A new index has been developed which allows derivatives trading based on Lloyd's global results, and thus a hedge or speculation on international underwriting results. Michael Wynne-Jones explains.

The index is intended for use as a hedging mechanism for insurance entities with global exposure, inside or outside Lloyd's, who wish to protect or modify their underwriting portfolio by buying or selling reinsurance, and to provide professional institutional investors with an opportunity to invest in the global insurance market.

The index value is calculated by INSTRAT, a part of Marsh & McLennan Securities Corporation, from information published by Lloyd's. It is intended that the contracts on the index should be traded either as put and call options (derivatives), or as reinsurance contracts using the value of the index as a trigger. INSTRAT and its sister companies have established the infrastructure required for both routes.

In its early days, the index will be produced for the whole market result only. As reporting of individual risk classes becomes more transparent, different indices for different classes of risk would allow portfolio holders to adjust their portfolios dynamically over time.

Structure of the index
The Global Underwriting Index is calculated using information from Lloyd's global results, which are published annually. It is based directly on the underwriting loss ratio, with one index point equal to 1% loss ratio. Thus a break-even result for Lloyd's is indicated by a loss ratio of 100%, and an index value of 100.00.The smallest change in loss ratio that is recognised by the index is 0.01%, or one basis point. Thus the index value is rounded to the nearest 0.01.Therefore, the holder of a position that yields money for higher settlement values of the index will make money from that position in a year of high claims. On this basis, derivatives based on the index can be used as a proxy for reinsurance.

Motivation for an index of Lloyd's results
For cedants, the following might be reasons for protecting their risk using the index:
• To hedge existing exposure to underwriting risk, (provided analysis shows that the existing portfolio is correlated with the Lloyd's global result).
• Since the risk being transferred is embodied in the index, not in the cedant's underwriting, there is no need to disclose the details of its own portfolio when buying the hedge.
• As the market in derivatives on the index becomes more active, increasing numbers of participants will be trading exposures to the index. Since the underlying exposure being traded is the same for all of them, transactions will be completed more quickly and efficiently than can be achieved with individually tailored contracts.

For investors wishing to earn premium by underwriting risk, the following might be reasons for selling reinsurance using the index:
• To undertake a broad spread of insurance risk, without needing to assemble a balanced portfolio of individually underwritten risks.
• The assumption of catastrophe insurance risk is likely to be uncorrelated with an existing portfolio of financial and capital market investments. This is likely to be beneficial to portfolio variance. However . . .
• It has been argued that insurance premium rates are high at times when capital is in short supply, and hence price/earnings ratios are low in stock markets and investment yields are low in both stock and bond markets. At such times, the return on capital in excess of the expected value of losses may be relatively attractive, in addition to the benefits of non-correlation.

Turning index points into cash
In the context of the index, the purchase of a call option is equivalent to buying unlimited liability reinsurance, and the purchase of a call spread is equivalent to buying limited liability reinsurance.

A further definition is required to determine the number of put and call options needed to hedge an exposure or create an investment of a certain size. The cash value of one index point is defined to be £1,000, which is multiplied by the number of index points by which an option is in the money.

In order to work efficiently, a market in traded options requires liquidity, which ensures that a participant wishing to make a trade is likely to be able to find a counterparty interested in participating in the opposite half of the trade. To help maintain liquidity, it is suggested that contracts should initially be bid and offered with strike prices in multiples of five index points, corresponding to 5% loss ratio.

Analysis of historical data will have some bearing on the price at which a buyer or seller might wish to enter a transaction. It is, however, much more likely to be a more subjective expectation of the year's underwriting result that determines the price of a transaction.

The best year on record for settlement values is 1994, with a hard market and low claims, resulting in a loss ratio of 70.28%, or 70.28 on the index. The worst year on record was 1989, with 147.97% (147.97 on the index).

Sources of non-underwriting risk
The credit risk of the counterparty with whom a transaction is carried out is the major source of non-underwriting risk for transactions based on the index. This is an important issue, since there is at present no clearing house to stand between the counterparties in a transaction. For this reason it is important that all participants in transactions must ensure that due diligence and credit-worthiness procedures are rigorously followed in respect of a proposed counterparty.
• Owing to the risks of trading with non-guaranteed counterparties, it is likely, in many cases, that a transaction will be required to be collateralised on either side with the maximum amount of money that could be payable by each counterparty.

Mechanics of put and call options
The value of an option, with a certain strike price, depends on the value at which the underlying index settles. The relationship between index value and option value is usually called the payout pattern. An option is in-the-money if it has a value at the settlement date, and is out-of-the-money if it has no value at the settlement date.

A call option has value if the index settles above the strike price, and is worth nothing if the index settles below the strike price. If the index settles above the strike price, the value of the call option is equal to the amount by which the index value exceeds the strike price.

A put option has value if the index settles below the strike price, and is worth nothing if the index settles above the strike price. If the index settles below the strike price, the value of the call option is equal to the amount by which the strike price exceeds the index value.

Since the writer of an option has a potentially unlimited liability, it is common practise to cover a position by buying an option that is further from the money than the option written. Thus a call option can be covered by buying an option with a higher strike price, and a put option can be covered by buying a put option with a lower strike price. Covered calls and covered puts are often written in a single transaction, and are referred to as call spreads and put spreads. The liability of the writer of a call spread or a put spread is limited to the difference between the strike prices of the two options comprising the spread.

For a cedant, the purchase of a call option on the index is equivalent to buying an unlimited aggregate excess-of-loss cover, attaching at the option's strike price. The purchase of a call spread is equivalent to buying a limited aggregate excess-of-loss cover. The spread is achieved by buying a call option at one strike price (the attachment point of the aggregate excess-of-loss layer), and selling a call option at a higher strike price (the exhaustion point of the aggregate excess-or-loss layer).

Disclaimer
This article is not an offer to sell, nor is it a solicitation of any kind. It is a technical report describing research that has been carried out by INSTRAT, with the aim of offering services to clients. It is provided for information purposes only. The information contained in this document is based on sources that are believed to be reliable at the time of issue, but its content is subject to change without notice. No responsibility can be taken by INSTRAT for the accuracy of the information contained in this document. Investment decisions may not be based on the analysis presented in this document.

The Lloyd's global result is determined using the calculations outlined in this document, from statistics published by Lloyd's. INSTRAT gives no guarantee that these statistics will continue to be published in the future. In the event that the format or content of the publications of Lloyd's should change, an independent actuarial authority will be engaged by INSTRAT to determine the index value.

Dr Michael Wynne-Jones is an engineer and former hedge fund analysts who joined INSTRAT in 1996 to specialise in insurance securitisation and alternative risk transfer structures.