Question

Problem 2 (15 points) You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky portfolio with an expected rate of return of 16% and a standard deviation of 20% and a treasury bill with a rate of return of 5%. a) what percentage of your complete portfolio should be invested in the risky portfolio il you want your complete portfolio to have a standard deviation of 9%? b) The slope of the capital allocation line formed with the risky portfolio and the risk- free asset is c) You have $500,000 available to invest. The risk-free rate as well as your borrowing rate is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return, you should borrow $__

Answer 1

a) Portfolio SD = SD x Weight

=> 9% = 20% x Weight

=> Weight = 45% should be the percentage of risky portfolio

b) Slope = Difference in returns / Difference in SD = (16% - 5%) / (20% - 0%) = 0.55

c) Assume you invest y in risky and 1-y in risk-free,

=> 22% = 16% x y + 8% x (1 - y)

=> y = (22 - 8) / (16 - 8) = 1.75 = 175%

1 - y = -75% is the weight of risk-free rate.

Hence, you need to borrow = 500,000 x 75% = $375,000