Consider the one-factor APT.Assume that two portfolios,A and B,are well diversified.The betas of portfolios A and B are 1.0 and 1.5,respectively.The expected returns on portfolios A and B are 19% and 24%,respectively.Assuming no arbitrage opportunities exist,the risk-free rate of return must be ____________.
A)4.0%
B)9.0%
C)14.0%
D)16.5%
E)none of the above

Question

Quizplus · Accepted Answer

According to the one-factor APT formula, the expected return on a portfolio can be estimated as:

E(R) = Rf + β × RP

Where Rf is the risk-free rate of return, β is the portfolio's beta, and RP is the risk premium, which is the excess return of the market over the risk-free rate.

Assuming that there are no arbitrage opportunities, the expected return on portfolio A can be estimated as:

19% = Rf + 1.0 × RP

Similarly, the expected return on portfolio B can be estimated as:

24% = Rf + 1.5 × RP

We can solve these two equations simultaneously to find the values of Rf and RP. Subtracting the first equation from the second, we get:

5% = 0.5 × RP

Therefore, RP = 10%.

Substituting this value of RP into either of the two equations above, we can solve for Rf:

19% = Rf + 1.0 × 10%
Rf = 9.0%

Therefore, the risk-free rate of return must be 9.0%. Answer: B

Consider the One-Factor APT