Courting Catastrophe

So You're Insuring Against Market Risk With Options? Think Again.

By By Kathryn M. Welling

Table: Insurance Exposure And What It Might Cost

An Interview With Andrew Smithers ~ There's no mistaking his current bias: bearish. After all, who else but a bear, one who last spring penned what none other than Morgan Stanley's Barton Biggs called the first "coherent, reasoned case for a secular bear market," would set about writing a series of reports exploring potential triggers for that most unhappy of investment events. But Andrew is no nattering nabob of negativitism, stubbornly, or with malice aforethought, committed to raining on the bulls' parade. He's far too cerebral for that.

Besides, as chairman of London's Smithers & Co., he has some 70 international fund-management companies depending on his economic consulting group for credible asset-allocation advice. So when he and his associates take up an issue, they do so with ferocious intellectual vigor -- and let the chips fall where they may.

It's no surprise, then, that when Andrew recently focused on the options markets, wondering if their phenomenal growth -- and the immense popularity among portfolio managers of using options to "insure" equity positions against market risk -- might not have a dark side, he enlisted the best and most disinterested help he could find: Mathematics don Stephen Wright, a member of the economics and politics faculty at Cambridge University. The report the two released last month, entitled "Stock Options: An Example of Catastrophe Myopia," not only argues cogently that most market participants don't recognize a number of risks inherent in their option activities, but also achieves the nearly impossible in quantifying, even roughly, the sorts of risks therefore being run.

Andrew was gracious enough to walk us through their conclusions when we rang him up recently.

Barron's: So you see catastrophe looming? Smithers: Let's step back. I started working on our options report as part of a program to look at various ways that a stock-market crash could possibly be triggered.

Q: You began with a bearish bias, in other words. A: Yes. The reasons for expecting a stock-market crash lie in its extreme overvaluation. But the reason and the occasion are always different. And we were not looking to do the relatively easy -- but not particularly helpful, from an investor's point of view -- thing, which is to simply say: "Nobody can predict the timing. All you can tell from the fact of the extreme overvalution is that you are running massive risk. And people tend to consistently underrate those risks." That's fine, as far as it goes. But we wanted to try to do a little bit better. We're not pretending we can predict the top. But we clearly think it's worth looking at various possible triggers. And one of the trigger mechanisms we looked at was the growth in the options market.

Q: You do expect the worst for stocks, though. A: That's always tricky to predict, especially because there have been so few instances in the past when the markets were as overvalued as they are currently. Only Wall Street in '29 and '37 and Japan in '89 were as overvalued as the present market. The next most overvalued was the '68-'72 market in the U.S. What happened after all of those, I'm afraid, was a decline that was not only large, but was fairly prolonged. In 1929, Wall Street took nearly three years to bottom. In '37, it took five years. And stocks lost 89% and 67%, or whatever, of their value in the process. So experience would suggest that we will have a crash both severe and fairly prolonged. Then again, we really don't have much experience, so people may react differently. But we certainly see the situation as very dangerous.

Q: That's comforting. And options only make it more so? A: Our options study's broad conclusion is that the growth of the option market does indeed pose a very serious threat to the stock market. But more likely one of accelerating a crash and possibly bringing additional financial stress to the financial-services industry at a most inopportune time, than one of triggering a crash itself.

Q: Portfolio insurance redux? A: Yes. Of course, no one today admits to using the sort of portfolio insurance which was employed in the mid-'Eighties. As you recall, portfolio insurance involved investors having a plan of how they would operate: They thought they could defend themselves from losing money by buying when the market went up and selling when it went down.

Q: By buying high and selling low! A: It did defy common sense. But people became quite happy about it because the mathematicians could nicely show that, indeed, it would work. The rub was an implicit assumption in the mathematics that share prices are what's known as continuous.

