Suppose there are k different stocks in a stock market. All of their prices are independent from each other. One year from now the price of the i-th stock will be $X_i^2$, where $X_i \sim \mathcal{N}(0,1) $ What is the distribution of the value of a portfolio after a year if I buy a $1 piece from each stock?
Will it be simple the Chi-squared distribution with parameter k?