Annualizing Sharpe Ratios for Monthly Decile Portfolio Returns
Summary
The document asks how to calculate ex post Sharpe ratios for decile portfolios formed from monthly returns and held for twelve months. It contrasts measuring excess returns over the full holding period with calculating monthly excess returns and annualizing the resulting Sharpe ratio. The risk-free benchmark in the example is the one-month Treasury bill rate.
The answer describes a monthly-frequency procedure: subtract the monthly risk-free rate from each portfolio return, calculate the average and standard deviation of those monthly excess returns, and form a monthly Sharpe ratio. It then says to annualize that ratio to express it in a twelve-month context. This gives a practical comparison framework across deciles, but the document does not specify the annualization formula or discuss assumptions such as serial correlation, overlapping holding periods, or whether monthly observations align with the portfolio return construction. It supplies no portfolio data or performance results.
Key ideas
- Calculate excess returns by subtracting the monthly risk-free rate from each monthly portfolio return.
- Use the average and standard deviation of monthly excess returns to compute a monthly Sharpe ratio.
- Annualize the monthly ratio to report it on a twelve-month basis.
- The example compares decile portfolios using monthly returns and a one-month Treasury bill benchmark.
- The document does not discuss serial dependence or provide empirical Sharpe estimates.
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# Calculating Ex Post Sharp Ratio's for decile portfolios # Calculating Ex Post Sharp Ratio's for decile portfolios Dear Stack community, I hereby would like to ask what the correct calculation is for calculating Ex Post Sharp Ratio's. If I am correct, I already know that I am supposed to divide the average excess return by the standard deviation of the excess returns. For my data I am using monthly return series, and I am using one month treasury bills as the risk free rate, I am comparing decile portfolio's which have twelve month buy and hold returns (which have been calculated as); Cumulative n-period return =(1+r1) * (1+r2) (1+r3) ... (1+rn) - 1 I am now wondering whether I should do the same for the risk free rate to get the cumulative twelve month risk free rate. And then take the average of this difference (excess return) for every portfolio. And divide this by the standard deviation of the total excess returns within each portfolio. Or whether instead I should take the difference on a monthly basis and annualize this number. And then take the standard deviation of these monthly excess returns and annualize it. To then divide the first by the latter. Is any of the two correct? Or do you have any other suggestions. Kind regards, Julien Maas ## Answer by Julien Maas (score 0) https://quant.stackexchange.com/a/77368 Based on this calculation by morningstar; https://awgmain.morningstar.com/webhelp/glossary_definitions/mutual_fund/mfglossary_Sharpe_Ratio.html It is possible to report the annualized Sharpe ratio, by first calculating the excess returns each month and the standard deviation of these excess returns to then calculate the Sharpe ratio for each month. Then we can annualize this number to get the annualized Sharpe ratio which puts the number in a twelve month context. In this case, because I want to report these for each decile portfolio I can take the monthly average excess return of the decile portfolio as the numerator and the monthly standard deviation of the excess returns of the decile portfolio as the denominator to calculate monthly Sharpe ratio's for each decile and then annualize these to get the annualized Sharpe ratio's for each decile.
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