Waking up to Risk

I don't know how many of you caught it, but there was an interesting little piece in the Gulf Times (the Qatar gulf, not the Mexico gulf) yesterday concerning the inherent weakness of the Sharpe Ratio as a measure of risk. Who was the star of this article? None other than Mr. Fooled by Randomness himself, Nassim Nicholas Taleb. Now Mr. Taleb is a very opinionated (not to  mention an extremely bright) man, make no mistake about it. I personally view this as a strength, since his views are provactive, grounded in math and statistics and often buck conventional wisdom. Among other things, he seems to think that investors are generally a bunch of dumb sheep who irrationally attribute investment skill to what is really only chance. I have to say I am pretty much a buyer of his theories. That said, his topic du jour is that of how the Sharpe Ratio doesn't properly reflect risk-adjusted returns since financial markets returns in specific (and social phenomena, in general) don't conform to a normal distribution, and that this measure is being used as a justification for investing in hedge funds.

The Sharpe ratio is a measure of risk-adjusted return. It is the difference between returns and a risk-free interest rate - often the yield on US Treasury bills - divided by the volatility or range of possible returns. It has been used in recent years to persuade investors such as pension funds that it is less risky to invest in hedge funds than equities. “It’s used for marketing. It looks sophisticated, but the volatility part is not a good measure of risk,” said Nassim Nicholas Taleb, a hedge fund investor and a professor in the sciences of uncertainty at the University of Massachusetts Amherst. 

“The Sharpe ratio is like a horoscope ... A startlingly high number of people rely on this bogus theory ... It’s a big scam by finance professors ... Finance is a craft not a science...” It (a normal distribution) cannot be applied to exceptional extreme events in finance such as large losses or gains that will continue to dominate the picture no matter how large the sample gets. “If the exception doesn’t matter in the long-run, then the law of averages applies ... If the exception continues to dominate the sample even if the sample becomes very large, you can’t use the normal distribution,” Taleb said. “It can’t be applied to socio-economic variables ... An example is stock market returns ... In the last 50 years, 10 days represented more than half of stock market returns.”

Now this is a very complicated issue that would take many posts to delve into, but Taleb hits on one of the key points that is often missed when discussing optimal portfolio construction including hedge funds. Two others are:

• Hedge fund returns generally exhibit negative skewness (akin to selling options, collecting premium, but being exposed to tail risk)
• Hedge fund returns generally exhibit high kurtosis (fat tails, meaning a higher incidence of "bust" than what would be considered normal)

There has been some excellent academic work in this area which I can dig up for readers, if they are interested. But I think the key point here is that a single statistic, even one as famous as the Sharpe Ratio, cannot begin to capture the risk/return characteristics inherent in hedge fund strategies. It is for the same reason that VaR (Value at Risk) is a flawed measure of a bank's riskiness, again given the assumptions that risks are normally distributed. What the banks themselves do internally and what sophisticated investors do is run a wide variety of stress tests, incorporating events that would show up as many, many standard deviations from the mean (and thereby having an expected occurrence of once in an eon, notwithstanding the fact that we seem to have an eon every few years) but which could well transpire. It is only by flexing the variables impacting a portfolio across a broad array of outcomes (including correlation) that a fair assessment of risk and return can be made.

Thanks, Mr. Taleb, for reminding us that investing is a serious business and calls for serious and thoughtful analysis, and that relying on a statistic to get comfortable with an investment is, in short, a fool's game.