Annualized Sharpe Ratio

Sharpe ratio scales with the square root of the number of periods when returns are i.i.d.

Multiply the daily Sharpe ratio by $\sqrt{252}$.

1. 1. Recall Sharpe ratio scaling

   For i.i.d. returns, mean scales linearly with time while standard deviation scales with the square root of time, so the Sharpe ratio scales with $\sqrt{n}$ over $n$ periods.

   $${\text{Sharpe}}_{\text{annual}}={\text{Sharpe}}_{\text{daily}}\times \sqrt{252}$$

2. 2. Compute

   ${\text{Sharpe}}_{\text{annual}}=0.10\times \sqrt{252}\approx 0.10\times 15.8745\approx 1.587$.

   $$0.10\times \sqrt{252}\approx 1.587$$

Answer: 0.10 * sqrt(252)