1) Suppose that stock returns are created by two-factor model. The returns on three well-diversified portfolios, A, B and C, are given by the given representations:
rA = 0.10 + F1
rB = 0.08 + 2F1 – F2
rC = 0.05 – 0.5F1 + 0.5F2
a) Describe what the factor representations above imply for variation and co movement in three stock returns. Illustrate how returns of stocks must be correlated between themselves.
b) Determine portfolio weights that one should place on stocks A, B and C to create pure tracking portfolios for 2 factors (that portfolios in which loading on appropriate factor is +1 and loadings on all other factors are 0).
c) If one was to introduce the new portfolio, D, with loadings of +1 on both of factors, what would the expected return on D have to be to rule out arbitrage?
d) Describe the concepts of idiosyncratic risk and factor risk in APT. What function does diversification play in APT?