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    Portfolio Return and Standard Deviation

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    Problem 2 (Chapter 13) Please use the following information to answer the following questions. The return on the risk-free asset is 4% and the return on the market is 14%.

    Security Standard Deviation Beta
    A 20% 1.2
    B 25% 0.8

    1) Which security (A or B) has the least total risk? __________________
    2) Which security (A or B) has the least systematic risk? __________________
    3) Which security (A or B) has the greatest diversifiable risk? ____________________
    4) What is the portfolio beta if you invest 35% in A, 45% in B and 20% in the risk-free asset?
    5) What is the portfolio expected return if you invest 35% in A, 45% in B and 20% in the risk-free asset?
    6) What is the portfolio expected return if you invest 140% in A and the remainder in the risk-free asset via borrowing at the risk-free interest rate?
    7) If you forecast the expected rates of returns for both Security A and security B, you get 14%. Which security should you buy/sell/hold as a result?

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    Solution Preview

    Please see attached file:
    Problem 2 (Chapter 13) Please use the following information to answer the following questions. The return on the risk-free asset is 4% and the return on the market is 14%.

    Security Standard Deviation Beta
    A 20% 1.2
    B 25% 0.8

    1) Which security (A or B) has the least total risk? __________________

    Security A has the least total risk as it has the lesser standard deviation (20 % as against 25% for B ) of the two securities.

    2) Which security (A or B) has the least systematic risk? __________________

    Security B has the least systematic risk as it has the lesser beta (0.8 as against 1.2 for a ) of the two securities.

    3) Which security (A or B) has the greatest diversifiable risk? ____________________

    Security B has the greatest diversifiable risk
    Total risk (=variance) = Systematic risk (=beta ^2 x Variance of the market ) + Diversifiable risk
    Since Security B has higher total risk and smaller systematic risk, Security B has the greatest diversifiable risk

    4) What is the portfolio beta if ...

    Solution Summary

    Answers questions on portfolio returns, standard deviation of return, beta, risk etc.

    $2.19

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