Assume that investors can borrow and lend at risk-free rate of 5%. The optimal t
ID: 2801305 • Letter: A
Question
Assume that investors can borrow and lend at risk-free rate of 5%. The optimal tangent portfolio on the efficient frontier has an expected return of 15%, and STD of 20%. John would like to construct his complete investment portfolio by allocating funds between the risk-free asset and the optimal tangent portfolio. Which of the following complete portfolios can John NOT achieve? a. Portfolio A with E(R)=17.5% and STD=25% b. Portfolio B with E(R)=13% and STD=18% c. Portfolio C with E(R)=10% and STD=10% d. Portfolio D with E(R)=5.5% and STD=1% e. None of the above.
Explanation / Answer
Reward to risk ratio on the tangent=(15%-5%)/20%=0.5
Hence, Portfolio should be on the line, E(r)=Rf+s.d.*reward-to-risk ratio=0.05+0.5*s.d.
Portfolio A: For STD=25%, E(R)=0.05+0.5*25%=17.5%
Portfolio C: For STD=10%, E(R)=0.05+0.5*1%=5.5%
Portfolio B: For STD=18%, E(R)=0.05+0.5*18%=14% All other portfolios are having E(r) same as predicted But we see that Portfolio B has E(R)=13% hence this portfolio cannot be achieved by John