E$.$ Your client has decided that the risk of the bond portfolio is acceptable and wishes to leave it as it is$.$ Now your client has asked you to use historical returns to estimate the standard deviation of Blandy$$s stock returns. $($Note: Many analysts use $4$ to $5$ years of monthly returns to estimate risk, and many use $52$ weeks of weekly returns; some even use a year or less of daily returns. For the sake of simplicity, use Blandy$$s $10$ annual returns.$)$

F$.$ Your client is shocked at how much risk Blandy stock has and would like to reduce the level of risk. You suggest that the client sell $25\%$ of the Blandy stock and create a portfolio with $75\%$ Blandy stock and $25\%$ in the high$-$risk Gourmange stock. How do you suppose the client will react to replacing some of the Blandy stock with high$-$risk stock? Show the client what the proposed portfolio return would have been in each year of the sample. Then calculate the average return and standard deviation using the portfolio$$s annual returns. How does the risk of this two$-$stock portfolio compare with the risk of the individual stocks if they were held in isolation?

G$.$ Explain correlation to your client. Calculate the estimated correlation between Blandy and Gourmange. Does this explain why the portfolio standard deviation was less than Blandy$$s standard deviation?

H$.$ Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio$$s risk?