Q: Which was possible only because none of those mathematicians had ever walked the exchange floor or traded a stock. A: Or else they'd forgotten the experience. There was a communications gap between mathematicians and practitioners -- one they discovered on Black Monday, October 19, 1987. A similar thing has happened today. Our message is that portfolio insurance hasn't gone away. Rather, it's being done today through the options market. If portfolio managers are nervous about the stock market, they say, "I'm scared stiff, but I don't want to be out, because who knows where the top is? I have to keep up with my colleagues to keep my job." So their rational response, under the circumstances, is to try to protect themselves to some extent against the worst -- a really big crash -- by hedging with options.

Q: What's wrong with that? A: Nothing, in theory. Stock options can, of course, be used either for speculation or as a form of insurance. Investors in the stock market who want to limit their exposure to market declines can, for example, buy a put. If their fears are realized, the profit on that put will limit their losses. But like all insurance, that coverage comes at a price: The more the market price of the underlying asset exceeds the exercise price of the option, the less will be their insurance coverage and the lower the price of the put. The price of the option is the equivalent of the premium paid for insurance. So, as in any insurance market, the options market allows a risk-averse investor to limit the extent of his exposure to the market.

Q: Okay A: The crucial difference is that unlike fire, life or auto insurance, the aggregate risk is not significantly less than the sum of the individual risks-because it is systemic risk, rather than specific. If a normal insurance market expands, this tends to reduce the impact of underlying risk, through the "law of large numbers," since most of the risks insured are specific.

Q: Meaning that most of the risk insurers usually cover is of individual accidents, not global catastrophes? A: Yes, those are two very different types of insurance. We make an analogy to the housing stock in America. When people insure their houses in America, they're insuring against specific risk. There's little risk that all the houses will burn down at once -- which would be systemic risk. But a stock-market debacle is a systemic risk -- it would affect all insured portfolios at once -- and is in fact as uninsurable as, say, a major nuclear disaster, in many people's view. In any event, this means that any reduction in the risk of those taking out insurance must be matched by the increased risk assumed by those providing the insurance. What's more, as the options market expands, the total amount of risk involved in stock-market fluctuations rises by even more than the increase in the market's value.

Q: Why is that? A: This is analogous to the increase in risk that accompanies an increase in debt. While there can be no increase in net debt, since every borrower must have an equal lender, the risk of default rises with the expansion of gross debt. Likewise, the expansion of the options market involves increased risks, because of its inherent differences from other insurance markets. What's more, the trouble with the options market is that share-price movements are highly correlated -- and this is increasingly becoming true of markets worldwide. Thus, while it is unimaginable that 89% of the U.S. housing stock would suddenly be wiped out, the equivalent disaster happened to the U.S. stock market between 1929 and 1932.

Q: You're implying that all the options activity undertaken to mitigate market risk is actually increasing it by an awesome amount? A: Well, by how much is the question. Because risk rises with amount of insurance being provided by the options market, it's important to be able to measure the size of that exposure -- and, unfortunately, the answer is far from simple.

Q: We were afraid of that. A: For traded options, information is widely available on the volume of trading and on the open interest, which is the number of contracts outstanding. But those numbers don't readily translate into money values -- and for the far larger market in over-the-counter options, not even those numbers are widely available.

Q: So, how can you assess risk? A: The ideal measure of the size of the options market would be an indication of the "insured value" it provides, which would be analogous to the value of the coverage provided by any other insurance market. In our report, we estimate that this insured value for just one relatively small, but important, sector of the options market -- the face value of all index put options traded on the Chicago Board Options Exchange -- amounted to $132 billion at the end of May.

Q: Based on what? A: We derived that measure of the insurance coverage provided by the CBOE market in stock-index options by multiplying the number of outstanding put contracts by the dollar value of each contract. Since the number of puts is roughly equal to the number of calls, this is about equal to half of the notional value of the entire options market. But bear in mind that in principle some portion of the outstanding calls may also represent a form of insurance. What's more, the rapid growth in the market is illustrated by the fact that this insured value of the CBOE's index options has increased over 12-fold in the past decade. It has more than doubled in the past two and a half years.

