Why are there assymetries in payoffs in particular classes of options—and what do they tell us about the future of markets? The subject, one of the most challenging puzzles in derivatives, was discussed at a roundtable discussion held in London on September 7, 1999.

PARTICIPANTS

Murali Ramaswami, senior vice president and global head of equity derivatives research, Lehman Brothers Nassim Taleb, president, Empirica Capital LLC Joe Kolman, editor, Derivatives Strategy Amine Belhadj-Soulami, head of equity derivatives trading for Europe, Paribas Vanessa Gilbert Gray, director of global equity derivatives, Dresdner Kleinwort Benson Robin Edwards, president, Sabre Fund Management Ltd. Chris Hall, senior trader, Saratoga

Murali Ramaswami: The question I’d like to ask is, What possible use can skew be to a portfolio manager or to other traders? The skew means that there’s a non-zero probability—a significant probability, in some cases—of getting large negative returns. If you have a high probability of large negative returns, what should it imply for option pricing and asset returns?

If you look at the Standard & Poor’s 500 data historically, you’d find that there are three decades—1926–1935, 1936–1945 and, more recently, 1986–1995—in which the returns would not look normal and in which there is significant skewness. The real returns are large and negative.

If you look at the option prices before and after October 1987, you’ll see a distinct break. Option prices begin to reflect an option’s risk premium—a crash premium—that comes from the experiences traders had in October 1987.

You see this kind of skewness in many equity markets.

To get the measure of today’s skew, you subtract the difference in volatility of a 90-strike three-month option from the 100-at-the-money option.If you plotted or collected those data every day over a period of time for the S&P 500, you’d find that the number turns out to be approximately 6 percent. For the DAX, it turns out to be approximately 4.5 percent or 4.6 percent. For the CAC 40, it’s about 4.8 percent. (See Figures 1–3.)

Let’s ask another question. If the current skew is high in relation to its history, how do you act on that information? In December 1998, the S&P skew was much higher than its average. The current skew for the S&P is slightly above its average. The current skew for the DAX it also a little bit above its average. But the current skew for the CAC is much higher than its average.

One way to take this information into account is to do what you do in other situations. If you think an asset is overpriced, you sell it. If you believe a current option skew is higher than its average, and you think it should be coming down, then you should be selling that skew. One way to execute the strategy is by selling a put spread. Another is to sell the out-of-the-money volatility through straddles, although this would be a speculative bet on the direction of the high-priced option volatility. If one had a market-directional view based on the option skew, the market index could be bought or sold short.

The other question—the one that investment managers may want to consider—is this: What are the implications of these skews for the future direction of the market? If I told you that today’s skews are quite high, you can tell me something about the future return of the market. The skew tells us that option traders are implicitly assuming and pricing into their options a fear of future market decline. If the skew embeds some risk or crash premium, you should see the results empirically in the numbers. You should find a significant relationship between skew and future market return.

Let’s look at three different markets and examine what happened after market skews went up. Did the market really go down or did it go up in a statistically significant way? If you examine that, you’ll find that the forward market return of the S&P 500 and the DAX went down after a rise in the skews. In the CAC 40, it’s the opposite. The higher the skews, the higher the subsequent market return.

In other words, if you look at the S&P and the DAX, statistically speaking, and try to measure the subsequent one-month return, and you do that repeatedly, and try to determine if there is any empirical correlation at all, you would find that the relationship is negative.

You can see the same thing in the Nikkei market. At the end of March, most of the commentators believed the Japanese market was going to head down. But at that time, you would have seen an extremely flat skew. It went against all predictions. In that context, it should have suggested that at least in the options market, the traders were more sanguine than the commentators. And we all know what happened in the first week in April and in the subsequent months. If you looked at the numbers in the Nikkei option market in March, you might have guessed that the market was poised to rally in April.

Nassim Taleb: I am extremely suspicious of statistical studies done on the skew, since the essence of the skew is the rare event. I will provide a simple example. In a recent interview in Derivatives Strategy, Mark Rubinstein justified his portfolio insurance activities, which failed during the stock market crash, by saying, “We simulated 60 years of data and we saw nothing in there.” It’s the equivalent of my saying, “Well, I examined 50 or 60 years of data on Mark Rubinstein’s life and saw that he didn’t die, and therefore I can reject the hypothesis of him being mortal at a high confidence level.”

Whenever you have skewness, conventional statistical methods do not converge properly. Nor do we have a way to know if our sample size is sufficient to draw adequate conslusions. You can “statisticize” all you want, but this may turn out to be pure verbiage. You can no longer accept hypotheses; you can only reject them. I cannot accept the hypothesis of a recommendation being a good trade; but I can possibly reject it if it blew up.

That’s principally why I am extremely suspicious and am against any form of statistical examination of the skew, other than for anecdotal reasons or illustrative purposes.

Joe Kolman: So what does the skew tell you?

