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 $\sqrt{252}$ ?