# How to derive the sharpe ratio for an intraday strategy

I have an intraday strategy, which will place 0-5 trades for each intraday trading session. (Note that some days it will not place any trades out). The average duration of a trade is around 33 minutes.

From my understanding, the sharpe ratio formula is calculated as mean of excess return of all the trades divided standard deviation of excess return of all the trades. $$E(Excess\; Return) / \sigma({Excess\;Return})$$ Excess return is return of a trade ($$trade\;side \times (\frac{executed\;price}{cost} - 1)$$) minus the risk free rate.

Now to calculate the annualized Sharpe ratio, it's normally multiply by $$\sqrt{252}$$. My question is would the calculation of sharpe ratio be different for my intraday strategy ? Would I use a different multiplier other than $$\sqrt{252}$$ ?

• I honestly do not understand why a detailed question like this is being closed ... Dec 6, 2022 at 13:38
• See quant.stackexchange.com/review/close/42382 . Appears to be a split decision, which on most sites would leave a question open. QF seems to close discussion fast and often. Dec 6, 2022 at 16:44
• Your question seems to have multiple (related) sub questions which is indeed not very focused. Are you able to split of one of the sub questions into a separate question? Note, that you're more likely to get answers on multiple focused questions: people that might be able to answer a part might not do so because they don't want to or can not answer another part. Dec 6, 2022 at 19:43
• ok removed the sub questions on transaction cost and margin. Please re-open the question Dec 7, 2022 at 4:42

My suggestion is: simulate you trading strategy over a test period of $$N$$ days. On days when there are no trades, the calculation is easy: the excess return is zero. On other days do a realistic simulation, including rules on position sizing based on your account balance that day (assume you start the first day with 1,000,000 USD), whether you use leverage or not, whether you allow overlap (opening a 2d trade while the first is still under way), what the transaction costs are, etc. Then from the $$N$$ daily returns compute the Sharpe Ratio in the normal manner.
• actually, if there are some buy and sell trades same day, can i just compute daily return as cumprod(1+rt) - 1, where rt is the series of returns from each individual trades ? Dec 7, 2022 at 9:56
• If two trades are run in parallel (or with overlap) for ex. buy Stock A and Stock B in the morning, sell them in the afternoon then the combined return is avg(rt). Only if the trades are sequential can you use the profits from the first trade in the second in which case the combined return is cumprod(1+rt) - 1. So the precise timing, and the existence of overlap is a crucial issue. Dec 15, 2022 at 9:45
• in my case, I am only trading one security, so buy and selling it in non-overlapping time interval. In that case , i can use cumprod(1+rt) - 1 then Dec 16, 2022 at 1:55