- Assume there is a $10$-year project whose annual return has normal distribution with parameters ${\rm N}\left(\mu,\sigma\right)$. $\mu$ and $\sigma$ are known.
- Now I wanna know what is the distribution of $10$-year return of this project $?$. I mean what is the type of $10$-year return distribution and its parameters $?$.
- e.g. in deterministic space if annual return is $15 \%$, $10$-year return will be $1.15^{10} - 1$
I think the answer is :$\mu_{new}\ =\ (1+\mu)^{10}-1$ and $\sigma_{new}\ =\ \left(1 + \sigma\right)^{10} - 1$.
Am I right $?$. Thanks.