Can You Really Measure Tail Risk?

CBOE's SKEW can - but it's not investable.

March 21, 2011

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507311_whale_tail_series_4Asset management has always been about risk management. Before the rise of Modern Portfolio Theory, arguably, it took two forms. The first was buying relatively conservative stocks for their dividends. The second was using balance sheet analysis to find a margin of safety for undervalued stocks – the Graham-Dodd approach.

Modern Portfolio Theory, building on Harry Markowitz’s mean-variance model, transformed risk management into an exercise in statistical probabilities. That was an argument for diversification, as opposed to concentration in a few stocks with relatively good histories. But the problem with a statistical analysis is that the sample is simply not robust enough. William Sharpe, another pioneer in MPT, once noted that we would need 1000 years of market data before we could understand stock movements with some rigour. At best, we have a comprehensive data series – in the U.S. – that goes back to 1926.

The result is a lot of distracting clutter in standard risk models. A normal, or Gaussian distribution is encoded as the default. But stock market reality doesn’t quite follow the model, for a variety of reasons. Instead, asset returns exhibit skewness and kurtosis. Kurtosis refers to the shape of the distribution – meaning an attenuated normal curve, often with extreme returns showing up with greater frequency than one would expect. Skewness refers to the median – is it higher, or lower than the mean or average return? Stock markets are negatively skewed, meaning that they show losses more frequently than gains. (What influences the average is when the gains are big, and overshadow past returns.)

Some attempt has been made to mitigate extreme (negative) returns through Value at Risk. But, since it’s based on the same incomplete data series as traditional mean-variance calculations, the advantages are limited. The alternative – or complement – is stress-testing. That involves submitting current portfolios to an historical wind tunnel, modelling performance under specific scenarios.

A useful exercise, but arguably not enough, since it’s based on what happened, not what will happen. The problem is, as George Soros puts it, reflexivity. That’s a modern term for the punters in the Keynesian beauty contest, where winning involves predicting not who is the prettiest, but whom one thinks others think is the prettiest. Double contingency would be a better phrase: each participant is trying to figure out how the other participant is going to react before they themselves act.

Sometimes, however, those expectations are, if not entirely predictable, at least indicated. This is where options markets serve to provide additional information about equity and bond markets. One tool is the introduction of investable VIX. VIX tracks the volatility implied in options prices. VIX may cover extreme events, or kurtosis, or better fat tails.

But VIX is not enough. It doesn’t deal with skewness, according to the Chicago Board Options Exchange (which also prints the VIX index). “Tail risk is the risk associated with an increase in the probability of outlier returns, returns two or more standard deviations below the mean. Think stock market crash, or black swan. This probability is negligible for a normal distribution, but can be significant for distributions which are  skewed and have fat tails. … [T]he distribution of S&P 500 log returns has a sizable left tail. This makes it riskier than a normal distribution with the same mean and the same volatility.”

VIX has a long track record. However, while it captures expected spikes in daily standard deviations over a one-month period, it doesn’t include tail risk, argues CBOE. So CBOE has introduced a new product: SKEW. The premise is that  “[t]he value of SKEW increases with the tail risk of S&P 500 returns. When there is no tail risk, SKEW is equal to 100.  Historically, SKEW has varied in a range of 100 to 150 around an average value of 115.”

Does it work? CBOE says: “Past history provides further guidance. From January 1990 to November 2010, SKEW reached an all time low of 101.09 on March 21, 1991. This was close to the end of the recession that started in July 1990. SKEW reached its all time high of 146.88 on October 16, 1998 in the midst of the Russian crisis, and the day after a surprise decision by the Federal Reserve Board to decrease both the target federal fund rate and the discount rate. The value of SKEW was also high in June 1990, immediately before the July 1990 recession, and in March 2006, a period of heightened concern about a possible bursting of the housing market bubble.”

Okay, that’s the backtest. So far so good. But is it investable? No, investors will have to buy their own options contracts during high implied skew periods.

Risk: the constant companion of reward, but not always easily investable. At least not yet.

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