Your uncle Bob has asked you for some financial advice. His retirement savings are currently invested as follows: $30,000 in the riskless asset and $70,000 in GM stock. Denote his portfolio by p. Suppose that the riskless return is rf = 0.07, that the expected return on GM stock is E (rGM ) = 0.166, and that the standard deviation on GM stock is σGM = 0.482.

(a) What is the expected return on his portfolio, p? What is the standard deviation of his portfolio, p?

(b) You worry that Bob’s portfolio is not very diversified and consider whether he could do better investing in a combination of the riskless asset (f) and a stock market index fund (m). Suppose the stock market index fund has an expected return of E (rm) = 0.15 and a return standard deviation of σm = 0.22. Construct a portfolio (denote it by p∗) of f and m that has the same expected return as Bob’s current portfolio (i.e. derive the appropriate mix of f and m).

(c) What is the standard deviation of the portfolio you suggested in (b)?