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Consider the one-factor APT. Assume that two portfolios, A and B, are well diversified. The betas...

Consider the one-factor APT. Assume that two portfolios, A and B, are well diversified. The betas of portfolios A and B are 0.5 and 1.5, respectively. The expected returns on portfolios A and B are 12% and 24%, respectively. Assuming no arbitrage opportunities exist, what must be the risk-free rate?

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Answer #1

The risk-free rate is computed as shown below:

0.12 = Risk free rate + 0.5 x Factor (Equation 1)

0.24 = Risk free rate + 1.5 x Factor (Equation 2)

Solving these two equations,

0.24 - 0.12 = 1.5 factor - 0.5 factor

0.12 = 1 factor

0.12 = factor

We can put this number in either of the 2 above mentioned equation and get risk free rate as

0.12 = risk free rate + 0.5 x 0.12

Risk free rate = 0.06 or 6%

Feel free to ask in case of any query relating to this question

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