In financial models, variables are often correlated, and the model must capture this statistical behavior. Variables that are correlated tend to move together but not in a completely predictable manner. Example: Price of two tech stocks are positively correlated. We can assume that the daily price changes in these two stocks are positively correlated.

$($a$)$ Suppose a client has a portfolio consisting of $12$ stocks. Assume unit time increment is one week. Compute the drift and volatility parameters from historical data.

$($b$)$ Discuss how you would do a simulation$-$optimization. That is$,$ solve a portfolio optimization problem with correlated stock val$-$ ues.