total $50 million, the costs to the company would then beonly $15 million, Another more popular alternative, involving lower reinsurance premiums, is tobuy a series of reinsurance contracts covering what are known as excess cost layers. The first layermight provide indemnification for losses between $30 million and $40 million; the next layer mightcover losses between $40 million and $50 million; and so on. Each reinsurance contract is known asan excess-of-loss reinsurance contract. The reinsurer has written a bull spread on the total losses. Itis long a call option with a strike price equal to the lower end of the layer and short a call optionwith a strike price equal to the upper end of the layer.*
The principal providers of CAT reinsurance have traditionally been reinsurance companies andLloyds syndicates (which are unlimited liability syndicates of wealthy individuals). In recent yearsthe industry has come to the conclusion that its reinsurance needs have outstripped what can beprovided from these traditional sources. It has searched for new ways in which capital markets canprovide reinsurance. One of the events that caused the industry to rethink its practices was HurricaneAndrew in 1992, which caused about $15 billion of insurance costs in Florida. This exceeded thetotal of relevant insurance premiums received in Florida during the previous seven years. IfHurricane Andrew had hit Miami, it is estimated that insured losses would have exceeded $40 billion.Hurricane Andrew and other catastrophes have led to increases in insurance/reinsurance premiums.
Exchange-traded insurance futures contracts have been developed by the CBOT, but have notbeen highly successful. The over-the-counter market has come up with a number of products thatare alternatives to traditional reinsurance. The most popular is a CAT bond. This is a bond issuedby a subsidiary of an insurance company that pays a higher-than-normal interest rate. In exchangefor the extra interest, the holder of the bond agrees to provide an excess-of-cost reinsurancecontract. Depending on the terms of the CAT bond, the interest or principal (or both) can beused to meet claims. In the example considered above where an insurance company wantsprotection for California earthquake losses between $30 million and $40 million, the insurancecompany could issue CAT bonds with a total principal of $10 million. In the event that theinsurance company’s California earthquake losses exceeded $30 million, bondholders would losesome or ail of their principal. As an alternative, the insurance company could cover this excess cost
layer by making a much bigger bond issue where only the bondholders’ interest is at risk.
CAT bonds typically give a high probability of an above-normal rate of interest and a lowprobability of a high loss. Why would investors be interested in such instruments? The answer isthat there are no statistically significant correlations between CAT risks and market returns.° CATbonds are therefore an attractive addition to an investor’s portfolio. They have no systematic riskso that their total risk can be completely diversified away in a large portfolio. If a CAT bond’sexpected return is greater than the risk-free interest rate (and typically it is), it has the potential to
improve risk-return tradeoffs.
SUMMARY
 
 
 
This chapter has shown that when there are risks to be managed, derivative markets have been veryinnovative in developing products to meet the needs of market participants.
> Reinsurance is also sometimes offered in the form of a lump sum if a certain loss level is reached. The reinsurer isthen writing a cash-or-nothing binary call option on the losses.
® See R. H. Litzenberger, D. R. Beaglehole, and C. E. Reynolds, “Assessing Catastrophe Reinsurance-LinkedSecurities as a New Asset Class,” Journal of Portfolio Management, Winter 1996, 76-86.684 CHAPTER 29
 
The market for weather derivatives is relatively new, but is already attracting a lot of attention.
Two measures, HDD and CDD, have heen developed to describe the temperature durine a monthawo measures, Fifi and Ci, nave been Gey LO Geserioe tne temperature Guring a montn.
These are used to define the payoffs on both exchange- -traded and over-the-counter derivatives. Nodoubt, as the weather derivatives market develops, we will see contracts on rainfall, snow, andsimilar variables become more commonplace.
In energy markets, oil derivatives have been important for some time and play a key role inhelping oil producers and oil consumers manage their price risk. Natural gas and electricityderivatives are relatively new. They became important for risk management when these marketswere deregulated and state monopolies discontinued.
Insurance derivatives are now beginning to be an alternative traditional reinsurance as a way forinsurance companies to manage the risks of a catastrophic event such as a hurricane or anearthquake. No doubt we will see other sorts of insurance (e.g., life insurance and automobileinsurance) being securitized in a similar way as this market develops.
Weather, energy, and insurance derivatives have the property that percentage changes in theunderlying variables have negligible correlations with market returns. This means that we can usethe actuarial approach for valuation. The actuarial approach for valuing a derivative involves usinghistorical data to calculate the expected payoff and then discounting this expected payoff at therisk-free rate.
SUGGESTIONS FOR FURTHER READING
 