Q: So you're saying the amount of insurance coverage being provided by the options markets in all their permutations is staggering? A: It's really the problems involved in obtaining accurate data on the options markets that are staggering. As a consequence, as we stress in our report, the figures that we produced should be used carefully to indicate orders of magnitude, rather than taken as gospel. The most reliable statistic is the one I just referred to, which is taken from data published by the CBOE, and can be calculated fairly straightforwardly -- but even it may include an element of double-counting due to inter-dealer transactions. Beyond that, the data in the [accompanying] tables are listed in descending order of reliability. They're based on incomplete data compiled by the Bank for International Settlements, the Central Bank Survey of Foreign Exchange and Derivatives Market Activity and lots of heavy lifting by Stephen Wright, my colleague at Cambridge -- who, if anything, strove to err on the side of conservatism. In any event, our conclusion is that some $1.4 trillion to $2 trillion of insurance against market risk is currently being provided by global options markets.

Q: A big number. A: Indeed. Even if considerably less than precise. Let me stress again that, given the sorry state of the available data, our estimates can only represent the order of magnitude of the insurance coverage currently being extended via options, whether traded index options, individual stock options, or OTC equity options in the U.S. or globally. Nonetheless, if our estimates are broadly correct, and the proportion of the U.S. equity market that is effectively insured approaches 10%, then the ultimate underwriters of this stock-market insurance are at risk to the extent of $280 billion-$400 billion -- should the stock market decline by 30%.

Q: But who are those ultimate underwriters -- the dealers? Every time we've asked, we've been told not to worry, everybody's "delta hedged" -- whatever that means. A: Well, that upwards of $400 billion exposure compares with the $33 billion of combined equity of the major dealers, Merrill Lynch, Morgan Stanley, J.P. Morgan, Bankers Trust and Goldman Sachs.

Q: You're implying they're how vulnerable? A: Our data indicate that a 30% market decline could cause serious financial strain, among the dealers, if they were underwriting all that risk. In practice, however, much of that risk is being assumed by the owners of investment portfolios, because the dealers normally hedge their exposure to the market's directional movements -- which is known as "delta" exposure -- with offsetting positions. That's delta hedging.

[Media]

Q: It sounds too good to be true. A: It is -- in the sense that, while the market's directional risks can be hedged, there are two other risks involved, known as "gamma" and "vega" exposures, that can't be hedged by the dealer community collectively, even though a dealer, in principle, might hedge against them.

Q: Sorry we asked. Can you translate? A: I'll try. Delta hedging underlies the whole principle of options pricing because it neutralizes the impact of changes in stock prices, in either direction, provided the price changes are small. The simplest example of delta hedging usually uses a transaction involving a single option and the underlying stock. In practice, of course, the underlying "stock" may be an index, which can't itself be bought and sold, but a futures contract on it can be. Anyway, if the stock price changes, the price of the option will also change, by an amount represented by the Greek letter delta -- and the relationship between those changes is stable for small fluctuations. Thus, the seller of an option can hedge himself against loss by taking a position in the stock opposite to the risk he's assumed in the option.

Q: You're saying that a dealer who would lose money on a call option he's sold, if the stock price rises, can hedge against that risk by buying enough stock to produce an equal profit? A: Exactly. And the amount of stock bought must equal delta times the exposure on the option, hence the term "delta hedging." The link between insurance and speculation becomes apparent, though, when you follow that relationship through.

Q: To you, perhaps. A: It's simply that buyers of puts want to reduce their exposure to the market. And since the delta-hedging traders want to have zero exposure to the market, they have to find other investors who want to increase their exposure. What's crucial here is that a trader who sells both calls and puts will tend to hedge his delta exposure automatically, thereby reducing his need to engage in transactions in the underlying stock. For example, back on July 10, one-month put and call options on the S&P 500, with an exercise price of 920, had almost identical deltas, with opposite signs, and almost exactly the same prices -- $20 and $22, respectively. A dealer selling 1,000 of each would have had liabilities of around $4 million -- the contracts are 100 times the index -- and would have been more or less "perfectly" delta hedged. If the market had then fallen 1%, the price of the put would have risen about $5 and the price of the call would have fallen around $4, leaving his liabilities little changed.

