing high-returns and relatively-low market beta in a period which contains price shocks from both financial and natural phenomena unparalleled in recent memory. These positive findings aside, however, the increased systematic risk detected in 2008 warrants further inquiry. I wi ll thus proceed to a discussi on of market factors which impacted the cat-market during this period. 3.5 Cat-Bonds and Counterparty Credit Risk Cat-bonds weathered the storm surprisingl y well during the financial catastrophes of 2008. However, not every catbond was immune to the mega-f ailures of that year. This disproved nave assertions of cat-bond invulnerability to financial perils. As discussed in Chapter 2, a cat-bond SPV insurers its principal through two complementary strategies: investment in high ly-rated fixed-income securities and a totalreturn swap with a counterparty. As long as either the counterpart y or the investments 82


them selves remain sound, the SPV should be ab le to meet its obligations. The SPV can handle the failure of one of its hedges, but not both. Not surprisingly, the 2008 financial crisis triggered just such an event. Lehman brothers acted as swap counter party to four catbonds. After Lehman filed for bankruptcy on September 15, these bond s were exposed to counterparty credit risk. Their contract with Lehman to replenish their principal became void. The SPVs themselves now had to withstand market ris k. This resulted in an immediate rating downgrade for all four bonds by Standard and Poors. A case-study for one of these bonds, Ajax Re, reveals the nature of this systemic risk. Ajax Re had the misfortune of having not only a poor swap counterparty but also poor underlying assets. Curiously, this insura nce bond hedged itself by investing in more insurance bonds. The reinsurer Aspen Re had fo rmed Ajax to reinsure a portion of its exposure to California earthquakes. Ajax, in turn, invested it s principal in Ballantyne Re bonds. Ballantyne Re itself was an SPV base d in Ireland, whose sole purpose was to manage reinsurance bonds. In particular, th e reinsurance company Scottish Re founded Ballantyne to collateralize its purchase of part of INGs life insurance book.102 The timeline of these two SPVs is important. Lehman Brothers had acted as primary bookmaker for Ballantynes creation in May 2006. At their inception the highest tranch of these Ballantyne bonds held AAA rati ngs from Standard and Poors, Fitch and Moodys.103 Lehman entered into the counterparty swap contract with Ajax in April 2007. Ajax thus purchased its position in Ballantyne Re soon therea fter. A mere five months later, this posit ion would deteriorate. 102 Scottish Re: Form 8-K Current Report, 103 Business Wire, Scottish Re Completes $2.1 billion Triple-X Securitization. 83


Beginning in Septem ber 2007 and c ontinuing through 2008 Fitch began downgrading Ballantyne Res bonds as it became apparent that their underlying investments were in subprime residential mortgage debt.104 While Lehman stood, the resulting decline in these Ballantyne bonds did not effect Ajax Res rating. The counterparty swap offered protection. Lehmans fall, however, made Ajaxs relationship to Ballantyne very important indeed. Ajax had purchased the A-2 tranche, the highest class of thes e bonds. At first the lower Ballantyne tranches earned downgrades as they defaulted on interest payments while in the A-2 tranche maintained its AAA rating, due to its third-party bond insurance with Ambac. Ambac was one of the largest guarantors of fixed-income securities. However in January 2008 Fitch downgraded Am bac itself from AAA to AA, a severe blow for a securities insurer.105 This downgrade trickled down into Ambacs customers including the Ballantyne A-2 bonds. With its swap insurance ru ined and its underlying assets rapidly declining in value, Ajax itself foundered. In a December 2008 report to shareholders Aspen, Ajaxs founder, stated that it did not expect to r ecover collateral from Aj ax should a California Earthquake occur. 106 To the markets surprise, Ajax did manage to make its March semiannual coupon payment but Standa rd and Poors retained it s assessment of CC for the company, forecasting a further downgrade to D in May when Ajaxs bonds were due to mature, no doubt without a full reimbursement.107 104Business Wire, Fitch Downgrades Ballantyne Re Class A-1 and B Notes; Remain on Rating Watch Negative. 105 Richard, Ambac's Insurance Unit Cut to AA From AAA by Fitch Ratings. 106 Aspen Insurance Holdings Limited Investor Presentatio n: December 2008, 17. 107 Ajax Re pays coupon, still at risk of default -S&P, 84


