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How sharp is the Sharpe ratio? An analysis of global stock indices

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Investors around the world use the Sharpe ratio, among other risk-adjusted measures, 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 excess return over the risk of the strategy or investment – ​​i.e. the return minus the risk-free rate divided by the volatility – and is one of the main performance indicators of the fund manager.

But hidden in 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, the Sharpe ratio and similar risk-adjusted measures can be erroneous and unreliable.

What are the implications of such a conclusion? A common rule is that the distribution of returns should be normal or Gaussian. If there is a 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 measure, we constructed monthly return distributions for 15 global equity indices to determine whether any had an asymmetry exacerbated to the point of questioning the applicability of the measure. The distribution of returns dates back to 1970 and was calculated on a monthly and annual basis. The monthly return distributions are shown below. Annual returns were qualitatively similar across the various indices studied.

We have classified the 15 indices according to their asymmetry. The S&P 500 was near the middle of the pack on this metric, with an average return of 0.72% and a median return of 1% per month. So the S&P distribution is leaning just a little to the left.

S&P 500 monthly return distributions, since 1970

Bar chart showing monthly return distributions of the S&P 500, since 1970

The complete list of indices classified according to their asymmetry is presented in the table below. Ten of the 15 indices present a left asymmetry or a risk of accident: they are more prone to pronounced dives 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 by global index

IndexMeanMedianMin.Max.STDAsymmetry
ASX 2000.58%1.01%-42.3%22.4%0.048-1.3
TSX0.60%0.88%-22.6%16%0.044-0.77
FTSE0.53%0.91%-27.6%13.7%0.045-0.73
Russell 20000.84%1.60%-21.9%18.3%0.055-0.55
S&P5000.72%1.00%-21.8%16.3%0.044-0.45
DAX0.67%0.74%-25.4%21.4%0.056-0.39
Nikkei0.54%0.91%-23.8%20.1%0.055-0.37
MXX1.23%1.16%-29.5%20.4%0.066-0.34
MOEX1.29%1.63%-30%33%0.079-0.29
CAC 400.64%0.98%-22.3%24.5%0.056-0.11
Hang Seng1.17%1.23%-44.1%67.3%0.0900.33
NSE1.50%1.05%-24%42%0.0760.53
KRX0.90%0.49%-27.3%50.7%0.0740.80
BVSP5.63%1.94%-58.8%128.6%0.1842.51
SSE1.65%0.63%-31.2%177.2%0.1516.26

The Shanghai Composite has shown the greatest degree of right skew over time, tending to break more than down, and otherwise generating average returns of 1.65% per month and median returns of 0.63% per month.

Breakdown of Shanghai Composite (SSE) monthly returns, since 1990

Chart showing the distributions of Shanghai composite monthly returns, since 1990

At the opposite end of the spectrum is Australia’s ASX. The ASX has the largest left skew of any index, with an average monthly return of 0.58% and a median monthly return of 1.01% since 1970.

Distributions of monthly Australian Stock Exchange (ASX) returns, since 1970

Chart showing Australian Stock Exchange (<span>ASX</span>) Monthly return distributions, since 1970″ loading=”lazy”/></figure></p><p class=Ultimately, 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 performance. risk adjusted. Therefore, metrics that take into account the asymmetry of returns may be better indicators in these markets.

Of the other indices, 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.

Disclaimer: Please note that the content of this site should not be construed as investment advice, and the opinions expressed do not necessarily reflect the views of CFA Institute.

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Editor’s note: The summary bullet points for this article were chosen by the Seeking Alpha editors.

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