This question pertains to a problem in the textbook "Investments" 10th edition by Bodie/Kane/Marcus, chapter 10, problem 8c.

I don't get why problem 8c solutions say that there is no arbitrage opportunities. For example, security A's beta is 0.8, and market risk premium is 12% (based on security B). Why isn't security A's risk premium 0.8*12% = 9.6% and hence exist arbitrage opportunities?

8. Assume that security returns are generated by the single-index model, BR where Ri is the excess return for security i and RM is the market's excess return.The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: E(Ri) Security (ei) 10% 0.8 25% 12 20 a. If o M 20%, calculate the variance of returns of securities A, B, and C. b Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C respectively. If one forms a well-diversified portfolio of type A securities, what will be the mean and variance of the portfolio's excess retums? What about portfolios composed only of type B or C stocks? c Is there an arbitrage opportunity in this market What is it? Analyze the opportunity graphically