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Interpreting Annualised Sharpe Ratios for Equity Index Benchmarks

Article Quant Q&A · Author: deon
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Summary

The document discusses comparing alternative energy equity indexes with broad benchmarks using monthly excess returns. The proposed calculation subtracts a one-month USD LIBOR rate from monthly logarithmic index returns, then divides the average excess return by the standard deviation of returns. Annualisation scales the mean by the number of months in a year and the monthly standard deviation by its square root.

The response cautions that a negative Sharpe ratio need not result from choosing an unsuitable risk-free rate or from the 2008 crisis alone: it can arise when the underlying average return is negative. It offers a broad-market tracking ETF's historical performance as an informal indication, rather than a direct calculation using the exact index series. The note does not assess whether the return convention, risk-free-rate alignment, or annualisation choices are appropriate, so those details still require careful checking in a rigorous benchmark study.

Key ideas

  • A Sharpe ratio compares average excess return with return variability.
  • Monthly returns can be annualised by scaling the mean and standard deviation differently.
  • A negative average return can produce a negative Sharpe ratio regardless of the chosen risk-free rate.
  • Evidence from a tracking ETF is only a proxy when the exact benchmark series is unavailable.

Tags

EquitiesStatisticsRisk management
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# Annualised Sharpe Ratio for Index vs Index Benchmarking


# Annualised Sharpe Ratio for Index vs Index Benchmarking












I am currently writing a paper about the performance characteristics of alternative energy equity indexes and am therefore comparing them to their benchmark indexes (msci world, etc). To calculate the Sharpe Ratio i first take the logarithmic difference of monthly index returns and then subtract it by 1 month LIBOR USD rate over my complete dataset (starting 2002). Afterwards i simply take the monthly mean excess return (as above) divided by the STDEV of the index returns. To annualise the mean monthly excess return and the STDEV i use the following formulas respectively: MEAN*12 and STDEV*SQRT(12).

My results are mostly negative Sharpe Ratios, now i am wondering if this has to do with the timeseries being affected by the 08 crisis and wether the 1 month LIBOR is the correct riskfree asset?

## Answer by phdstudent (score 3)

https://quant.stackexchange.com/a/18746

I do not have access to the exact time-series of the MSCI world, but looking at the returns from the tracking ETF, since 2001 the average return is negative. Thus regardless of the risk-free you use you will get a negative sharpe ratio.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.