Suppose that there are two independent economic factors FI and F2. The risk-free rate is 6%, and all stocks have independent firm-specific components with a standard deviation of 45%. The following are well-diversified portfolios: Portfolio Beta on F1 Beta on F2 Expected Return 1.5 2.0 31 B 2.2 -0.2 27 Table 1: Scenarios for 2 stocks with 2 Factors What is the expected return-beta relationship in this economy? Solution BKM ch. 11, p. 335 # 2 E(r,) =1, + BP[E(x)-r, ]+ Bap[E(r2)-r,] We need to find the risk premium [rp] for each of the two factors: rp1 = [E(ri)-rf] and rp2 = [E(r2)-red To do so, the following system of two equations with to unknowns must be solved: 21 = 6 + 1.5 x rp, + 2.0 x rp2 27 = 6 +2.2 x rp1 + (-0.2) x rp2 The solution to this set of equation is rp1 = 10% and rp2 = 5% Thus, the expected return-beta relationship is: E(r,)=6% + By,p.10%+ Bz.p .5%