Q: So, what's the problem? A: As I said, delta hedging only protects an options dealer from small changes in the market price. Because unlike the payoff on a bet with a bookmaker, for example, the payoff to a purchaser of an option is determined by the scale of the change in the price of the underlying stock -- and in a non-linear way. It is as if a bookie paid out more on a winning horse depending on the square of the winning distance. If, for instance, in the options situation I just outlined, the market had instead quickly fallen 10%, the call would have become essentially worthless, while the put would have soared to about $90 -- roughly the difference between exercise price and the new stock price. So the dealer's liability would have swelled to $9 million, assuming no change in underlying volatilities. This is what's known as "gamma exposure."

Q: Can't Wall Street's rocket scientists eliminate that risk, too? A: Well, if prices move relatively slowly and smoothly, gamma exposure can be limited by "rebalancing" portfolios, which involves progressively changing the degree of delta hedging as the delta itself changes. But it can never be entirely eliminated. This is a crucial difference between the actual practice of dealing in options and the textbook theories underlying the standard Black-Scholes pricing model. That model assumes that it's possible to rebalance portfolios on a continuous basis -- and therefore that writing options and delta hedging is a riskless activity. Which, of course -- Nobel Prize or not -- it can never be, in practice.

Q: Still, can't that risk be hedged? A: Sure, but there's a crucial difference between delta hedging and gamma hedging. As I said, the activity of writing options has a tendency to be self-hedging against delta risk, which means that any systemic price risk is underwritten semi-automatically and in advance. But the only way to hedge gamma exposure is to buy as well as to sell options -- and that simply moves the gamma exposure from one dealer to another. So, while any individual dealer can be gamma hedged, the financial community as a whole can't avoid gamma exposure -- and in practice, this risk is largely borne by options dealers.

Q: There's no escape? A: Let me put it this way: The only way the dealer community as a whole could avoid gamma exposure would be if long-term investors assumed equal exposure to both put and call options -- as both buyers and sellers. That would run against the natural tendencies of those investors and create credit-exposure problems. In fact, should such a situation occur, the primary raison d'etre of options dealers -- to act as intermediaries who remove credit risk -- would disappear.

Q: Okay, what do you figure this gamma risk amounts to? A: Translating it into a figure for all equity options, comparable to the figure we produced on the value of the insurance coverage being provided by options and the potential payout, just can't be done with any precision. The gamma exposure of the market as a whole is almost certainly significantly lower, in relation to the market's overall size, because long-dated options have markedly lower gammas than short-dated ones. But it seems reasonable to assume that the exposure of the entire market to a rapid 10% price shock would be something on the order of 1% of the face value of all options, or around 2% of the "insured values" shown in the table, given a rough equality in the number of puts and calls. This implies that aggregate losses to options dealers could run $10-$15 billion in the U.S. and up to $40 billion worldwide, in a 10% correction, if other markets fell in sympathy. Furthermore, it should be noted that gamma exposure doesn't increase proportionately with the size of the market shock, but rather with its square.

Q: You mean a 20% drop in the market would increase the gamma risk by a factor of four -- to $40-$60 billion? A: Yes, if it were a 1987-style decline. If prices decline slowly, as I said, the gamma risk can be reduced, but only at the expense of creating severe selling pressure on underlying stocks and in the futures market, as the writers of options struggle to rebalance their portfolios. And that institutional selling would inevitably imply an accentuation of any decline, once it starts in earnest. What's more, there's an additional risk that options dealers can't collectively hedge away, which is their exposure to the market's own estimate of volatility, or their vega exposure.

