Consider the following two-factor model for the returns of three stocks. Assume that the factors and...

Transcribed Image Text:

Consider the following two-factor model for the returns of three stocks. Assume that the factors and epsilons have means of zero. Also, assume the factors have variances of .01 and are uncorrelated with each other. = .13 + 6 + 4 + A 1 1 B = .15 + 2 + 2 + EB rc = .07 + 5F, == IF, +c If var(A) = .01 var(B) = 0.4 var(ec) = .02, what are the variances of the returns of the three stocks, as well as the covariances and correlations between them? Write out the factor betas, factor equations, and expected returns of the following portfolios: (1) A portfolio of the three stocks in exercise 6.3 with $20,000 invested in stock A, -$20,000 invested in stock B, and $10,000 invested in stock C. (2) A portfolio consisting of the portfolio formed in part (1) of this exercise and a $3,000 short position in stock C of exercise 6.3. How much should be invested in each of the stocks in exercise 6.3 to design two portfolios? The first portfolio has the following attributes: factor 1 beta = 1 factor 2 beta = 0 The second portfolio has the attributes: factor 1 beta = 0 factor 2 beta = 1 Compute the expected returns of these two portfolios. Then compute the risk premiums of these two portfolios assuming the risk-free rate is Consider the following two-factor model for the returns of three stocks. Assume that the factors and epsilons have means of zero. Also, assume the factors have variances of .01 and are uncorrelated with each other. = .13 + 6 + 4 + A 1 1 B = .15 + 2 + 2 + EB rc = .07 + 5F, == IF, +c If var(A) = .01 var(B) = 0.4 var(ec) = .02, what are the variances of the returns of the three stocks, as well as the covariances and correlations between them? Write out the factor betas, factor equations, and expected returns of the following portfolios: (1) A portfolio of the three stocks in exercise 6.3 with $20,000 invested in stock A, -$20,000 invested in stock B, and $10,000 invested in stock C. (2) A portfolio consisting of the portfolio formed in part (1) of this exercise and a $3,000 short position in stock C of exercise 6.3. How much should be invested in each of the stocks in exercise 6.3 to design two portfolios? The first portfolio has the following attributes: factor 1 beta = 1 factor 2 beta = 0 The second portfolio has the attributes: factor 1 beta = 0 factor 2 beta = 1 Compute the expected returns of these two portfolios. Then compute the risk premiums of these two portfolios assuming the risk-free rate is