It is interesting to note that in the defaults for both the Ballantyne bonds and Ajax bonds, the s ponsoring reinsurers, Scottish Re and Aspen, held no responsibility and did not experience any negative e ffect on their overall ratings Though their reputation might suffer some ill-effects their balance sheets did not. Both companies use language in their annual reports assuring investors that they bear no financial obligation to the bondholders. It may also be worth considering Lehmans role in the selection of the underlying assets. According to Goldman spokesman Mi chael DuVally Lehman made decisions on the investments as the swap counterparty.108 The entire debacle exhibits both a classic narrative of the 2008 financia l melt-down as well as a growing edge for the cat-bond market as a whole. Designing more transparen t insurance for the SPVs collateral will be one of the most important challe nges for future cat-bond issues. 3.6 Analysis II: Specific Impact of Le hmans Collapse on the Cat-Market Although a web of failures ensnared Aj ax, it was Lehm ans Bankruptcy that catalyzed the bonds downfall and the wide r cat-markets stagnation. New cat-bond issues ceased for 2008 after September 15 and did not recommence until February 2009. Moreover, a visual inspection of the level of the Swiss Re Index in during this period provides further motivation for studying at the specific impact of Lehmans collapse on the cat-market as a whole. The peak in Figure 3.3 occurs on August 29, 2008 and the first trough occurs on September 19, August 2008. 108 Cat Bonds Survive Earthquakes, Decline After Lehmans Collapse, 85


Figure 3.3: Swiss Re U.S. Wind Index Level: Jan 2008 Feb 2009109 174 176 178 180 182 184 186 2008Q1 2008Q2 2008Q3 2008Q4 2009Q1 This period of Lehmans apparent effect on th e cat-market is a subset of period (2) from Experiment I. I thus propose that Lehmans collapse caused a significant amount of the correlation with other asset classes as observed in peri od (2) of Experiment I. However, any experiment testing Lehman s effect on the cat-market must also take into consideration the im pact of Hurricane Ike, which made landfall in Texas early on September 13, 2008. This date coincides ex actly with the beginning of the large descent in the Swiss Re Wind i ndex level early in the third-qu arter as seen in figure 3.3. The investigation of Ikes insured losses thus predates Lehmans collapse by several days and its impact coincides with Lehmans. Part of the challenge in creating an experimental model is thus choosing variables that will extract the individual information in both shocks. Indeed both Ike and Lehmans collap se should be incorporated into a model attempting to represent the explanatory factors of 2008. 109 Data Source: Swiss Re. 86


3.6.1 The Model for Analysis II To test this hypothesis I incorporate two dummy variables into my original model as stated in (3.2) for Analysis I. Whereas Analysis I examined th e same model (3.2) in two different periods, Analysis II will look at two different models in the same period. Analysis II covers September 30, 2005 through February 20, 2009, which coincides with period (2) from the previous experiment. The baseline model will be (3.2) from Experiment I and the experimental m odel (3.3) will incorporate dummy variables for Ike and Lehman Brothers. I will also incorporate the cross-effects of Lehmans collapse on the S&P 500, the Dow Corporate I ndex, and the Moodys Baa Yield index. I define the experimental model as follows: log( Wt/Wt-1) = 0 + 1log( Dt/Dt-1) + 2log( St/St-1) + 3log ( Mt) + 4log( Dt/Dt-1) Lt + 5log ( Mt) Lt + 6log ( St/St-1) Lt + 7Lt+ 8It + ut (3.3) where Lt = The dummy variable for Lehman Brothers Collapse, which takes value of 0 before September 15, 2008 and 1 thereafter. It = The dummy variable for Hurricane Ike, which equals 1 from September 12, 2008 until October 31, 2008 and zero else. Equation (3.3) includes both a multiplicative component for L and an intercept component. Thus 4, 5, and 6, the differential slope coefficients, estimate a regime change coinciding with L in the slopes of the Dow Corporate index the Moodys Baa index and the S&P 500, respectively. Likewise, 7, the intercept differential, estimates a change in 0, the intercept, that coincides with L. A significant t -score for 5 would thus indicate a vertical sh ift in the model as a whole corres ponding to the eff ects of Lehmans collapse. 87


