# 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.

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?

• It also has to be done that way because almost everyone out there is doing it on daily returns. This enables clearer comparisons between strategies. Jun 10, 2012 at 9:14
• @Zarbouzou that's incorrect: Yes everyone scales Sharpe ratio to annualized terms, but it can be scaled from any other sample duration (using "annualization factors" as noted in the original post). Jul 14, 2014 at 21:28
• By this argument, shouldn't one use microsecond returns? Jun 20, 2018 at 18:20

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.

• Could you give an example? I didn't understand how to compare frequencies from the paper you linked to. Jun 11, 2012 at 0:38
• Calculate SR. The SE is given in Eq (9). To get the t-stat SR / SE(SR). Note the T in the Eq. is sample size. I hope this helps. Jun 11, 2012 at 7:51
• The paper above is not accessible. You can use this address instead: alo.mit.edu/wp-content/uploads/2017/06/… Feb 13, 2020 at 23:48
• @DavidBellot updated as suggested. Feb 14, 2020 at 4:58