A friend asks your advice about her investments. She holds in her brokerage account $20,000 worth of a Blackrock mutual fund and $5,000 in risk-free bonds. She asks you whether she should re-allocate her assets. You are analyzing the returns of the Blackrock fund and you compare them with the Vanguard index fund. You expect the Blackrock fund to have an expected return of 13% and a standard deviation of 30%. The Vanguard fund has an expected return of 10% and a standard deviation of 20%. Risk-free bonds currently yield 2%. Assume that borrowing and lending rates differ. In particular, the borrowing rate equals 8% and the lending rate equals 2%.

-What is the expected return and standard deviation of your friend's current portfolio? E[r]=.108, sigma=.24 E[r]=.13, sigma=.24 E[r]=.13, sigma=.3 E[r]=.02, sigma=.3

-Can you find a new portfolio investing in the Vanguard fund and the risk-free bond (but not the Blackrock fund) that has higher expected return and same standard deviation as your friend's current portfolio? It is not possible to create a portfolio using Vanguard and the risk free asset that has a higher expected return and the same risk as the current portfolio Yes-you need to invest 1.2*(25,000)=$30,000 in Vanguard and short the risk-free asset