Investors world wide use the Sharpe ratio, amongst other risk-adjusted metrics, to check the performance of mutual fund and hedge fund managers, in addition to asset classes and individual securities. The Sharpe ratio attempts to explain the surplus return in relation to the chance of the strategy or investment – i.e. return minus the risk-free rate of interest divided by volatility – and is probably the most essential measures of fund manager performance.
But hidden within the Sharpe ratio is the belief that volatility – the denominator of the equation – captures “risk” in its entirety. Of course, if volatility doesn’t fully reflect the chance profile of the investment, the Sharpe Ratio and similar risk-adjusted measures could also be flawed and unreliable.
What are the implications of such a conclusion? A standard statement is that the return distribution have to be normal or Gaussian. If the returns of the safety, strategy or asset class differ significantly, the Sharpe ratio may not accurately describe “risk-adjusted returns.”
To test the effectiveness of the metric, we constructed monthly return distributions for 15 global stock market indices to find out whether any of those indices exhibit skewness so severe as to query the metric’s applicability. The distribution of returns dates back to 1970 and was calculated on each a monthly and annual basis. The monthly return distributions are shown below. The annual return results were qualitatively similar across the assorted indices examined.
We ranked all 15 indices in line with their skewness. The S&P 500 was near the center of the pack on this metric, with a median return of 0.72% and a median return of 1% per thirty days. The S&P distribution subsequently tends barely to the left.
Monthly return distributions of the S&P 500 since 1970
The complete list of indices ordered by their skewness is shown within the table below. Ten of the 15 indices are skewed to the left or have a crash risk: they’re more at risk of sharp nosedives than to steep climbs. The least skewed distributions were those of the French CAC 40 and the Heng Seng in Hong Kong, SAR.
Monthly returns in line with Global Index
| index | Mean | Median | Minimum. | Max. | HOURS | Skewness |
| ASX200 | 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 exhibited the best degree of right-skewing over time, tending to trend upward reasonably than downward, and otherwise yielded a median return of 1.65% per thirty days and a median return of 0.63% per thirty days.
Monthly return distribution of Shanghai Composite (SSE), since 1990
At the opposite end of the spectrum is the Australian ASX. The ASX is essentially the most left skewed of any index, with a median monthly return of 0.58% and a median monthly return of 1.01% since 1970.
Australian Stock Exchange (ASX) monthly return distributions since 1970
Ultimately, the BSVA in Brazil, the Shanghai Composite in China and, to a lesser extent, the ASX in Australia simply have an excessive amount of skewness of their returns to validate the Sharpe Ratio as an appropriate measure of their risk-adjusted performance. Therefore, metrics that bear in mind the variability of returns could also be a greater measure in these markets.
Of the opposite indices, seven had fairly symmetrical distributions and five had moderately skewed distributions. All in all, this means that the Sharpe ratio still has value as a performance metric and is probably not as outdated or ineffective as its critics claim.
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Photo credit: ©Getty Images/NPHOTOS