Figure 3.6: Dow Corporate B ond Index Jan 2008 Feb 2009 180 185 190 195 200 205 210 215 2008Q1 2008Q2 2008Q3 2008Q4 2009Q1 Figure 3.5: Moodys Baa Seasoned Yield Index Jan 2008 Feb 2009 6.4 6.8 7.2 7.6 8.0 8.4 8.8 9.2 9.6 2008Q1 2008Q2 2008Q3 2008Q4 2009Q1 88


Figure 3.7: S&P 500 Jan 2008 Feb 2009 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 2008Q1 2008Q2 2008Q3 2008Q4 2009Q1 Examining Figures 3.4, 3.5, and 3.6 provide the motivation for including slope differentials for the Dow Corporate in dex, the Moodys Baa index and the S&P 500. Each has a clear shock soon after September 15. However, it is also worth testing if the slopes of the rates themselves change si gnificantly. I hypothesize that the external, qualitative, variable of Lehman Brothers collapse is affecting the motion in the rates of all three of these indices in a similar manner. Lehman Brothers was a market leader and its downfall caused severe systemic risk to both the equity and fixe d-income markets. Note also, that I, the dummy variable for Ike, ha s only an intercept differential coefficient in. This is because I do not beli eve Ike had significant cross-effects in the three other indices. The main purpose of the Ik e dummy is to measure the extent to which models level, or rather its intercept, was shocked by Ike. This is vital. Forgoing this variable would impart all of th e level-shock to the Lehman va riable, when this is clearly 89


false. The price shock clearly begins before Lehm ans bankruptcy and the investigation of Ikes losses caused docume nted anxiety in the market. 3.6.2 Selecting the Persistency of the Du mmies for Ike and Lehmans Collapse. I will n ext outline my procedure in c hoosing how many observations to include for each dummy variable. The Ike dummy variable begins on Friday, September 12 as Ikes Texas landfall early on the 13th became imminent. The Ike dummy ends on October 31, one week after a new model by Risk Management Solutions, one of the industrys largest computer modelers, placed a higher upper-bound on insured damages due to Ike.110 Although doubts lingered into 2009 regarding the true extent of Ikes losses, the October 24th date caps the most significant adjustment in this estimate. The seven weeks of this dummy variable thus should capture th e period of greatest anxi ety in prices due to Ike. For further validation of seven-week pe rsistence in the Ike dummy, I cite the Swiss Re Wind Indexs behavi or during Katrina in 2005. Since 2005 was a comparatively stable year for the overall capital markets, one can view Katrinas impact on the Wind Indexs level as an experiment which observe s a hurricane-related s hock, but controls for shocks in the financial sector. First, recall that (3.3) uses an intercept differential to model Ikes effect. In other words, the Ike dummy is a simple intercep t term. This means that the Ike dummy will register shocks to the level of (3.3) as a whole. The most recent comparable hurricane to Ike was Hurricane Katrina. However, Hurrican e Katrinas price shock to the Swiss Re U.S. Wind Index lasted only seven weeks, even though estimates for insured losses due to Katrina were higher than those for Ike. Indeed, the Swi ss Re Wind Index declined for 110 RMS Revises Hurricane Ike Industry Loss Estimate to $13-21 Billion, 90


only three weeks after A ugust 29, the date of Katrinas landing in L ouisiana. After these three weeks the index climbed for four w eeks for a full recovery by October 14. The index then increased consis tently through the years e nd. Even the announcement of Kamp Res Trigger on November 6 appears to have led to an even steeper climb after a small dip on November 4. Incredibly, even with this major-hurricane shock and the resultant default of a bond, the Wind Inde x still returned 7 percent for 2005. Thus although natural shocks and even hurricane-related defaults do impact the cat-market, the market seems to have already prepared itself for such losses and will tend to make a quick recovery. Clearly, the shock observed in Figure 3.3 in 2008 is of a more severe and persistent nature. I thus believe that Ike made the bulk of its contribution to this index behavior within the first seven weeks after its landfall. This choice follows the pattern of Katrina and also coincides with the important estimate adjustment provided by RMS. The Lehman Brothers dummy variable be gins on Friday, September 19, the first observation after Lehman filed for bankruptcy, and persists until the end of the series on February 20, 2009. Again, I have chosen the persistence of this dummy very deliberately. Investors and bond-sponsors were mentally prep ared for an event like Ike and had, in a sense, already built its risk in to their model structure. However, Lehmans collapse would shake this structure to its co re. Both bond issuers and investors became more wary of this newly recognized counterparty-risk. Moreover, questions about the health of remaining counterparties like Goldman Sachs and other investment banks lingered th rough February 2009. Incidentally, February 2009, although the end of the data set, also co incides with the firs t new cat-bond issue in 91


