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Summary It is difficult to understand exactly what the CBOE Skew Index means, and even more difficult to find a use for it. This has not prevented some commentators from using it as an indicator for the S&P 500, usually in conjunction with the better-known VIX Index. I find no reason to believe that the SKEW Index serves as a useful indicator, and not much logic for thinking that it would. SKEW is useful only to a rather restricted group of professional hedge traders, such as swaps dealers, and can safely be ignored by the rest of us. Given its inexhaustible creativity, it was only a matter of time before the CBOE created an indicator that challenges investors to find a use for it. Meet the SKEW Index ($SKEW:IND). Yet as obscure and difficult to interpret as this index is, there are some who believe it is an indicator for the S&P 500. This article disputes that contention. What is it? The CBOE Skew Index, unveiled in 2011, provides an index of traders’ vertical skew expectations, based on analysis of the volatility smile of deeply-out-of-the-money S&P 500 index options. All of which is jargon, except to option aficionados. But SKEW is just another way of measuring the extent to which investors expect the distribution of security returns to be non-normal. That is, it indicates the degree to which the median return is expected to differ from the mean, and the extent to which the distribution will include more and/or more extreme outliers. On the downside, the latter are known as “black swans” ─ a term I dislike, since it confuses empirical uncertainty with probability (the probability that black swans existed when probability theory was being developed was 100%; uncertainty based on Eurocentric data is a completely separate matter). In option terms, the non-normality of returns means that the assumptions about future volatility embedded in option prices are not symmetrical with respect to strike prices, so that the put and the call at the same strike price do not have the same implied volatility. Thus ─ since most (but by no means all) equity returns are negatively skewed ─ buyers of puts generally assume (and pay for) higher volatility than call buyers. If puts and calls at a given out-of-the-money strike have the same implied volatility, their graphic representation forms a “smile” that indicates that traders assume a normal distribution of returns from the underlying. In most cases, there is a difference between the implied volatility of puts and calls, and the “smile” is more like a smirk: The smirk tells us that option traders do not expect the returns on the underlying to be normally distributed, and in the case shown above, that the outliers will tend to be on the downside. How Has it Behaved? Since the beginning of 2010, the index has developed like this: It requires some explanation. A reading of 100 indicates an expected normal distribution of S&P 500 returns. The higher the reading, the more skewed to the right of the mean traders expect returns to be ─ and the more likely and/or more severe the negative outliers will be. A reading of 100 indicates that the expected probability of a ≥3σ negative outlier is 0.15% (roughly the likelihood of being dealt a full house in five card straight poker with no wild cards), while a reading of 145 indicates a 2.81% expected probability (a bit better than the chance of rolling a double six on a single throw of dice). The trend is disturbing ─ it suggests that traders expect an increasing number of negative outliers, or more damaging ones. It may be that they do, but I suspect that a better explanation is that, since the crash, there has been increased investor interest in “tail insurance,” demand for which is likely to have pushed the index upward. Thus, I believe that the trend does not represent investors’ response to a specific forecast of disaster, but a more widespread realization of the availability and perhaps advisability of insurance. This does not just represent the hedging activity of hedge funds and sophisticated institutions: any product that offers a downside floor, such as the structured notes popular with private bank clients, is hedged in the options market by its issuer. Not surprisingly, such products have become increasingly popular since the crash. What Does It Mean? This is the $64,000 question, because it is not at all clear what the extent to which a tail event might mean, since a tail event, by definition, is something unexpected. ‘Implied volatility’ is a portmanteau term, carrying the freight not contained in the other variables of the Black-Scholes model, all of which are much more precisely defined. It is in effect the bucket into which everything that determines the price of an option ─ other than those narrowly defined variables ─ is placed, including the price markup that options writers demand. This markup varies with market conditions. Put writers may demand higher prices based solely on their perception that they can get them, without reference to volatility forecasts, and purchasers may accommodate them because they are forced by their circumstances (for instance, as issuers of structured products) to hedge, regardless of whether they think the insurance is well priced. To suggest that every change in the volatility smile implies a change in risk perceptions is nonsense. This raises relatively few issues for interpreting the meaning of the VIX Index, because supply and demand for options is significantly determined by perceptions of the identifiable, near-term and “ordinary” risks that the VIX Index measures. But skew is a different matter: there would be no tail events if they were widely anticipated, and even the most extreme possible reading of SKEW implies only a 3% implied probability of one. While changes in demand for out-of-the-money puts is certainly related to fear of tail events, I believe that it is implausible to argue that it can be predictive of them. Much demand for deeply-out-of-the-money puts is inherently “lumpy,” as a new product is launched or a seasoned product’s hedge must be rolled. How Does SKEW Differ from the VIX? The relationship between SKEW and the VIX is an obvious question. The difference was quite significant in the period illustrated here: the linear regression on the VIX trended downward, so they had mildly negative correlation at -0.20, and the VIX was more volatile (σ = 8.0% vs. 2.5%): Over this 6½ year period, the S&P 500’s correlation with the VIX was -0.77, and 0.22 with SKEW, but over shorter periods correlation varied ─ not so dramatically for the VIX, which has a pretty stable correlation with the S&P 500 over time, but very considerably for SKEW: The low correlation between SKEW and the S&P 500, and especially the very substantial variability of the relationship (peak 0.63 and trough -0.17 around the 0.22 average) support my contention that SKEW has little predictive power for the S&P. This should not be so terribly surprising, since the skewness of S&P 500 returns is itself far from stable over time. Comparing this chart with the charts above suggests that SKEW is not even an especially strong indicator for S&P 500 skewness: Note that this chart uses a longer rolling time period. The 90-day results were so volatile as to be virtually unreadable ─ even using 260 data points, the standard error of skewness is 14.9%. The calculation of standard error of skewness is so generous to uncertainty that it constitutes yet another reason to be doubtful of the predictive value of the CBOE Skew Index. There are some other differences between SKEW and the VIX that have attracted comment ─ in particular, when the former spikes, it tends to do so in isolated, one-day spurts, and promptly returns to its earlier level, while the VIX tends to sustain elevated or depressed levels over the course of a week or two. Thus, when SKEW dropped 16 points on October 15 last year, it snapped back completely the next day. In contrast, the VIX spiked upward on the 9th, and did not recover its earlier level until the 23rd. This has been interpreted as the difference between expectation of elevated but still “normal” volatility ( Scalper1 News
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