A portfolio manager forms two well‐diversified portfolios that are each sensitive to the single factor. The following information is available: Portfolio Expected Return Factor Sensitivity A 0.16 1.5 B 0.10 0.5 Based on the information given, calculate the risk‐free rate and the risk premium associated with the factor, based on the single-factor arbitrage pricing theory (APT) Portfolio C that has a factor sensitivity of 2.0 to the factor. Calculate the expected return on Portfolio C. 3. Suppose the portfolio manager forms two more portfolios, Portfolios D and E. Portfolio D has been formed by investing 50% in Portfolio A and 50% in Portfolio C. The expected return and factor sensitivity for Portfolio E are 18.5% and 1.75, respectively. Evaluate whether any arbitrage opportunity exists and comment on how an investor may exploit it.
A portfolio manager forms two well‐diversified portfolios that are each sensitive to the single factor. The following information is available: Portfolio Expected Return Factor Sensitivity A 0.16 1.5 B 0.10 0.5 Based on the information given, calculate the risk‐free rate and the risk premium associated with the factor, based on the single-factor arbitrage pricing theory (APT) Portfolio C that has a factor sensitivity of 2.0 to the factor. Calculate the expected return on Portfolio C. 3. Suppose the portfolio manager forms two more portfolios, Portfolios D and E. Portfolio D has been formed by investing 50% in Portfolio A and 50% in Portfolio C. The expected return and factor sensitivity for Portfolio E are 18.5% and 1.75, respectively. Evaluate whether any arbitrage opportunity exists and comment on how an investor may exploit it.
Chapter8: Analysis Of Risk And Return
Section: Chapter Questions
Problem 6P
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- A
portfolio manager forms two well‐diversified portfolios that are each sensitive to the single factor. The following information is available:
|
Portfolio |
Expected Return |
Factor Sensitivity |
|
A |
0.16 |
1.5 |
|
B |
0.10 |
0.5 |
- Based on the information given, calculate the risk‐free rate and the risk premium associated with the factor, based on the single-factor arbitrage pricing theory (APT)
- Portfolio C that has a factor sensitivity of 2.0 to the factor. Calculate the expected return on Portfolio C.
3. Suppose the portfolio manager forms two more portfolios, Portfolios D and E. Portfolio D has been formed by investing 50% in Portfolio A and 50% in Portfolio C. The expected return and factor sensitivity for Portfolio E are 18.5% and 1.75, respectively. Evaluate whether any arbitrage opportunity exists and comment on how an investor may exploit it.
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