# When the Sharpe ratio falls flat

Is it reasonable for investors and grantees to use the Sharpe ratio in their decision-making process?

Before answering “yes”, think about how the Sharpe ratio works. It attempts to compare returns to risk by taking a portfolio’s excess return (i.e. the difference between the portfolio’s return and the risk-free rate) and dividing it by the standard deviation of the portfolio excess return. This measure is then compared to certain alternative portfolios to discern which offers the highest degree of risk compensation; The higher the number the better. Comparing Sharpe ratios might be the most commonly used tool for selecting funds or assessing the portfolio impact of adding a new asset class.

But he has some problems.

The funny thing is that Sharpe ratios can be negative. Let’s say we’re comparing the performance of mutual funds that all underperformed the risk-free rate (because the markets just crashed, say). If we choose the one with the highest Sharpe ratio, we choose the fund with the greatest volatility, rather than the least, since a negative number divided by a large number is greater than that negative number divided by a small number.

Another kind of annoying thing about the Sharpe ratio is that since the standard deviation measures both upward and downward deviations, the ratio gives the same eye to big wins and big losses. Some say this approach forces us to “assume that investors are indifferent between upside risk and downside risk” when investors are in fact risk averse; more strongly, the ratio is accused of “penalizing positive volatility”. On the other hand, it can be argued that a steady streak of moderate wins is better than a bulkier approach of small wins with a huge odd. It is also possible that portfolios that have gained a lot in a short time will lose a lot just as quickly.

A potentially bigger problem is that market returns may not be normally distributed. Readers who have visited my home office will know that I maintain a framed rendition of The Anscombe Quartet (painted by Hudson Valley artist Thomas Levine) on my wall. It’s a reminder that data sets that appear identical when described by their mean or variance can in fact vary widely. In the case of the Sharpe ratio, the problem is that the mean and standard deviation only adequately describe sets that are normally distributed. It’s just not a good way to compare sets where standard deviation doesn’t describe risk – for example, the returns of derivative funds (like the dear departed Allianz Structured Alpha Fund).

Which brings us back to our original question: is it reasonable to use the Sharpe ratio?

Derek Horstmeyer, a professor at the George Mason University School of Business, along with students Katherine Vargas Medina and Lincoln Berkson, recently took a look. In a Publish published on the CFA Institute’s Enterprising Investor blog, the trio analyze how normal the distributions of returns for various markets have been. Looking at monthly return data going back to 1970 for a range of global stock markets, they find:

[T]The BSVA in Brazil, the Shanghai Composite in China and, to a lesser extent, the ASX in Australia simply have too much asymmetry in their returns to validate the Sharpe ratio as an appropriate measure of their risk-adjusted performance. Therefore, metrics that take into account the asymmetry of returns may be better indicators in these markets. Among other clues [including the S&P 500], seven had fairly symmetrical distributions and five had moderately skewed distributions. All told, this suggests that the Sharpe ratio still has value as a performance metric and may not be as outdated or inefficient as its critics claim.

As Horstmeyer explained in a phone interview, the takeaway is that based on the “general normality of returns, we can say that we can use the Sharpe ratio to compare mutual fund managers from placement”.

But there is a small problem here, which goes right to the question of what history can tell us about the future. Some have speculated that stock market returns over time show part of the compensation for the risk of crashes that didn’t happen (and not just those that did). In his 1988 article “The Equity Risk Premium: A Solution”, Thomas Rietz writes that he can solve the mathematical “mystery” of high stock returns by adding “a low-probability, depression-like third state”. He explains:

With the addition of a crash state, the model explains both high equity risk premia and low risk-free returns…. it does so with reasonable degrees of time preference and risk aversion, provided the crash is plausibly severe and not too unlikely.

The returns look so good, in other words, because this possible crash was never encountered in the dataset. And Horstmeyer, for his part, is quick to acknowledge that the data he used for his recent research “covers a very good period of history.”

It’s good to know that in diets like the one we’ve had for the past half century, the Sharpe ratio is useful. Yet its value for long-term decision making is likely to be limited.

To give a specific example, if you’re an advisor looking to answer a couple’s questions about long-term risk and return, it’s still a bit ironic to take too much comfort from long-term data. There’s a kind of weird, half-hidden survival bias here: if the US market crashed hard and never rebounded, this pair probably wouldn’t have particularly much wealth to manage!

*Accept? To disagree? Let us know what you think – email Alex Rosenberg at [email protected]*