Arditti, F., L. Cai, and M. Cao, “Whether to Hedge,” RISK Supplement on Weather Risk, 1999, pp. 9-12.
Canter, M. S., J. B. Cole, and R. L. Sandor, “Insurance Derivatives: A New Asset Class for the CapitalMarkets and a New Hedging Tool for the Insurance Industry,” Journal of Applied Corporate Finance,Autumn 1997, 69-83.
Clewlow, L., and C. Strickland, Energy Derivatives: Pricing and Risk Management, Lacima Group, 2000.Eydeland, A., and H. Geman, “Pricing Power Derivatives,” RISK, October 1998, pp. 71-73.Geman, H., “CAT Calls,” RISK, September 1994, pp. 86-89.
Hanley, M., “A Catastrophe Too Far,” RISK Supplement on Insurance, July 1998.
Hunter, R., “Managing Mother Nature,” Derivatives Strategy, February 1999.
Toskow D “Clacteinitn Gpetars Transition The Py al 19 (1998) 95_59Joskow, DP. “Electricity Sectors in Transition,” The Liner Ey Journal, 19 (1998), 25-52.
Kendall, R., “Crude Oil: Price Shocking,” RISK Supplement on Commodity Risk, May 1999, p. 6.
Lilzenberger, R. H., D. R. Beaglehole, and C. E. Reynolds, “Assessing Catastrophe Reinsurance-linkedSecurities as a New Asset Class,” Journal of Portfolio Management, Winter 1996, 76-86.
QUESTIONS AND PROBLEMS(ANSWERS IN SOLUTIONS MANUAL)
 
29.1. Distinguish between the actuarial approach and the risk-neutral approach to valuing aderivative. Under what circumstance do they give the same answer?
29.2. Suppose that each day during July the minimum temperature is 68° Fahrenheit and the
maximum temperature is 82° Fahrenheit. What is the payoff from a call option on thecumulative CDD during July with a strike of 250 and a payment rate of $5,000 per degree day?Insurance, Weather, and Energy Derivatives 685
29,3.
29.4,
tSUn
29.7.29.8.
29.9.29.10.
tthe vo 3 thee ma. Would you cxpcct ine voratuity of tic tinrec-mon
“The CDD for a particular day is the payoff from a call option on the day’s averagetemperature.” Explain.
Suppose that you have 50 years of temperature data at your disposal. Explain carefully theanalyses you would you carry out to value a forward contract on the cumulative CDD for aparticular month.
Would vou expec Tatility of the
than the volatility of the spot price. Explain.
. What are the characteristics of an energy source where the price has a very high volatility and a
very high rate of mean reversion? Give an example of such an energy source.How can a gas producer use derivative markets to hedge risks?
Explain how a 5 x 8 option contract for May 2003 on electricity with daily exercise works.Explain how a 5 x 8 option contract for May 2003 on electricity with monthly exercise works.Which is worth more?
Explain how CAT bonds work.
Consider two bonds that have the same coupon, time to maturity, and price. One is a B-ratedcorporate bond. The other is a CAT bond. An analysis based on historical data shows that theexpected losses on the two bonds in each year of their life is the same. Which bond would youadvise a portfolio manager to buy and why?
ASSIGNMENT QUESTIONS
 
 
29.11.
An insurance company’s losses of a particular type are to a reasonable approximation normallydistributed with a mean of $150 million and a standard deviation of $50 million. (Assume nodifference between losses in a risk-neutral world and losses in the real world.) The one-year risk-free rate is 5%. Estimate the cost of the following:a. A contract that will pay in one year’s time 60% of the insurance company’s costs on 4pro rata basisb. A contract that pays $100 million in one year’s time if losses exceed $200 million.mney,CHAPTER 30 Hy
DERIVATIVES MISHAPS AND WHATWE CAN LEARN FROM THEM
Since the mid-1980s there have been some spectacular losses in derivatives markets, Tables 30.1and 30.2 provide a list of some of these losses. In Table 30.1 the losses were made by financialinstitutions; in Table 30.2 they were made by nonfinancial organizations. What is remarkableabout the list is the number of cases where huge losses arose from the activities of a singleemployee. In 1995, Nick Leeson’s trading brought a 200-year-old British bank, Barings, to itsknees; in 1994, Robert Citron’s trading led to Orange County, a municipality in California, losingabout $2 billion. Joseph Jett’s trading for Kidder Peabody lost $350 million. John Rusnak’s lossesof $700 million for Allied Irish Bank came to light in 2002. The huge losses at Daiwa, Shell, andSumitomo were also each the result of the activities of a single individual.
The josses should not be viewed as an indiciment of the whole derivatives industry. Thederivatives market is a vast mulltitrillion-dollar market that by most measures has been out-standingly successful and has served the needs of its users well. The events described in the tahlesrepresent a tiny proportion of the total trades (both in number and value). Nevertheless, it is worthconsidering carefully the lessons we can learn from them. This is what we will do in this finalchapter.
30.1 LESSONS FOR ALL USERS OF DERIVATIVES
 
