Annualizing the Sharpe Ratio from Daily Returns

Summary

The document examines how to convert a daily Sharpe ratio into an annual figure. It illustrates the issue with a daily mean return and standard deviation, then compares compounding the average return over a year with scaling volatility by the square root of the number of periods. The replies give two practical clarifications: the conventional annualization of a daily Sharpe ratio is to multiply it by the square root of the assumed periods per year, and the numerator should use excess returns after subtracting the risk-free rate.

The discussion highlights that annualizing the mean return through compounding and scaling standard deviation are not interchangeable operations in a Sharpe calculation. Its guidance is brief and does not derive the relationship or discuss assumptions such as serial correlation, changing volatility, or the choice of trading-day convention. The square-root scaling is therefore a common convention whose appropriateness depends on return behavior and the sampling frequency.

Key ideas

• A common convention annualizes a daily Sharpe ratio by multiplying it by the square root of the annual observation count.
• The Sharpe numerator should use mean excess return after subtracting the risk-free rate.
• Compounding a mean return and scaling volatility are distinct operations.
• The square-root rule depends on assumptions about how returns behave over time.

Tags

# Sharpe Ratio - Daily vs Annual


# Sharpe Ratio - Daily vs Annual












How do I go from daily to annual sharpe?

Say I have an asset with average daily return of `0.1%` and a daily return standard deviation of `1%`.

My daily sharpe ratio is `0.1%/1% = 0.1`

Now let me annualize, assuming 365 trading days. 0.1% daily return is `(1+0.1%)^365 - 1 = 44% ` per year. (fixed, thanks commentors). While 1% sd becomes `1%*sqrt(365) = 19.1%` annualized.

My annual sharpe is `44/19.1 = 2.30`

Now I think that's not correct, because others calculate yearly return linearly as `0.1% * 365` instead of compounding `(1.01)^365-1` but I don't see how that makes sense.

Thanks, Paul

## Answer by Julie Taylor (score 1)

https://quant.stackexchange.com/a/66283

I think standard is to do sqrt(365) * daily Sharpe ratio

## Answer by Patrick Burka (score 0)

https://quant.stackexchange.com/a/82347

when calculating your Sharpe ratio, you need to subtract the risk free rate from the mean of the returns in the numerator.

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