Question

You invest $100 in a portfolio of stock JET and a risk-free asset with a return of 5%. JET has an expected return of 12% and a standard deviation of 10%. What is the percentage of your portfolio in the risk-free asset if your portfolio’s standard deviation is 9%? A. 30% B. 90% C. 50% D. 10%

Answer 1

stock JET = $100, risk free return Rf  = 5%, expected return R1 = 12%,

portfolio standard deviation = p = 9%

weight of risky asset = w1  ; weight of risk free asset = 1-w1  ;

standard deviation of risky asset = 1 = 10%;

standard deviation of risk free asset = 0 as their returns are same in all states of the world.

p = 9% = w11 + w22 +2w11w22*rho12

0.09 = w1*0.10 + (1-w1) *0 + 0

w1 = 0.09/.10 = 0.90 = 90%

weight of risky asset = w1  = 90%. Hence, option B is the correct answer.