First, we consider the lessons appropriate to all users of derivatives whether they are financial ornonfinancial companies.
Define Risk Limits
It is essential that all companies define in a clear and unambiguous way limits to the financial risksthat can be taken. They should then set up procedures for ensuring that the limits are obeyed.Ideally, overall risk limits should be set at board level. These should then be converted to limitsapplicable to the individuals responsible for managing particular risks. Daily reports shouldindicate the gain or loss that will be experienced for particular movements in market variables.These should be checked against the actual losses that are experienced to ensure that the valuationprocedures underlying the reports are accurate.
It is particularly important that companies monitor risks carefully when derivatives are used.This is because, as we saw in Chapter 1, derivatives can be used for hedging, speculation, and
686Derivatives Mishaps and What We Can Learn from Them 687
 
Table 30.1 Big iosses by financial institutions
Allied Irish BankThis bank lost about $700 million from speculative activities of one of its foreign exchangetraders, John Rusnak, that lasted several years. Rusnak covered up his losses by creatingfictitious options trades.
BaringsThis 200-year-old British bank was wiped out in 1995 by the activities of one trader, NickLeeson, in Singapore. The trader’s mandate was to arbitrage between Nikkei 225 futures quotesin Singapore and Osaka. Instead he made big bets on the future direction of the Nikkei 225using futures and options. The total loss was close to $1 billion.
Chemical BankThis bank used an incorrect model to value interest rate caps in the late 1980s and as a result lost$33 million.
DaiwaA trader working in New York for this Japanese bank lost more than $1 billion in the 1990s.
Kidder PeabodyThe activities of a single trader, Joseph Jett, led to this New York investment dealer losing$350 million trading U.S. government securities and their strips. (Strips are created when each ofthe cash flows underlying a bond is sold as a separate security.) The loss arose because of amistake in the way the company’s computer system calculated profits.
Long-Term Capital ManagementThis hedge fund lost about $4 billion in 1998. The strategy followed by the fund wasconvergence arbitrage. This invoived attempting to identify two nearly identical securities whoseprices were temporarily out of line with each other. The company would buy the less-expensivesecurity and short the more-expensive one, hedging any residual risks. In mid-1998 the companywas badly hurt by widening credit spreads resulting from defaults on Russian bonds. The hedgefund was considered too large to fail. The New York Federal Reserve organized a $3.5 billionbailout by encouraging 14 banks to invest in the fund.
Midland BankThis British bank lost $500 million in the early 1990s largely because of a wrong bet on thedirection of interest rates. It was later taken over by the Hong Kong and Shanghai Bank.
National Westminster BankThis British bank lost about $130 million from using an inappropriate model to value swapoptions in 1997.
Sumitomo
A single trader working for this Japanese bank lost about $2 billion in the copper spot, futures,
and options market in the 1990s. .
                  
arbitrage. Without close monitoring it is impossible to know whether a derivatives trader hasswitched from being a hedger of the company’s risks to a speculator or switched from being anarbitrageur to being a speculator. Barings is a classic example of what can go wrong. NickLeeson’s mandate was to carry out low-risk arbitrage between the Singapore and Osaka marketson Nikkei 225 futures. Unknown to his superiors in London, Leeson switched from being anarbitrageur to taking huge bets on the future direction of the Nikkei 225. Systems within Baringswere so inadequate that nobody knew what he was doing.
The argument here is not that no risks should be taken. A treasurer working for a corporation ora trader in a financial institution or a fund manager should be allowed to take positions on the688 CHAPTER 30
 
