Say I have a market-making strategy that trades intraday. I start with a flat position and finish flat too. I end up with a daily P&L $p_{today}$. Over a year of trading I get $\vec{p} = (p_1,\dots,p_{252})$.
There is no way to calculate returns here. As such I calculate $$Sharpe = S(\vec{p}) = \sqrt{252} \cdot \frac{\mathbb{E}[\vec{p}]}{\sqrt{\mathbb{V}[\vec{p}]}} = \sqrt{252} \cdot \frac{mean(p)}{sd(p)}$$
My questions are :
- Am I right to do it like this?
- Do you usually bootstrap your Sharpe? (I do not but I am interested in your view of it.)