Question B4 Assume that you are using a two-factor APT model, with factors A and
ID: 1172835 • Letter: Q
Question
Question B4 Assume that you are using a two-factor APT model, with factors A and B, to find the fair expected return on a well-diversified portfolio Q that has an actual expected return of 11%. Portfolio Q's factor loadings (i.e., Q's betas on each of the two factors) and the factors, risk premiums are shown in the table below. The risk-free rate is 3%. Factor Q's factor Factor Risk Premium loading (Beta) 1.2 0.6 5.0% -4.0% a) What would be the expected return on the portfolio Q if it were fairly priced? b) Suppose that in addition to Q and the risk-free asset, portfolios for factors A and B are tradable (i.e., you can take long or short positions in them). Construct a "replicating" portfolio P with identical risk to Q by investing in, A, B, and the risk-free asset. What are the weights of P in each of these three assets? What is the expected return of portfolio P?Explanation / Answer
a.
expected return = Rf + BETAfactor1 (factor premium 1) + BETAfactor2 (factor premium 2)
substituiting the values
= 3% + 1.2(5%) + (-0.6)(-4%)
= 11.4%
b.
FACTOR PREMIUM OF A = 5% I.E.
RM - RF = 5%
RM - 3% = 5%
RM = 8%
REQUIRED RETURN = BETA (RM)
SOLVING BASED ON ABOVE INFO
INSTRUMENT PROPORTION ACTION BETA RMARKET RETURN
A 2 BUY 1.2 8 19.2%
B -1 SELL -0.6 8 (4.8%)
RF -1 SELL 1 3 (3% )
TOTAL 11.4%
HENCE PORTFOLIO CONSTRUCTED.
3.
there exists arbitrage opportunity as expected return is 11.4% and actual return is 11%.
excess 0.4% arbitrage opportunity available.