Q: Not more Greek! A: Suffice it to say an increase of five points in assumed volatility, which is roughly comparable to the increase seen in the immediate aftermath of the '87 crash, would increase the collective liabilities of CBOE options dealers on short-dated options by around $500 million. And vega, in contrast to gamma, increases with the maturity of the option, so the total exposure of the market as a whole would be larger, in relation to its face value. Nonetheless, it would probably be less than the 2% of face value we estimated for gamma exposure.

Q: Why bother with a mere trifle? A: Because changes in gamma and vega can -- and almost certainly will -- be reinforcing. Thus, should the market plunge 10%, the gamma exposure will give rise to large losses. But it's also likely that the market's estimate of vega will also increase, giving rise to additional losses. The parallel here with the role of portfolio insurance in the '87 crash is obvious. One of the morals of the crash was that put options were preferable to portfolio insurance, which couldn't work when the market moved rapidly. But the subsequent shift to insuring against market risk via the options market has merely passed the problem on to different risk takers, rather than eliminating it. The investors who took the hit in '87 were the owners of ordinary share portfolios, with capital equal to 100% of their exposure. Those at risk today include dealers, whose capital is a mere fraction of their exposure. And it seems to us very unlikely that they are reserving adequate capital against those risks.

Q: But aren't they being pretty well paid to take those risks? A: In a word, no. While dealers' models for option pricing -- in sharp contrast to the old portfolio insurance model -- seek to allow for price discontinuity, the risks of price discontinuity depend on the size of the aggregate options exposure, relative to the size of the stock market. Thus, if discontinuity were truly allowed for, options prices would have grown over the last decade as the options market grew relative to the stock market. Options, like any form of insurance, should be priced in relation to the risks involved, including the increase in risk that accompanies an increase in the market's size. Instead, as Stephen's work demonstrated convincingly, options prices, in practice, have been almost solely determined by recent changes in actual market volatility. Indeed, the collective memory of the options market appears to be very short-term in nature, with implied volatility -- which should be based on risk assessment -- instead simply responding to events of the past six months.

Q: Then why haven't we seen more spectacular flame-outs, among dealers? A: Because these are systemic risks, remember, to which the dealers are exposed. Even if the options are not correctly priced, the dealers will usually find the business profitable. Yet on rare but dramatic occasions it will be spectacularly unprofitable. Human nature being what it is, that sort of very rarely manifested risk habitually gives rise to what's known in insurance circles as "catastrophe myopia." And that, in turn, leads to underpricing and undercapitalization. Conditions which are also encouraged by what's endearingly known as "moral hazard," if the state is regarded as the lender of last resort. Meaning that the taxpayer will ultimately be on the hook for all that "insurance."

Q: We're beginning to get the idea that you think the options market may pose a serious threat to the old bull's health. A: The risks to the stock market and the economy, not to mention options dealers, are considerable. If the market plunges, dealers will be obliged to rebalance their portfolios by selling stocks, just to reduce their exposure to further declines. This requirement to sell into a decline will tend to increase the volatility of the market and render it more liable to self-reinforcing spirals. And it's possible, though probably unlikely, that such a spiral could set off the crash to which the market's extreme overvaluation makes it vulnerable. What's more likely is that the phenomenal growth in the size of the options markets will accentuate the magnitude of any crash set off by other forces. It's also more likely to increase the size of the market's price discontinuities -- meaning the extent to which large price movements take place without permitting transactions at intermediate prices. As an aside, it may be that "circuit breaker" rules, which shut markets when prices move by more than a given amount, will intensify rather than limit the problems of price discontinuities -- they don't limit the dealers' risks, simply their ability to cover them. Finally, the undercapitalization of options dealers, relative to the risks they're assuming, vastly increases the risks of bankruptcies among the dealers, should the market suffer a sharp break. And that, in turn, would also reinforce the problems created by a stock-market crash.

Q: Gee, thanks, Andrew-we think.

-- dax (3@h.f), October 18, 1999