Table 30.2 Big Losses by Nonfinancial Organizations
Allied LyonsThe treasury department of this drinks and food company lost $150 million in 1991 scliing calioptions on the U.S. dollar-sterling exchange rate.
Gibson GreetingsThe treasury department of this greeting card manufacturer in Cincinnati lost about $20 millionin 1994 trading highly exotic interest rate derivatives contracts with Bankers Trust. They latersued Bankers Trust and settled out of court.
Hammersmith and FulhamThis British Local Authority lost about $600 million on sterling interest rate swaps and optionsin 1988. All its contracts were later declared null and void by the British courts much to theannoyance of the banks on the other side of the transactions.
MetallgesellschaftThis German company entered into long-term contracts to supply oil and gasoline and hedgedthem by rolling over short-term futures contracts (see Section 4.6). It lost $1.8 million when itwas forced to discontinue this activity.
Orange CountyThe activities of the treasurer, Robert Citron, led to this California municipality losing about $2billion in 1994. The treasurer was using derivatives to speculate that interest rates would not rise.
Procter and GambleThe treasury department of this large U.S. company lost about $90 million in 1994 tradinghighly exotic interest rate derivatives contracts with Bankers Trust. (One of the contracts isdescribed in Section 25.8.) They later sued Bankers Trust and settled out of court.
ShellA single employee working in the Japanese subsidiary of this company lost $1 billion dollars in
| unauthorized trading of currency futures. |
future direction of relevant market variables. What we are arguing is that the sizes of the positionsthat can be taken should be limited and the systems in place should accurately report the risksbeing taken,
Take the Risk Limits Seriously
What happens if an individual exceeds risk limits and makes a profit? This is a tricky issue forsenior management. It is tempting to turn a blind eye to violations of risk limits when profitsresult. However, this is shortsighted. It leads to a culture where risk limits are not taken seriously,and it paves the way for a disaster. In many of the situations listed in Tables 30.1 and 30.2, thecompanies had become complacent about the risks they were taking because they had taken similarrisks in previous years and made profits.
The classic example here is Orange County. Robert Citron’s activities in 1991-93 had been veryprofitable for Orange County, and the municipality had come to rely on his trading for additionalfunding. People chose to ignore the risks he wag taking because he had produced profits.Unfortunately, the losses made in 1994 far exceeded the profits from previous years.
The penalties for exceeding risk limits should be just as great when profits result as when lossesresult. Otherwise, traders that make losses are liable to keep increasing their bets in the hope thateventually a profit will result and all will be forgiven.Derivatives Mishaps and What We Can Learn from Them 689
Do Not Assume You Can Outguess the Market
Some traders are quite possibly better than, others. But no trader gets it right all the time. A traderwho correctly predicts the direction in which market variables will move 60% of the time is doingwell. If a trader has an outstanding track record (as Robert Citron did in the early 1990s), it islikely to be a result of luck rather than superior trading skill.
Suppose that a financial institution employs 16 traders and one of those traders makes profits inevery quarter of a year. Should the trader receive a good bonus? Should the trader’s risk limits beincreased? The answer to the first question is that inevitably the trader will receive a good bonus.The answer the second question should be no. The chance of making a profit in four consecutivequarters from random trading is 0.54 or 1 in 16. This means that just by chance one of the16 traders will “get it right” every single quarter of the year. We should not assume that thetrader’s luck will continue and we should not increase the trader’s risk limits,
Do Not Underestimate the Benefits of Diversification
When a trader appears good at predicting a particular market variable, there is a tendency toincrease the trader’s limits. We have just argued that this is a bad idea because it is quite likely thatthe trader has been lucky rather than clever. However, let us suppose that we are really convincedthat the trader has special talents. How undiversified should we allow ourselves to become in orderto take advantage of the trader’s special skills? The answer is that the benefits from diversificationare huge, and it is unlikely that any trader is so good that it is worth foregoing these benefits tospeculate heavily on just one market variable.
An example will illustrate the point here. Suppose that there are 10 stocks, each of which has anexpected return of 10% per annum and a standard deviation of returns of 30%. The correlationbetween the returns from any two of the stocks is 0.2. By dividing an investment equally among the10 stocks, an investor has an expected return of 10% per annum and standard deviation of returnsof 14.7%. Diversification enables the investor to reduce risks by over half. Another way ofexpressing this is that diversification enables an investor to double the expected return per unitof risk taken. The investor would have to be extremely good at stock picking to achieve the sameresult by investing in just one stock.
Carry out Scenario Analyses and Stress Tests
The calculation of risk measures such as VaR should always be accompanied by scenario analysesand stress testing to obtain an understanding of what can go wrong. These techniques werementioned in Chapter 16. They are very important. Human beings have an unfortunate tendencyto anchor on one or two scenarios when evaluating decisions. In 1993 and 1994, for example,Procter and Gamble and Gibson Greetings were so convinced that interest rates would remain lowthat they ignored the possibility of a 100-basis-point increase in their decision making.
It is important to be creative in the way scenarios are generated, One approach is to look at 10 or20 years of data and choose the most extreme events as scenarios. Sometimes there is a shortage ofdata on a key variable. It is then sensible to choose a similar variable for which much more data isavailable and use historical daily percentage changes in that variable as a proxy for possible dailypercentage changes in the key variable. For example, if there is little data on the prices of bondsissued by a particular country, we can look at historical data on prices of bonds issued by othersimilar countries to develop possible scenarios.690 CHAPTER 30
30.2. LESSONS FOR FINANCIAL INSTITUTIONS
 
