Hedging Catastrophe Risk Using Industry Loss

AUGUST 2012

AIRCURRENTS: HEDGING CATASTROPHE

RISK USING INDUSTRY LOSS WARRANTIES BY MICHAEL WEDEL, ASA EDITED BY MEAGAN PHELAN, CCM

EDITOR’S NOTE: In this article, Michael Wedel, Manager in AIR’s Consulting and Client Services Group, discusses how industry loss warranties are used to hedge catastrophe risk—as well as how AIR’s CATRADER® software can be used to evaluate hedge effectiveness.

INTRODUCTION Reinsurers, hedge funds, and insurance-linked securities (ILS) THE ARTICLE: Discusses how industry loss investors (collectively “funds,” and separately, “the fund”) look for warranties are used to hedge catastrophe risk and ways to construct a diversified portfolio of risk that provides strong how AIR’s CATRADER software evaluates a hedged portfolio. and consistent profits. Funds achieve this goal by ceding the risk

they do not want to cover while keeping or adding new risk they HIGHLIGHTS: AIR’s CATRADER software helps identify do want to cover. effective hedges, including those that can result in arbitrage opportunities—the ability to take advantage of price Occasionally, during construction of a strong and diversified discrepancies between reinsurance contracts with similar risk portfolio, a fund may uncover financial instruments (including profiles. industry loss warranties, or ILWs) that have similar risk attributes but substantially different pricing. Such mismatch results in an arbitrage opportunity, whereby a fund can take advantage of price discrepancies between two contracts that cover a similar risk profile. In this example, the fund determines that the annual probability that losses in excess of the indemnity contract’s retention will occur This article provides an illustrative example. is 2.75%.

PORTFOLIO CONSTRUCTION The settlement timeline of indemnity losses is time-consuming Assume a fund writes a USD 5 million excess of loss (“XOL”) and relatively nontransparent—time consuming because it may reinsurance contract based on indemnity losses to a primary take years for claims to be reported and nontransparent because insurance company (or “cedant”) writing residential exposure in losses are reported by the cedant. Therefore, the fund may look for Florida. This indemnity contract could have been purchased through opportunities to hedge their catastrophic risk exposure. One such the traditional reinsurance market or through an alternative risk method to hedge is through purchase of an industry loss warranty transfer vehicle, such as a catastrophe bond. In this example, the (see sidebar, Industry Loss Warranties). price to the cedant, or rate on line, associated with the contract is 18.00%. In other words, the fund receives an 18.00% premium on INDUSTRY LOSS WARRANTIES the USD 5 million of coverage they provide. Industry loss warranties (“ILWs”) are a type of reinsurance contract in which one party purchases financial protection from another in If, due to a hurricane, losses to the cedant are in excess of the the event that insured industry losses from a catastrophic event are indemnity contract’s retention, the fund will be responsible for greater than a predefined trigger amount. For example, one party paying the cedant USD 5 million. The fund is able to assess the may purchase a Florida hurricane ILW that pays out USD 5 million if likelihood that this will happen by performing a detailed modeling insured industry losses arising from a single Florida hurricane exceed of the cedant’s portfolio against 10,000 years of simulated USD 50 billion. Industry loss determination is fast and reasonably hurricane activity within AIR’s CLASIC/2™ software. The fund can transparent, and thus easy to understand and trade. A variety then apply reinsurance contract terms in CATRADER®. AUGUST 2012 | HEDGING CATASTROPHE RISK USING INDUSTRY LOSS WARRANTIES BY MICHAEL WEDEL, ASA EDITED BY MEAGAN PHELAN, CCM of ILWs exist; some are based on all perils occurring in the U.S., An additional analysis is required to determine whether the same others are based specifically on California earthquakes or Florida simulated events impacting the indemnity contract are impacting hurricanes, and others, on non-U.S. perils, including European this ILW, but before evaluating results from that analysis, consider windstorms. the following terms that define the basis risk scenarios that could result given participation in an indemnity contract and purchase of For the purposes of this example, assume the fund has two ILW an ILW. contracts available to it: a USD 30 billion Florida hurricane ILW and a USD 50 billion Florida hurricane ILW. The USD 30 billion • Negative Basis Risk2: In this scenario, the fund has to ILW has a rate on line of 17.50% (as of May 2012)1 and the USD compensate the cedant and does not receive the ILW payout. 50 billion ILW has a rate on line of only 11.00% (as of May 2012), • No Basis Risk: A scenario that causes a payment under both the commensurate with its lower risk profile. If a fund purchases USD indemnity contract and the ILW. 5 million of coverage based on the USD 30 billion ILW, the cost • Positive Basis Risk: In this scenario, the fund does not have to of the hedge is USD 875,000 (or 17.50% of USD 5 million). By compensate the cedant and does receive the ILW payout. contrast, if a fund purchases 5 million of coverage based on the 50 billion Florida hurricane ILW, the cost of the hedge is USD 550,000 Figure 1 illustrates these basis risk scenarios for the fund in our (11.00% of USD 5 million). example, and in consideration of both the purchase of the USD 50 billion ILW, which—as previously discussed—is triggered with an Similar to the detailed modeling of the cedant’s portfolio, using the annual probability similar to that of the indemnity contract, and of same 10,000 years of simulated hurricane activity, the fund can the USD 30 billion ILW. assess the likelihood that losses from hurricane activity would be in excess of either ILW’s trigger amount; this time by analyzing losses Hedging with a USD 50 Billion ILW Hedging with a USD 30 Billion ILW (Rate on line = 11%) Rate on line = 17.50% 3.00% 0.03 to total industry exposure in Florida. 2.65%