the six m onths since Lehmans collapse. Even so, new issues for 2009 still trail behind previous years as issuers take time to i nnovate solutions to th e counterparty problem. Furthermore, the four bonds for which Le hman was counterparty continued to limp through the market into early 2009. Thus the structural and psyc hological effects of Lehmans collapse clearly persist until th e end of the data-set in February 2009. 3.6.3 Results from Analysis II The m ost conclusive result from Analys is II is the clear importance of the Lehman Brothers intercept differential. Th e results are summarized in tables A.2.1 and A.2.2 found in Appendix II. As expected bot h the Lehman dummy and the Ike dummy had negative coefficients, reflecting the nega tive price shocks due to these phenomena. The Lehman Brothers intercept differential ha d a p-value of 0.06. This is a particularly strong finding considering it has been mitigat ed by the seven-week contribution of the Ike intercept differential, wh ich had a p-value of 0.16. Though still highly significant, the estimati on of the experimental model in (3.3) as a whole had less explanatory power for the Swiss Re Wind index than the baseline model did. To repeat, the baseline, period (2 ) for equation (3.2), had an adjusted Rsquared of 0.28, significant at the 0.005 level. The baselines F-statistic was also highly significant at 21.65, with a p-va lue of zero. In comparison, e quation (3.3) had a slightly higher adjusted R-squared at 0.32 but a much lower F-score of 9.97. This F score, however, still had a p-value of zero. The t-tests for the Lehman slope differenti als also provide significant information on systemic risk. The Dow slope differential ha s a highly significant coefficient with a pvalue of 0.04. The Moodys slope differential is also fairly significan t with a p-value of 92


0.09, whereas the S&P slope differential was insignificant. It is inte resting to note that with thes e new variables in the model, the Dow Corporate Index itself becomes insignificant as well, with a very high p-value of 0.8. In contrast, the S&P 500 and the Moodys index maintain their relative significan ce from the baseline with p-scores of 0.007 and 0.07 respectively. Curiously, removing the insignificant S&P 500 slope differential gives a different picture of the data. This revi sed model is thus as follows: log( Wt/Wt-1) = 0 + 1log( Dt/Dt-1) + 2log( St/St-1) + 3log ( Mt) + 4log( Dt/Dt-1) Lt + 5log ( Mt) Lt + 7Lt+ 8It + ut (3.4) Table A.2.3 provides the full results for this new regression. Once this model removes the insignificant Lehman dummy for the S&Ps slope, the S&P 500 coefficient itself, 2, becomes much less significant, i.e. 2s p-value jumps from 0.007 to 0.12 with this change. The Moodys Yield coefficient, 3 also doubles its p-value from 0.07 to 0.14. While these p-values in (3.4) for the S&P and Moodys still indicate some explanatory value, their influence is much re duced. The Dow Corporate coefficient 1 remained clearly insignificant wi th a p-value of 0.781, indicating a cl ear lack of explanatory power after controlling for Lehman Brothers e ffect. Indeed, the Dows slope differential 2 remained significant with a p-value of 0.06 even after the S&P slope differentials removal. The Lehman Brothers intercept coefficient 7 also maintained its explanatory value with a p-value of 0.08 The estimation of (3.3) and its modification in (3.4) impart a few core conclusions. The first is that the intercept differential for the Lehman dummy recorded a 93


