Suppose there are N identical stocks. Each stock has dividendgrowth following iid Normal (mu, sigma^2). That is,


D_i,t+1 / D_it ~ N(mu, sigma^2)


for stock i between time t and t+1.


Now let’s compute the dividend growth of the entire marketin aggregate:


(sum_{i=1}^{N} D_i,t+1) / (sum_{i=1}^{N} D_it)


Could you find which distribution this one follows?

Thank you