CHAPTER 8

AN INTRODUCTION TO ASSET PRICING MODELS

Answers to Questions

1. It can be shown that the expected return function is a weighted average of the individual returns. In addition, it is shown that combining any portfolio with the risk-free asset, that the standard deviation of the combination is only a function of the weight for the risky asset portfolio. Therefore, since both the expected return and the variance are simple weighted averages, the combination will lie along a straight line.

2. Expected Rate of Return * F

M * P * * B RFR *A

E

Expected Risk (( of return)

The existence of a risk-free asset excludes the E-A segment of the efficient frontier because any point below A is dominated by the RFR. In fact, the entire efficient frontier below M is dominated by points on the RFR-M Line (combinations obtained by investing a part of the portfolio in the risk-free asset and the remainder in M), e.g., the point P dominates the previously efficient B because it has lower risk for the same level of return. As shown, M is at the point where the ray from RFR is tangent to the efficient frontier. The new efficient frontier thus becomes RFR-M-F.

3. Expected Rate of Return

M C B RFR A

E

Expected Risk