# Portfolio Return and Standard Deviation

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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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.

Bond vs stock indices; expected portfolio return; standard deviation of a portfolio

1. Why are bond market indices more difficult to construct and maintain than stock market indices?

2. An investor wishes to construct a portfolio consisting of a 70% allocation to a stock index and a 30% allocation to a risk free asset. The return on the risk-free asset is 4.5% and the expected return on the stock index is 12%. The standard deviation of returns on the stock index 6%. Calculate the expected return on the portfolio and the expected standard deviation of the portfolio.

3.

Asset (A) Asset (B)

E(RA) = 16% E(RB) = 10%

(sA) = 9% (sB) = 7%

WA = 0.5 WB = 0.5

COVA,B = 0.0009

a. What is the expected return of a portfolio of two risky assets if the expected return E(Ri), standard deviation (si), covariance (COVi,j), and asset weight (Wi) are as shown above?

b. What is the standard deviation of this portfolio?

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