Assume that stock returns are generated by a two-factor model. The returns on three well-diversified portfolios, A, B and C, are given by the following representations:

=0.10+

1

rA=0.10+F1

=0.08+2

1

-

2

rB=0.08+2F1-F2

=0.05-0.5

1

+0.5

2

rC=0.05-0.5F1+0.5F2

1. Discuss what the factor representations above imply for the variation and comovement in the three stock returns. Show how the returns of the stocks should be correlated between themselves.
2. