Reference no: EM133052178
Suppose that there are two independent risk factors F1 and F2. Thus, a two-factor model for portfolio i is given by ri = E[ri] + βi1F1 + βi2F2+ ei.
The risk-free rate of return is 4%, the standard deviations of factors 1 and 2 are σ1 = 20% and σ2 = 15%, respectively. Consider two portfolios A and B:
Portfolio Mean return Beta on F1 Beta on F2 σ(ei)
A 15.6% 0.5 1.2 5%
B 13.2% 1.5 0.4 10%
Specifically, note that E[rA] = 15.6% and E[rB] = 13.2%.
Assume that the market is in equilibrium and, therefore, the following relationship holds:
E[ri ] = rf + βi1(E[r1] - rf ) + βi2(E[r2] - rf ), where E[r1] and E[r2] are the expected returns on the factor portfolios 1 and 2, respectively.
a) Calculate the total standard deviation of portfolio A and portfolio B.
b) Prove that the covariance between portfolio i and portfolio j is given by σij = βi1βj1σ 21 + βi2βj2σ22.
c) Compute the covariance between portfolio A and portfolio B.
d) Compute the expected returns on the factor portfolios, E[r1] and E[r2].
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