Overlapping returns

Daily excess returns are iid with variance $\sigma^2$. You compute 20-day forward returns $Y_t$ on each of $N=500$ consecutive days. (a) Show that for $N\ge h$, exactly, $\operatorname{Var}(\bar Y)=\frac{\sigma^2}{N^2}\sum_{k=-(h-1)}^{h-1}(N-|k|)(h-|k|)$. (b) Evaluate it for $h=20$, $N=500$, and compare with $h^2\sigma^2/N$ and the naive $h\sigma^2/N$. (c) A research note reports $t=4.0$ using the naive standard error. What is the corrected $t$?