2.50% 0.025 2.21% y y i l t i l t 1.91% b 2.00% b 0.02 a a b b o o r 1.50% r 0.015 P P l l a a u 1.00% u 0.01 n n n 0.54% n A 0.50% 0.33% A 0.005 0.10% 0.00% 0 Negative Basis Risk No Basis Risk Positive Basis Risk Negative Basis Risk No Basis Risk Positive Basis Risk Figure 1. Basis risk quantification helps to make a more informed decision (Source: AIR).

Focusing first on the figure’s left hand panel, which is specific to the USD 50 billion ILW, we see, from left to right:

• There is an annual probability of 0.54% that indemnity losses occur Table 1 compares the likelihood that losses in excess of each of the in excess of the indemnity contract’s retention but insured industry three contracts’ trigger amounts, respectively, occur. The 2.75% losses are below the ILW’s trigger, USD 50 billion. figure in row one means that hurricane losses in excess of the • There is an annual probability of 2.21% that indemnity losses occur indemnity contract’s trigger amount occur to the cedant’s portfolio in excess of the indemnity contract’s retention and insured industry 275 times out of the 10,000 simulated years. Insured industry losses losses are in excess of the ILW’s trigger, USD 50 billion. in Florida in excess of USD 50 billion occur with a similar probability, • There is an annual probability of 0.33% that insured industry losses 2.54%, suggesting this ILW might have a similar risk profile to the occur in excess of the ILW’s trigger, USD 50 billion, but indemnity original indemnity contract. losses are below the indemnity contract’s retention.

Table 1. Contract Detail and Probability of Losses in Excess of Trigger Level

Contract Applies to Area Trigger-type Premium Probability of Losses in (binary) Excess of Trigger Level Indemnity XOL Florida Indemnity 18.00% 2.75% contract USD 30 billion Florida Florida Industry Loss 17.50% 4.56% Hurricane ILW

USD 50 billion Florida Florida Industry Loss 11.00% 2.54% Hurricane ILW

2 AUGUST 2012 | HEDGING CATASTROPHE RISK USING INDUSTRY LOSS WARRANTIES BY MICHAEL WEDEL, ASA EDITED BY MEAGAN PHELAN, CCM

