New spin on an old metric
Feb 3rd, 2009 | Filed under: Performance, Analytics & Metrics, Today's Post
In a story earlier this month about the appeal of low volatility, The Economist’s Buttonwood column observed:
“This obsession with smoothness grew, in part, from the way that fund managers’ returns are analysed. Half a century ago little information was available and clients barely knew whether their fund manager was outperforming his peers. Eventually benchmarks were established and managers were judged on whether they beat the industry, or the stockmarket, average.
“But beating the average was not enough. Academics pointed out that it was possible to outperform in the short term, simply by taking a lot of risk. That led to the widespread use of the Sharpe ratio as a measurement tool. The ratio, devised by a Nobel-prize winning economist, looks at the relationship between investment returns and their variability. The higher the ratio, the more reward there is for a given amount of risk.”
Obviously, blindly following the Sharpe ratio can lead to Madoff-esque traps. But researchers with Northwater Capital Management of Toronto (see previous post) recently wondered if the Sharpe ratio could be better used as a measure of the marginal effect of adding an asset to a portfolio. In a new white paper by Simon Chan and Adrian Hussey (available here), the firm wonders:
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Certainly an interesting addition to the Sharpe Ratio, but the Sharpe Ratio also assumes a normal distribution of returns, which we’ve all seen isnt the case in the world today.
How ridiculous. It is obvious and does not require a thesis to discover whether an investment adds or detracts to the Sharpe ratio. Analysis paralysis! Gone are the days when basic mathematics were performed in one’s head.
The Sharpe ratio of a fund alone does not determine the impact it has on the Sharpe ratio of the portfolio. The original portfolio composition is as important as the fund being added to the portfolio. This is worth stressing when practitioners routinely screen out potential investments by ranking based on Sharpe ratio alone, without considering the characteristics of the portfolio itself. Furthermore, it is important to pick a risk reward measure that captures the perceived risk factors. One can capture non-normality of the return distribution by introducing higher moments. Martellini and Ziemann (2007) looked at the impact of higher order components on portfolio selection. The marginal analysis presented can be done with alternative measures of risk.
This article is certainly not the best that I have seen on the subject, and In my opinion, doesn’t do very much to either educate managers regarding new uses of the Sharpe ratio, nor provide a new tools for managers in analyzing the effect of changes to their portfolio. First, if one truly understands the Sharpe ratio it would be quite an obvious interpretation to use it in both global terms and also as a measure of the prudence of partial changes. Second, it is quite clear that the Sharpe ratio itself has significant shortcomings – most notably its assumption of normalcy. In the aftermath of a very serious economic downturn which was caused in no small part due to the reliance on simple statistical methods who’s assumptions turned out not to be correct, I would argue that it is quite dangerous to over inflate the utility of a tool such as the Sharpe ratio.
Sharpe Ratio is useful for quick mental calculations, but has many flaws in it and cannot be used for portfolio management on a stand-alone basis. Usage of Sharpe alongwith higher statistical moments is paramount and the order of the day.
This article fails to address to the following points:
As noted by previous readers, the ratio assumes normalcy of return distribution; whereas introduction of options and option spreads in the portfolio gives way to skewness and kurtosis. In addition to that, as seen in the recent past (2nd half of 2008), liquidity risk measurement plays an important role in portfolio management decisions. Using Sharpe ratio for these estimations renders it useless. Also, Sharpe ratio overlooks serial correlation in the data set, which in turn overstates Sharpe Ratio.