clear negative shock in both m odels, even w ith the Ike dummy stealing a portion of the explanatory value during the most dramatic price adjustment. The second conclusion is that Dow Corporate Bond Index itself lo st explanatory significance once the model controlled for its change in slope during the Lehman dummy. This could perhaps be evidence of the cat-bonds tr aditional low-correlation in the absence of external intervention. The third conc lusion is that both the S&P 500 and Moodys Baa Yield Index maintain some degree of explanatory value even after controlling for structural breaks in these indices due to Lehman. This finding could indicate the true systemic risk of cat-bonds during period (2). Indeed, anecdotal evidence suggests that many institutional investors were forced to sell th eir cat-holdings in orde r to cover losses in other portfolio segments. Ind eed, this makes sense given th at cat-bonds were one of the few investments to make any positive return at all in 2008. The intuition of increased selling as a systemic risk in 2008 is conf irmed by the fact that 2008 saw the highestlevels of cat-bond trading in the secondary market on recor d, a 13 percent increase from 2007.111 3.7 Adaptations in New-Bond Issues After a nearly six-m onth hiatus in bo nd issues, In February 2009 the French reinsurer SCOR reopened new issues of cat-bonds with the SPV Atlas V. Atlas V provides three years of hurricane and earthqu ake coverage to the U.S. market using a double trigger that combines the PCS loss inde x with estimated losses calculated by AIR modeling. The Atlas sold a relatively large issu e of $200 million in collateral which it has invested in U.S. government-back debt obligations. The trust fund will remain 111 Insurance-linked Securities Market Update, 1 and 5. 94


transpa rent. Goldman Sachs is serving as sw ap counterparty. The c ontract ensures that Goldman will replenish any losses in the fund on a frequent basis.112 Liberty Mutual has similarly solved its approach to credit risk through taking on Goldman Sachs as counterparty for its $225 m illion dollar bond, Mystic Re 2, issued in March 2009. The bonds collateral is invested in high class no n-mortgage debt and U.S. treasuries.113 The most recent cat-bond issue by Allian z, Blue Fin 2, sets a precedent for the market not only in reducing counter-party cred it risk but also in modeling a mutually beneficial public-private relationship. Issu ed on April 7, 2009 out of the Cayman Islands, the bond was increased from its original capacity of $150 million to $180 million due high investor demand. Goldman Sachs and Aon Benfield Securities packaged the Blue Fin 2, which pays 135 bps over LIBOR in coupon and has received BBrating from Standard and Poors. AIR provided modeling services. Instead of using a counterpartyswap arrangement to insure the collateral, Blue Fin 2 will place its collateral in floatingrate notes issued by the AAA-rated Kreditans talt fuer Wiederaufbau (Credit Bank for Redevelopment). This bank is owned by the Ge rman federal government and its notes are likewise guaranteed by the government. Blue Fin 2 will provide three years and nine months of coverage for hurricane and ear thquake losses throughout the United States.114 3.8 Conclusions In this chapter I m odeled the increased market correlation of cat-bonds with the general market. I found that when compared to a baseline period, the period from 2005 to 2009 showed significant increases in market co rrelation, particularly in 2008. I argue that 112 SCOR reopens market for catastrophe bonds, Market Wire. 113 ART Deal Directory, 114 Evans, 1 and 2. 95

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the Lehm an Brothers bankruptcy was partia lly responsible for this increased comovement and adapt the model to quantify this contributi on. Follow-up analysis reveals that Lehman Brothers indeed had a signi ficant negative shock on the cat-bond market. In spite of this concern, the cat-bond market remained remarkably resilient through the 2008 market turbulence, returning 2 percent on the year. Its long term returns were around 10 percent and its 5 year coeffici ents with the market confirmed the claims of zero-correlation proponents. Moreover, I do not view the market co-movement of 2008 as indicative of a new trend. Instead I would characterize 2008 as real-world experiment from which the cat-market will r ecover and adapt to maintain its distinctive traits. The cat-markets entanglement in Lehmans downfall stem med from a market convention rooted not in greed, but in risk-aversion. The system of total-return-swaps and trust funds is designed to protect capital, not grow it. Market innovations even in the firs t few months of 2009 are hopeful and bode well for coming cat-bond issues. Improveme nts are possible in transparency and counterparty swap accountability. Specifically, Blue Fin 2s partnership with a bank associated with the German federal governme nt is a good example of the possibilities in increasing protection through public/private partnerships. As bond sponsors pursue this core value of protection the market will emer ge stronger and wiser than before Lehmans collapse. 96