 
We now move on to consider lessons that are primarily relevant to financial institutions.
Monitor Traders Carefully
In trading rooms there is a tendency to regard high-performing traders as “‘untouchable” and notto subject their activities to the same scrutiny as other traders. Apparently Joseph Jett, KidderPeabody’s star trader of Treasury instruments, was often “too busy” to answer questions anddiscuss his positions with the company’s risk managers.
It is important that all traders—particularly those making high profits—be fully accountable. Itis important for the financial institution to know whether the high profits are being made by takingunreasonably high risks. It is also important to check that the financial institution’s computersystems and pricing models are correct and are not being manipulated in some way.
Separate the Front, Middle, and Back Office
The front office in a financial institution consists of the traders who are executing trades, takingpositions, etc. The middle office consists of risk managers who are monitoring the risks beingtaken. The back office is where the record keeping and accounting takes place. Some of the worstderivatives disasters have occurred because these functions were not kept separate. Nick Leesoncontrolled both the front and back office in Singapore and was, as a result, able to conceal thedisastrous nature of his trades from his superiors in London for some time. Although full detailsare not available, it appears that a lack of separation of the front and back office was at leastpartially responsible for the huge losses experienced by Sumitomo bank in copper trading.
Do Not Blindly Trust Models
Some of the large losses in Table 30.1 arose because of the models and computer systems beingused. Perhaps the most famous systems problem was the one experienced by Kidder Peabody.Joseph Jelt would buy some strips (i.e., zero-coupon bonds) and then do a forward trade to sellthem in the future. The strips pay no interest and so, as explained in Chapter 3, the forward priceis higher than the spot price. Kidder’s system reported the difference between the forward priceand the spot price as a profit at the time of the trade. Of course, the difference represented thecost of financing the strip. But, by rolling the forward contracts forward, Jett was able to preventthis financing cost from accruing to him. The result was that the system reported a profit of$100 million and Jett received a big bonus when in fact there was a loss in the region of$350 million.
Examples of incorrect models leading to losses are also provided by Chemical Bank andNational Westminster Bank. Chemical Bank had an incorrect model for valuing interest rate capsand National Westminster Bank had an incorrect model for valuing swap options.
If large profits are being made by following relatively simple trading strategies, there is a goodchance that the models underlying the calculation of the profits are wrong. Similarly, if a financialinstitution appears to be particularly competitive on its quotes for a particular type of deal, there isa good chance that it is using a different model from other market participants, and it shouldanalyze what is going on carefully. To the head of a trading room, getting too much business of acertain type can be just as worrisome as getting too little business of that type.Derivatives Mishaps and What We Can Learn from Them 691
Be Conservative in Recognizing Inception Profits
When a financial institution sells a highly exotic instrument to a nonfinancial corporation, thevaluation can be highly dependent on the underlying model. For example, instruments with long-dated embedded interest rate options can be highly dependent on the interest rate model used. Inthese circumstances, a phrase used to describe the daily marking to market of the deal is markingto model. This is because there are no market prices for similar deals that can be used as abenchmark.
Suppose that a financial institution manages to sell an instrument to a client for $10 millionmore than it is worth—or at least $10 million more than its model says it is worth. The$10 million is known as an inception profit. When should it be recognized? There appears tobe quite a variation in what different investment banks do. Some recognize the $10 millionimmediately, whereas others are much more conservative and recognize it slowly over the life ofthe deal.
Recognizing inception profits immediately is very dangerous. It encourages traders to useaggressive models, take their bonuses, and leave before the model and the value of the deal comeunder close scrutiny. It is much better to recognize inception profits slowly, so that traders have themotivation to investigate the impact of several different models and several different sets ofassumptions before committing themselves to a deal.
Do Not Sell Clients Inappropriate Products
