A release-checked easy problem for training Expected Value.
Question
Suppose you purchase a $1$ share of stock $A$. A share of stock $A$ has mean return $2$ and return variation $4$. You also want to purchase stock $B$. $1$ share of $B$ has mean return $3$ and return variation $9$. Additionally, the returns of $A$ and $B$ are correlated with coefficient $-1/2$. How many shares of stock $B$ should you purchase so that the variance of your portfolio consisting of both $A$ and $B$ is minimum?
Practice focus
This Probability problem is tagged Expected Value. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.