# 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?

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

...you invest 35% in A, 45% in B and 20% in the risk-free asset?

For a portfolio
Beta of portfolio= beta p=summation of wi* beta i= w1* beta 1 + w2*beta 2+ w3beta 3 + w4beta 4+---

Security Weight (wi) Beta beta i wi beta i Explanation
Security A 35.00% 1.20 0.4200 =35.%*1.2
Security B 45.00% 0.80 0.3600 =45.%*0.8
Treasury Bill 20.00% 0.00 0.0000 =20.%*0
Total= 100.00% 0.7800

(Note beta of risk free asset =0)
Beta of the above portfolio= 0.78

5) What is the portfolio expected return if you invest 35% in A, 45% in B and 20% in the risk-free asset?

We will use Capital Asset Pricing Model (CAPM) to answer this question

CAPM (Capital Asset Pricing Model) equation is:
r A= r f + beta A (r m - r f)

risk free rate= r f = 4% (Given)
beta of stock= beta A= 0.78 (calculated above)
return on market portfolio= r m = 14%
required return on portfolio r A = to be determined
Plugging in the values
r A = 11.8 % =4.%+0.78*(14.%-4.%)