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Conclusion: 2009 and Beyond When sorrows come they come not single spies, but in battalions. -Hamlet, IV.v.78-79 The insurance crisis in Florida mo tivated this discussion of cat-bonds. Unfortunately, the first quarter of 2009 ha s not brought positive news for Florida, particularly in State Farms intent to leav e the state. State Farm is by far the largest private insurer in the Florida market w ith over a million homeowner policies and 14 percent of Floridas premiums.115 This is three times the volume held by any other private company. Its only peer is Citizens its elf, which remains the largest residential insurer, with 22 percent of the markets premiums and 1.04 million policies.116 State Farm president, Jim Thompson, repor ted that even without major storms hitting Florida in the last three years th e firm was hemorrhaging cash at $20 million a month. This current trajectory would cause the Florida branch s insolvency by 2011.117 State Farm, in response, app lied to raise its rates by 47 percent in July of 2008. The Office of Insurance Regulation denied this application on January 12, 2009 and State Farm announced its plans to leave the state soon thereafter State Farm would phase out all million residential policies in Florida over three years. It would, however, maintain its lucrative auto, health and lif e insurance books in Florida.118 The Florida Legislature thus finds itself again weighing the necessity of keeping private insurers in operation and the ramifica tions of exorbitant policy rates. While the 115 Status of the Florida Hurricane Catastrophe Fund, The Florida Senate. 116 Presentation to House Insurance, Business & Financial Affairs Policy Committee Feb 3, 2009, Citizens. And Citizens Corporate Financials, Citizens. 117 Harrington and Liberto, 1. 118 Barr, 1. 97

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FHCF esti mated it had $5 billion more post-storm bonding capacity than in 2008, this still left a $13 billion potential shortfall.119 To make matters worse, The U.S. treas ury notified the legi slature during the 2009 legislative session that they did not have the authority to exte nd a line of credit to Florida for financing hurricane risk.120 In 2007 Florida congressm an Ron Klein drafted legislation that would have created an inst itution that would have such authority. As envisioned by Klein, this N ational Risk Consortium woul d have standardized the catmarket and offered additional coverage. Unfo rtunately for Florida, the bill (H.R.3355) has been tabled for two years. Future resear ch could well examine the benefits and costs to the federal government of forming such an institution. Nevertheless Florida policymakers mu st not only decide how to manage Hurricane risk in 2009 but also in the years to come. In this thesis I demonstrate that catbonds provide clear savings over a Buffett-style deal if a triggering storm occurs and only minor additional costs if does not. From an investors standpoint I demonstrate catbonds advantages not only in their sustained 10 percent returns, but also due to their low correlation with other assetclasses over the long-term. These advantages aside, a growing edge for the cat-market remains finding reliable methods of insuring its collateral. To illustrate this necessity I model the persistent effect of the Lehman Brothers collapse on the hurricane cat-bond market. Over all, the cat-market sustained hurricaneforce winds both in the Gulf of Mexico a nd on Wall Street. It emerged in 2009 shaken, but not beaten, and remains an attractive op tion for insurers and investors alike. 119 Dunkelberger, Cat Fund may see glimmer of relief, 6B. 120 March, Treasury Wont Aid Cat Fund, 1B. 98

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Appendix 1: Analysis I Tables Table A.1.1 "Baseline 1" Period (1): 1/14/2005-5/30/2008 Included observations: 177 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Coefficient S.E t-Statistic Prob. R2 0.017275 Intercept -0.00578 0.007532 -0.767332 0.4439 Adj R2 0.000233 Dow Corp. Bond 0.020878 0.0338190.617364 0.5378 S&P 500 0.01431 0.0093 261.534471 0.1267 F-stat 1.013692 Moody's Baa Yield 0.004269 0.0040 481.054563 0.2931 Pr(F) 0.388041 Table A.1.2 "Experimental" Period (2): 10/07/2005 2/20/2009 Included observations: 177 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Coefficient S.E. t-Statistic Prob. R2 0.272932 Intercept 0.021165 0.005617 3.768002 0.0002 Adj R2 0.260324 Dow Corp. Bond 0.140467 0.0526872.666063 0.0084 S&P 500 0.026993 0.013117 2.057838 0.0411 F-stat 21.64731 Moody's Baa Yield -0.01007 0.0029 8 -3.379278 0.0009 Pr(F) 0.000000 Table A.1.3 Period (2.a): 10/07/2005 12/28/2007 Included observations: 117 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Coefficient S.E. t-Statistic Prob. R2 0.034239 Intercept 0.005106 0.0122 0.418502 0.6764 Adj R2 0.008599 Dow Corp. Bond 0.037601 0.0427730.879084 0.3812 S&P 500 0.028965 0.014607 1.982983 0.0498 F-stati 1.335393 Moody's Baa Yield -0.001331 0.006554 -0.203128 0.8394 Prob(F) 0.266463 99