If, by comparison, the fund buys the USD 30 billion ILW (instead PORTFOLIO MANAGEMENT IN CATRADER of the USD 50 billion ILW), there is a lower annual probability of To fully benefit from industry loss warranties, potential buyers need negative basis risk (0.10% as opposed to 0.54%) and a higher credible ways to quantify and manage basis risk. AIR’s CATRADER annual probability of positive basis risk (1.91% versus 0.33%). software, which helps users differentiate between risks that exist when considering two different financial instruments, is well suited By participating in the indemnity contract, the fund receives a to perform the analysis of the hedge outlined above. In order to premium: 18.00% on the USD 5 million of coverage it provides. model the hedged portfolio, a user sets up two programs—the If the fund buys the USD 30 billion hedge, it will almost entirely first for the indemnity contract and the second based on industry eliminate the risk of loss to its portfolio (0.10% annual probability hurricane losses in Florida. Under the ‘Options’ tab, within the of a USD 5 million loss), obtain a USD 5 million payout from the Florida ILW program, the user must select “Contract Gain,” ILW with an annual probability of 1.91%, and receive USD 25,000 which causes losses under the contract to be portrayed as gains. (the difference between the rate it is receiving for the indemnity For example, if a USD 30 billion event occurs, triggering the ILW, contract, 18% of USD 5 million, and the rate it is paying for CATRADER will show this as a negative USD 5 billion payout. The the USD 30 billion ILW, 17.50% of USD 5 million). Alternatively, ILW payout is combined with positive losses from the indemnity the fund could buy a USD 50 billion hedge for the given price contract to determine the net payout from the event for the (11.00%). In this case, as the modeled loss results in Figure 1 hedged portfolio. Positive net payouts are losses to the hedged revealed, the fund has a higher negative basis risk, a lower positive portfolio (negative basis risk) and negative net payouts are gains basis risk, and receives USD 350,000 (the difference between the (years of positive basis risk). rate it is receiving for the indemnity contract, 18% of USD 5 million, and the rate it is paying for the ILW, 11.00% of USD 5 million). CONCLUSION The increased popularity of alternative risk transfer vehicles provides Even upon quantifying the risk associated with two different catastrophe risk managers with more tools to manage risk well. financial instruments, selecting which instrument to purchase is Using CATRADER, risk managers can identify effective hedges no trivial task. In this example, the USD 50 billion ILW, while less and quantify the risk associated with their portfolio. Through this expensive, is associated with a higher negative basis risk—although, process, they may even uncover arbitrage opportunities. notably, chances of negative and positive basis risk are quite similar, which may make this ILW appealing to some. The USD 30 billion ILW, meanwhile, though more expensive, hedges nearly all of the fund’s negative basis risk, a very attractive prospect to others.

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1PRICE GUIDANCE REFLECTS MARKET CONDITIONS AS OF MAY 2012. AS OF AUGUST 2012, PRICE GUIDANCE HAS DECREASED–15.00% FOR A USD 30 BILLION ILW AND 9.00% FOR A USD 50 BILLION ILW–RESULTING IN A MORE ATTRACTIVE HEDGING OPPORTUNITY. 2NOTE THAT THE DEFINITIONS OF BASIS RISK PROVIDED ABOVE ARE APPLICABLE TO THIS ANALYSIS AND MAY DIFFER IN OTHER SITUATIONS. FOR EXAMPLE, ‘NO BASIS RISK’ SOMETIMES INCLUDES ALL SIMULATED YEARS OF EQUAL PAYMENT—INCLUDING SIMULATED YEARS IN WHICH ZERO MODELED LOSS OCCURS.

ABOUT AIR WORLDWIDE AIR Worldwide (AIR) is the scientific leader and most respected provider of risk modeling software and consulting services. AIR founded the catastrophe modeling industry in 1987 and today models the risk from natural catastrophes and terrorism in more than 90 countries. More than 400 insurance, reinsurance, financial, corporate, and government clients rely on AIR software and services for catastrophe risk management, insurance-linked securities, detailed site-specific wind and seismic engineering analyses, agricultural risk management, and property replacement-cost valuation. AIR is a member of the Verisk Insurance Solutions group at Verisk Analytics (Nasdaq:VRSK) and is headquartered in Boston with additional offices in North America, Europe, and Asia. For more information, please visit www. air-worldwide.com.