It is tempting to sell corporate clients inappropriate products, particularly when they appear tohave an appetite for the underlying risks. But this is shortsighted. The most dramatic example ofthis is the activities of Bankers Trust (BT) in the period leading up to the spring of 1994. Many ofBT’s clients were persuaded to buy high-risk and totally inappropriate products. A typical product(e.g., the 5/30 swap discussed in Section 25.8) would give the client a good chance of saving a fewbasis poinis on its borrowings aud a small chance of costing a large amount of money. Theproducts worked well for BT’s clients in 1992 and 1993, but blew up in 1994 when interest ratesrose sharply. The bad publicity that followed hurt BT greatly. The years it had spent building uptrust among corporate clients and developing an enviable reputation for innovation in derivativeswere largely lost as a result of the activities of a few overly aggressive salesmen. BT was forced topay large amounts of money to its clients to settle lawsuits out of court. It was taken over byDeutsche Bank in 1999.
Do Not Ignore Liquidity Risk
Financial engineers usually base the pricing of exotic instruments and instruments that traderelatively infrequently on the prices of actively traded instruments. For example:
1. A financial engineer often calculates a zero curve from actively traded government bonds(known as on-the-run bonds) and uses it to price bonds that trade less frequently (off-the-runbonds).
2. A financial engineer often implies the volatility of an asset from actively traded options anduses it to price less-actively traded options.
3. A financial engineer often implies the parameters of the process for interest rates from
actively traded interest rate caps and swap options and uses it to price products that arehighly structured.692 CHAPTER 30
This practice is not unreasonable. However, it isidangerous to assume that less-actively tradedinstruments can always be traded at close to their theoretical price. When financial marketsexperience a shock of one sort or another there is often a “flight to quality”. Liquidity becomesvery important to investors, and illiquid instruments often sell at a big discount to their theoreticalvalues. Trading strategies that assume large volumes of relatively illiquid instruments can be sold atshort notice at close to their thcorctical valucs are dangerous.
An example of liquidity risk is provided by Long-Term Capital Management (LTCM). Thishedge fund followed a strategy known as convergence arbit dt attempted to identify twosecurities (or portfolios of securities) that should in theory sell for the same price. If the marketprice of one security was less that of the other, it would buy that security and sell the other. Thestrategy is based on the idea that if two securities have the same theoretical price their marketprices should eventually be the same.
In the summer of 1998 LTCM made a huge loss. This was largely because a default by Russia onits debt caused a flight to quality. LTCM did not itself have a big exposure to Russian debt, but ittended to be long illiquid instruments and short the corresponding liquid instruments (e.g., it waslong off-the-run bonds and short on-the-run bonds). The spreads between the prices of illiquidinstruments and the corresponding liquid instruments widened sharply after the Russian default.Credit spreads also increased. LTCM was highly leveraged. It experienced huge losses and therewere requirements to post collateral that it was unable to meet.
The LTCM story reinforces the importance of carrying out scenario analyses and stress testing tolook at what is likely to happen in the worst of all worlds. LTCM could have tried to examineother times in history when there have been extreme flights to quality to quantify the liquidity risksit was facing.
Beware When Everyone Is Following the Same Trading Strategy
It sometimes happens that many market participants are following essentially the same tradingstrategy. This creates a dangerous environment where there are liable to be big market moves,unstable markets, and large losses for the market participants.
We gave one example of this in Chapter 14 when discussing portfolio insurance and the marketcrash of October 1987. In the months leading up to the crash, increasing numbers of portfoliomanagers were attempting to insure their portfolios by creating synthetic put options. They boughtstocks or stock index futures after a rise in the market and sold them after a fall. This created anunstable market. A relatively small decline in stock prices could lead to a wave of selling byportfolio insurers. The latter would lead to a further decline in the market, which could give rise toanother wave of selling, and so on. There is little doubt that without portfolio insurance the crashof October 1987 would have been mutch less severe.
Another example is provided by LTCM in 1998. Its position was made more difficult by the factthat many other hedge funds were following similar convergence arbitrage strategies. After theRussian default and the flight to quality, LTCM tried to liquidate part of its portfolio to meet itscash needs, Unfortunately, other hedge funds were facing