Arbitrage Pricing Theory 2 factor Model
Hi,
I am taking up a class on Portfolio Management and can't seem to find the answer to the following questions:
Assume a two-factor APT. Further assume that the three portfolios below are well diversified such that all firm-unique risk is zero The expected return and the beta with respect to the two factors for the three portfolios are given as follows.
Portfolio, Expected Return (%) Factor 1 Beta Factor 2 Beta
A 12.0 1 0.5
B 13.4 3 0.2
C 12.0 3 - 0.5
Suppose all three portfolios are correctly priced according to APT.
1. What is the risk-free rate (in percent terms)? What are the factor risk premia (in percent terms)? Show your work and briefly discuss what is going on as you answer this question.
2. Using your results in question 1, write the equation of the plane that must describe equilibrium expected returns on any well-diversified portfolio P based on the above two factor APT.
3. Suppose there is a fourth portfolio D with observed expected return of 10%, factor 1 beta of 2 and factor 2 beta of 0. Is there an arbitrage opportunity? Why or why not? Show your work and a brief discussion of what is going on as you answer this question.
4. If an arbitrage opportunity exists, design an arbitrage portfolio involving the correctly priced portfolios (which need not be all of these portfolios) and portfolio D. Show that it involves zero investment, zero risk and positive profit.
