How can I calculate a cumulative density function or probability density function for investment returns based on expected return of a stock and volatility of a stock?
My current solution is below, but I am looking for feedback on whether it is correct or not, or solutions using alternative assumptions.
Assuming returns are normally distributed, the probability of returns is given by: $$ \text{Lognormal}((\mu-\sigma^2/2)T,\ \sigma\sqrt{T}) $$
Where $\mu$ is the expected return of the stock and $\sigma$ is the volatility of the stock.