Annualizing Sharpe Ratios from Monthly Returns

Summary

The note addresses a common frequency mismatch when calculating an annual Sharpe ratio from monthly asset returns. The questioner subtracts an annual risk-free rate from the average monthly return, while annualizing the standard deviation. The accepted response identifies the issue: the mean return must also be converted to an annual basis before comparing it with the annual risk-free rate.

For the stated quiz setup, the response scales the monthly average return by twelve, subtracts the annual risk-free rate, and divides by monthly standard deviation multiplied by the square root of twelve. The quiz instructions specify population standard deviation, though the response’s spreadsheet formula uses the sample-standard-deviation function; that distinction can affect the result. The calculation also relies on the stated annualization convention and does not discuss compounding or whether a different periodic risk-free-rate conversion would be appropriate for other Sharpe-ratio definitions.

Key ideas

• Match the return and risk-free rate frequencies before calculating a Sharpe ratio.
• Under the quiz’s convention, annualize the monthly average return by multiplying it by twelve.
• Annualize monthly standard deviation by multiplying it by the square root of twelve.
• The quiz specifies population standard deviation, while the suggested spreadsheet function calculates sample standard deviation.

Tags

# Multi-year annualized Sharpe Ratio


# Multi-year annualized Sharpe Ratio












I'm taking a quiz, and trying to calculate the annualized Sharpe ratio of 11 years' worth of SPY fund monthly returns vs. a risk free investment return of 1.5%. When I write the function in Excel as `=(AVERAGE(G3:G145)-0.015)/(STDEV(G3:G145)*Sqrt(12))`, I'm getting -0.16. In my spreadsheet, G3:G145 is the range of monthly returns for the SPY fund. The possible answers for the question on the quiz are .56, .53, .50, and .48, so clearly I'm far off. What would be the correct way to write this formula in Excel?

Also, here are the exact instructions given by the quiz:

> The annual Sharpe Ratio calculates the difference between the annual return of a stock and the annual return of a risk-free investment in government bonds - then divides that difference by the annualized standard deviation of returns of the stock. Estimate the annualized standard deviation of returns by multiplying the monthly population standard deviation of returns by the square root of 12.

## Answer by Alex C (score 2, accepted)

https://quant.stackexchange.com/a/22282

You have to annualize the monthly avg return also:

=(12*AVERAGE(G3:G145)-0.015)/(STDEV(G3:G145)*Sqrt(12))

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