Q Random returns for two well–diversified portfolios at time t are given by: rAt
ID: 2717548 • Letter: Q
Question
Q
Random returns for two well–diversified portfolios at time t are given by:
rAt= 0:27 + 2F1t+ 0:8F2t
rBt= 0:161 +F1t+ 1:1F2t;
where F1and F2 are unexpected parts of factor 1 and 2 returns, respectively. (One can think that factor one is GDP and factor two is an inflation). The risk free rate is 1:0%.
a. Construct factor portfolio for factor 1 by combining portfolios A, B, and T-bills.What are the weights of these portfolios in factor portfolio 1? What is the expected return of factor portfolio 1?
b. Solve questionafor factor portfolio 2
c. Assume that the market does not allow arbitrage strategies and so the two–factor APT holds. Find the expected returns on portfolio C which betas with respect to factors 1 and 2 are 0.5 and 1.2, respectively
Explanation / Answer
T-bill = 1 %
rAt= 0:27 + 2F1t+ 0:8F2t
rBt= 0:161 +F1t+ 1:1F2t;
combination = 0.431+3F1t+1.9F2t
weights of these portfolios = Wa = .37
W(b )= 1- W(a) = 1-.37 = .63
expected return of factor portfolio 1 = Risk free return + market risk premium
= 1 % + 2% = 3%
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.