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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?

#### Solution Preview

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.

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