Answer-first summary for fast verification
Answer: 4.0%
## Explanation Using the one-factor APT model: $$E(R_p) = R_f + \beta_p \times \lambda$$ For Portfolio X: $$8\% = R_f + 0.8\lambda$$ For Portfolio Y: $$16\% = R_f + 2.4\lambda$$ Subtract the first equation from the second: $$(16\% - 8\%) = (R_f + 2.4\lambda) - (R_f + 0.8\lambda)$$ $$8\% = 1.6\lambda$$ $$\lambda = 5\%$$ Now substitute back into Portfolio X's equation: $$8\% = R_f + 0.8 \times 5\%$$ $$8\% = R_f + 4\%$$ $$R_f = 4\%$$ Therefore, the risk-free rate is **4.0%**.
Author: LeetQuiz Editorial Team
Ultimate access to all questions.
An analyst gathers the following information about two well-diversified portfolios in an economy satisfying a one-factor arbitrage pricing theory model:
| Portfolio | Expected Return | Factor Sensitivity |
|---|---|---|
| X | 8.0% | 0.8 |
| Y | 16.0% | 2.4 |
The expected returns reflect a 1-year investment horizon and all investors agree on the expected returns of these portfolios. The return on the risk-free asset is closest to:
A
3.0%
B
4.0%
C
5.0%
No comments yet.