Taleb: One of the most counterintuitive things about the skew is the following: We have a divorce between expectation and frequency. The skew does not deliver the expectation of return as much as it delivers the frequency of profits or losses. The skew simply means that the moves that are likely to occur are going to be small, and that those that are unlikely to take place will be large. You may have a 10 percent probability of a nine-point move down against a 90 percent probability of a one-point move up. Using the designation “bearish” or “bullish” in this context is entirely futile.

Amine Belhadj-Soulami: When the market skew is quite steep, it tells me that the market is quite likely to go up. Big jumps or big crashes happen as a surprise. When you have an extremely steep skew, it means that a crash has been discounted already and people are already paying this risk premium and expecting a crash to happen. And that’s precisely why it doesn’t happen. Because there is no surprise.

In the past, I’ve noticed that a strong move of the market up or down was concomitant with a low level of volatility. Whenever volatilities are quite high, the risk premium people are willing to pay is too expensive, and the market doesn’t move as much as the option market tells you it will. The implied volatilities are pricing in a risk premium that is too high.

“When you have an extremely steep skew, people are expecting a crash to happen. And that’s precisely why it doesn’t happen. Because there is no surprise.” —Amine Belhadj-Soulami Paribas

At the moment, that’s what we are witnessing. Everybody who remembers the crash of 1997 is willing to pay this added risk premium. So I think this will help the market continue to go up.

Taleb: That is an extremely wise statement. When the skew is positive and is followed by higher returns, it doesn’t necessarily mean that it’s rational to be long.

I would like to warn further about data mining. You can always say that when you have a full moon and you have high skew in the CAC 40, the DAX has gone down two days in a row and it’s a Friday, you would have historically had a great trade by buying pork bellies. You can find a lot of things in hindsight by data mining, particularly the connection between the steepness of the skew and rainfall in Paris.

But let us remember what the skew means. The skew is telling you that you are likely to make money and unlikely to lose money, because when you lose money you are going to lose a lot of money. Does that mean it is rational to be long the market? Not necessarily. That’s also the reason we cannot measure, ex post, whether it was a good trade or not.

Ramaswami: I am not saying anything about the components of the skew magnitude or what it is made up of. It could be made up of the premium you need because of failures in settlement, failures in completing the trade or because of gap risk—or demand or supply at any given point in time. I am only focusing on one potential element that goes into the pricing: the perception of future market direction by option traders. When the skew is higher than its average or much below its average, is there any information in that difference? If you told me there’s no information in that difference, I’d be surprised.

Chris Hall: Right before the 1997 correction, they were giving away puts in the DAX. They were so cheap that the main concern was how many you could afford to finance. One of the reasons volatility went up the next day was because the clearinghouses insisted that these puts be bought back. I think a certain amount of skew is the clearinghouse fear of what’s going to happen.

Why does the skew go up? Because a bank issues a vast number of warrants and starts to buy puts to cover that exposure. So suddenly the market-makers in the pits are short puts; their clearinghouse tells them to buy them back, and so the skew goes up. This is only one of the many possible actions that could cause a short squeeze and drive the put volatility up. This is an imperfect situation with too many human factors for it to be simply market return.

Apart from interest rates and dividends, volatility is the one thing I can put into my model to generate my values—and that volatility is my feeling on the market. If my clearinghouse is telling me that I need to buy puts to cover my downside, then I have to put my skew up. As a market-maker, I’m setting the skew and I don’t necessarily have corporate research telling me that the market is more likely to go up or down.

Vanessa Gilbert Gray: You can also infer valuable information about skew by observing client over-the-counter deal flows. For example, if institutional or corporate clients are hedging by either buying puts or executing collars, then the effect on skew will be quickly reflected in the market and can be dramatic. Similarly, if large retail products are being issued with capped calls, skew may move considerably as the banks involved in providing the assets to back these products hedge themselves.

Regulatory aspects can also have an effect. For example, there has been significant solvency-hedging activity among U.K. insurance companies in the past few years. We have seen short-term hedges put on for up to £3 billion of FTSE notional. That kind of size can have an extremely dramatic effect on the skew, and yet tells you absolutely nothing about investor sentiment—since the hedge has not been put in place because of a bearish view, but rather to meet regulatory requirements for solvency measures.

“Skew is heavily influenced by supply and demand factors, more than by academic or technical arguments or fundamental views on the direction of a market.” —Vanessa Gilbert Gray Dresdner Kleinwort Benson

I guess what I am saying is that skew is heavily influenced by supply and demand factors—much more so, I believe, from a trading perspective than by academic or technical arguments or even from fundamental views on the direction of a market.

Robin Edwards: We talked about the skew phenomenon existing in equity markets. I presume it exists in the bond markets and currency markets. Do the differences in the skews between the various markets explain something about the skew itself?

Kolman: The skew is quite pronounced in the emerging-market currencies. In the Russian ruble, the peso and the eastern European currencies, we see pronounced skews over time. But it takes the shape of a volatility smile, as opposed to the one-sided skew that you’re seeing here.

