Choosing Return Frequency for Sharpe Ratios in Pair Trading

Summary

The document considers how to calculate and annualize the Sharpe ratio for a mid-frequency pairs strategy whose positions typically last several days and whose trades occur a few times per month. The questioner expects monthly returns to show mostly realized profits, while daily returns capture interim gains and losses, and suspects the monthly calculation may produce a higher annualized ratio.

One response recommends daily returns because they provide more observations and can make the estimated standard deviation more precise; it uses yearly returns as an example of a sparse sample. Another suggests comparing the statistical significance of estimates using a t-statistic that accounts for sample size and degrees of freedom. The discussion offers guidance, not calculations or evidence from the strategy itself. Return frequency, dependence across observations, and the handling of open positions can affect estimates, so the choice should reflect the evaluation objective and consistent return measurement rather than assuming annualization makes different samples equivalent.

Key ideas

• Daily returns provide more observations than monthly returns for estimating a Sharpe ratio.
• The response argues that a larger sample can improve the precision of the standard deviation estimate.
• A second answer recommends considering a t-statistic when comparing estimates based on different frequencies.
• The discussion does not calculate either Sharpe ratio or assess the strategy’s actual performance.

Tags

# How should I compute the Sharpe Ratio for mid-frequency pair trading strategy?


# How should I compute the Sharpe Ratio for mid-frequency pair trading strategy?












I have a pair trading strategy with positions that last 3-5 days and trades 2-3 times a month. By design, all the trades are profitable until the cointegration is broken.

Should I calculate the Sharpe ratio with daily or monthly returns? (annualizing afterwards in each case)

With monthly returns, most positions will be closed so I will have mostly profits (and maybe a loss if there's an open position at the end of the month).

With daily returns, I will have partial profit and losses each day.

I haven't done the calculations yet, but seems to me that the annualized Sharpe ratio of the monthly returns will be higher than the one with the daily returns, even with the difference of the annualization factors $\sqrt{12}$, $\sqrt{252}$ respectively.

## Answer by chrisaycock (score 6, accepted)

https://quant.stackexchange.com/a/3594

Sharpe should only be computed from daily returns because finer granularity leads to a larger sample size. The larger sample makes the standard deviation metric more accurate. As a counter-example, how reliable would the Sharpe be using yearly returns?

## Answer by Suminda Sirinath S. Dharmasena (score 2)

https://quant.stackexchange.com/a/3595

I think that it is better to look at t-stat than at the Sharpe Ration itself with data using different frequencies (thus different df) in order to determine which Sharpe Ratio stat is more accurate.

The calculation can be found in this paper: The Statistics of Sharpe Ratios.

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