Investors around the world use the Sharpe Ratio, along with 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 is a measure that aims to describe the excess return relative to the risk of a strategy or investment. It is calculated by subtracting the risk-free rate from the return, and then dividing it by the volatility. The Sharpe Ratio is considered one of the key indicators of fund manager performance.
However, the Sharpe Ratio relies on the assumption that volatility captures the entirety of “risk.” If volatility fails to accurately reflect the investment’s risk profile, then the Sharpe Ratio and similar risk-adjusted measures may be flawed and unreliable.
What are the implications of this conclusion? One common implication is that the distribution of returns must be normal, or Gaussian. If there is significant skewness in the returns of a security, strategy, or asset class, then the Sharpe Ratio may not accurately describe “risk-adjusted returns.”
To test the effectiveness of the Sharpe Ratio, we analyzed monthly return distributions for 15 global stock market indices. We examined whether any of these indices exhibited significant skewness that could question the applicability of the measure. The return distributions were analyzed from 1970 onwards, on both a monthly and annual basis. The monthly return distributions are presented below. The annual return results showed similar patterns across the various indices studied.
We ranked all 15 indices based on their skewness. The S&P 500 index fell in the middle of the pack, with an average monthly return of 0.72% and a median monthly return of 1%. This indicates a slight left skew in the distribution.
S&P 500 Monthly Return Distributions, Since 1970
The complete list of indices ranked by their skewness is presented in the chart below. Ten out of the 15 indices exhibited left skewness, indicating a higher likelihood of significant downturns compared to steep upward climbs. The least skewed distributions were found in France’s CAC 40 and Hong Kong’s Heng Seng index.
Monthly Returns by Global Index
| Index | Mean | Median | Min. | Max. | STD | Skewness |
| 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 |
| MXX | 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 index exhibited the highest degree of right skewness over time, indicating a tendency to experience significant upward movements compared to downturns. It generated average monthly returns of 1.65% and median monthly returns of 0.63%.
Shanghai Composite (SSE) Monthly Return Distribution, Since 1990
On the opposite end of the spectrum is the Australian ASX. The ASX has the most left skewness among all the indices, with an average monthly return of 0.58% and median monthly return of 1.01% since 1970.
Australian Stock Exchange (ASX) Monthly Return Distributions, Since 1970
For the BSVA in Brazil, the Shanghai Composite in China, and to a lesser extent, the ASX in Australia, there is too much skewness in the returns to consider the Sharpe Ratio as an appropriate measure for risk-adjusted performance. Skewness-adjusted metrics may be more suitable in these markets.
Among the other indices, seven had fairly symmetrical distributions, and five had moderately skewed distributions. This suggests that the Sharpe Ratio still holds value as a performance metric and may not be as outdated or ineffective as its critics argue.
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All posts are the opinion of the author. Therefore, they should not be considered as investment advice, and the opinions expressed do not necessarily reflect the views of CFA Institute or the author’s employer.
Image credit: ©Getty Images/NPHOTOS
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