Taleb: The skew is principally a result of the restriction of the supply of some category of options, rather than some consensus estimate by option traders. Since 1987, equity option traders have not been able to sell too many lower-strike puts, because the clearinghouse would look at what would happen if there were a repeat of the crash and prevent them from having a large loss in such a situation. In the currencies, you have a similar phenomenon. Since the blowup last August in U.S. dollar/yen, a lot of option traders have not been able to do puts on the dollar, which has exacerbated the skewness there.

Before 1987, there was no significant skew in the equities, but we had a skew in the bonds. The calls on the bonds were cheap, because people would do covered writes on the bonds and sell puts. It was common wisdom among market-makers that if you sold out-of-the-money calls on a bond, you could always buy them back in a rally, since volatility did not increase.

Then, of course, in the crash of 1987, when bonds snapped back up close to 10 percent, you could not buy them back. Since then, the skew has become symmetric in the bonds. In fixed-income markets, the skew is symmetric, but it’s more of a smile then a skew.

So we see skews appearing periodically in markets, depending on the mood of risk managers, typically after the fact, because they fear a repeat of the events. Usually this should tell you that these events will not repeat themselves, because, as Amine pointed out, people are prepared and these events usually happen when people are not prepared. In U.S. dollar/yen, the skew fluctuates. The only market that is relatively flat is the euro. Practically everything else in the financial markets has a skew.

Belhadj-Soulami: I would also emphasize the role of the flow. The number of players in the skew market is limited. We’ve been focusing on the three-month maturity, but on the long-term skew there’s a huge imbalance between what clients want and what professionals can provide. As a result, we have a huge increase in long-term skew. There’s no theoretical explanation for it. It’s simply the way it is. As long as clients are willing to pay the level they are paying, and as long as the supply remains limited, the trend will remain the same.

Gray: I agree. It’s important to keep an eye on what clients are up to. Recently, a German structured product was launched for nearly half a billion euros. The investor was buying a put spread on the euro stocks. One of my traders was telling me this morning that if we see a couple more trades like that, we’ll have a dramatic easing off in the skew on the euro stock markets for longer-term trades. So traders need to keep a close eye on what clients are up to, because it will have quite a significant effect.

Belhadj-Soulami: The impact of the flow on the skew is even more important in the long run than what you can expect to make by rehedging your position and comparing it to the historical skew. Because you are rewarded or punished immediately by the move in the implied skew, all the banks have to mark to market.

Kolman: How correlated are skews to volatility? We know that when markets decline—especially equity markets—volatility goes up, and when they rise, volatility falls. So what’s the correlation between this skew effect and volatility?

Taleb: The skew, by definition, is the correlation between volatility and direction. By definition, the skew tells you that you’re going to have a higher variance at lower prices, and lower variance at higher prices. The conventional interpretation of the skew is as follows: When you plot the returns of a given security, you see a fat tail on the left and a thin tail on the right. The median is higher than the mean in the sense that most observations are higher than the mean return. What is interesting is that the same result can be obtained with a process that has a stochastic volatility, with volatility negatively correlated to the return—that is, it increases when the market goes down and decreases when the market goes up.

“This is what people in Chicago say about traders who sell the skew: ‘They eat like chickens and defecate like elephants.’” —Nassim Taleb Empirica Capital

Incidentally, the skew has historically been extremely wrong. When the S&P 500 was around 400 in 1992, it predicted a volatility of 5 percent should the market rally to 1,300 within the next seven years. What happened is that volatility went to 22 percent instead. This tells you something about the quality of the prediction delivered by the market.

Ramaswami: Today, S&P 500 volatility is coming down, but the skews have not come down a whole lot. In fact, the skew was much higher at lower levels of volatility some time ago. So levels of volatility are just as important to determine future returns.

Taleb: Not statistically. Only ex ante. When I look at the skew and it’s positively sloped, it tells me that the market is more likely to go down. If it’s negatively sloped, it’s telling me that the delivered implied expected returns—not the statistically observed ones—are going to be small positive returns, and that there will be plenty of them.

Ramaswami: Empirically, after the fact, exposures do turn out to be positive for the CAC 40 and negative for the S&P 500 and the DAX. Clearly, we have to take into account the level of volatility. But skewness is the difference between two volatilities, and that difference could be different depending on the level of volatility.

Kolman: What lessons can we learn from the skew?

Taleb: Don’t sell the skew, and don’t try to read too much into the skew. Just be realistic. You can always find some relationship between a skew and a later event—something we at Empirica Capital call pseudo-empiricism. When puts are cheap, it indicates that people aren’t really afraid of a crash and are getting complacent. I would probably be more inclined to believe in a crash if puts are cheap—not when puts are expensive.

This is what people in Chicago say about traders who sell the skew: “They eat like chickens and defecate like elephants.” In Greenwich, Conn., they say: “The fund had only one bad quarter.”

Ramaswami: This is turning out to be point-counterpoint. We do have some lessons to learn from skews. Skews mean something to volatility traders, who can execute put spreads or other trades based on the skews vs. whatever other comparisons they want to make. But the skews also have implications for the direction of the market. The skew spread expresses the consensual estimate of option traders in the derivatives market, and there must be some information you can extract from that.

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