Power and window length

A single firm has a one-day abnormal return $A$ on day 0 and idiosyncratic sd $\sigma$. Using the constant-mean approximation $\operatorname{Var}(CAR)\approx\sigma^2(L_2+L_2^2/L_1)$ and a normal approximation to the $t$-test with critical value 1.97, derive the power of a two-sided 5% test as a function of $L_2$. Evaluate it for $A=5\%$, $\sigma=1.5\%$, $L_1=240$ and $L_2\in\{1,3,11\}$, and compare with the simulated values 0.91, 0.49 and 0.16 in the notes.