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Table A.1.4 Period (2.b): 1/11/2008 2/20/2009 Includ ed observations: 59 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Coefficient S.E. t-Statistic Prob. Intercept 0.017674 0.009315 1.897287 0.063 R2 0.371709 Dow Corp. Bond 0.176278 0.065998 2.670961 0.0099 Adj R2 0.337439 S&P 500 0.021795 0.014773 1.475377 0.1458 F-stat 10.84636 Moody's Baa Yield -0.008517 0.004719 -1.804775 0.0766 Prob(F) 0.000011 Tabl e A.1.5 Long-Term Period(3): 4/09/2004 2/20/2009 Includ ed observations: 255 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Coefficient S.E t-Statistic Prob. Intercept 0.013091 0.008241 1.588503 0.1134 R2 0.015093 Dow Corp. Bond 0.109171 0.079674 1.370217 0.1718 Adj R2 0.003321 S&P 500 0.022713 0.0151 24 1.501788 0.1344 F-stat 1.282149 Moody's Baa Yield -0.006096 0.004133 -1.474817 0.1415 Prob(F) 0.281009 Appendix 2: Analysis II Tables Table A.2.1 Baseline 2 Period (2): 10/07/2005 2/20/2009 Included observations: 177 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Coefficient S.E. t-Statistic Prob. R2 0.272932 Intercept 0.021165 0.005617 3.768002 0.0002 Adj R2 0.260324 Dow Corp. Bond 0.140467 0.0526872.666063 0.0084 S&P 500 0.026993 0.013117 2.057838 0.0411 F-stat 21.64731 Moody's Baa Yield -0.01007 0.0029 8 -3.379278 0.0009 Pr(F) 0.000000 100

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Table A.2.2 Eq.(3.3) Period (2): 10/14/2005 2/20/2009 Includ ed observations: 176 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Coefficient S.E. t-Statistic Prob. R2 0.323147 Intercept 0.002332 0.000217 10.75084 0 Adj R2 0.290723 Dow Corp. Bond 0.010333 0.042124 0.2453 0.8065 S&P 500 0.027871 0.0102 75 2.712575 0.0074 F-stat 9.96627 Moody's Baa Yield -0.037113 0.020801 -1.784173 0.0762 Prob(F)0 Dow Lehman 0.175233 0.086166 2.033672 0.0436 S&P 500Lehman -0.017091 0.0199 45 -0.856929 0.3927 Moody's Lehman 0.106962 0.062369 1.71499 0.0882 Lehman Intercept -0.001805 0.000957 -1.886482 0.061 Ike Intercept -0.006112 0.004367 -1.399506 0.1635 Tabl e A.2.3 Eq. (3.4) Period 2: 10/14/2005 2/20/2009 Includ ed observations: 176 after adjustments White Heteroskedasticity-Consistent Standard Errors & Covariance Coefficient S.E t-Statistic Prob. R2 0.319231 Intercept 0.002328 0.000218 10.67183 0 Adj R2 0.290866 Dow Corp. Bond 0.011911 0.042953 0.277298 0.7819 S&P 500 0.017352 0.011206 1.548408 0.1234 Prob(F) 11.25425 Moody's Baa Yield -0.032538 0.021923 -1.484194 0.1396 Prob(F) 0 Dow Lehman 0.16671 0.087522 1.904781 0.0585 Moody's Lehman 0.096199 0.063678 1.510705 0.1327 Lehman Intercept -0.001731 0.000976 -1.773509 0.078 Ike Intercept -0.005686 0.004379 -1.298396 0.1959 101

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