Investors around the world use the Sharpe ratio, among other risk-adjusted metrics, to compare the performance of mutual fund and hedge fund managers, as well as asset classes and individual securities. The Sharpe ratio attempts to describe the excess return relative to the risk of the strategy or investment, i.e. the return minus the risk-free rate divided by volatility, and is among the leading indicators of the performance of fund manager
But hidden within the Sharpe ratio is the assumption that volatility, the denominator of the equation, captures “risk” in its entirety. Of course, if volatility does not fully reflect the risk profile of the investment, then the Sharpe ratio and similar risk-adjusted measures can be flawed and unreliable.
What are the implications of this conclusion? A common one is that the distribution of returns must be normal or Gaussian. If there is significant asymmetry in the returns of the security, strategy or asset class, the Sharpe ratio may not accurately describe “risk-adjusted returns”.
To test the effectiveness of the metric, we constructed distributions of monthly returns for 15 global stock indexes to determine whether any had skewed enough to question the applicability of the measure. The distribution of yields dates back to 1970 and was calculated on a monthly and annual basis. The monthly distributions of profitability are presented at once. The annual profitability results were qualitatively similar between the different indices studied.
We ranked the 15 indices according to their ease. The S&P 500 was near the middle of the pack on this measure, with an average return of 0.72% and an average monthly return of 1%. Therefore, the S&P distribution is slightly skewed to the left.
Distributions of monthly S&P 500 returns, since 1970
The complete list of indices ranked by their ease is presented in the chart below. Ten of the 15 indices have a left tilt or crash risk: they are more prone to sharp dips than sharp rises. The least skewed distributions were those of the CAC 40 in France and the Heng Seng in Hong Kong, SAR.
Monthly returns by global index
| index | To mean | average | Min. | Max. | std | Ses |
| ASX 200 | 0.58% | 1.01% | -42.3% | 22.4% | 0.048 | -1.3 |
| TSX | 0.60% | 0.88% | -22.6% | 16% | 0.044 | -0.77 |
| FTSE | 0.53% | 0.91% | -27.6% | 13.7% | 0.045 | -0.73 |
| Russell 2000 | 0.84% | 1.60% | -21.9% | 18.3% | 0.055 | -0.55 |
| S&P 500 | 0.72% | 1.00% | -21.8% | 16.3% | 0.044 | -0.45 |
| DAX | 0.67% | 0.74% | -25.4% | 21.4% | 0.056 | -0.39 |
| Nikkei | 0.54% | 0.91% | -23.8% | 20.1% | 0.055 | -0.37 |
| NSC | 1.23% | 1.16% | -29.5% | 20.4% | 0.066 | -0.34 |
| MOEX | 1.29% | 1.63% | -30% | 33% | 0.079 | -0.29 |
| CAC 40 | 0.64% | 0.98% | -22.3% | 24.5% | 0.056 | -0.11 |
| Hang Seng | 1.17% | 1.23% | -44.1% | 67.3% | 0.090 | 0.33 |
| NSE | 1.50% | 1.05% | -24% | 42% | 0.076 | 0.53 |
| KRX | 0.90% | 0.49% | -27.3% | 50.7% | 0.074 | 0.80 |
| BVSP | 5.63% | 1.94% | -58.8% | 128.6% | 0.184 | 2.51 |
| SSE | 1.65% | 0.63% | -31.2% | 177.2% | 0.151 | 6.26 |
The Shanghai Composite has shown the greatest degree of correct insomnia over time, tending to crash more than bear down and otherwise generate average returns of 1.65% per month and average returns of 0.63% per month.
Monthly distribution of Shanghai Composite (SSE) returns, since 1990
At the opposite end of the spectrum is the Australian ASX. Of all the indices, the ASX has the furthest session to the left, with an average monthly return of 0.58% and an average monthly return of 1.01% since 1970.
Australian Stock Exchange (ASX) monthly return distributions, since 1970
In the end, the BSVA in Brazil, the Shanghai Composite in China, and, to a lesser extent, the ASX in Australia, have just too much skew in their returns to validate the Sharpe ratio as an adequate measure of their equity-adjusted performance. risk As a consequence, metrics that take into account the skewness of returns may be better indicators in these markets.
Of the other indices, seven had fairly symmetrical distributions and five had a moderately skewed one. All in all, this suggests that the Sharpe Ratio still has value as a performance metric and that it may not be as outdated or ineffective as its critics claim.
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All posts are the opinion of the author. Therefore, they should not be construed as investment advice, nor do the views expressed necessarily reflect the views of the CFA Institute or the author’s employer.
Image credit: ©Getty Images/NPHOTOS
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Derek Horstmeyer
Katherine Vargas Medina
Lincoln Berkson
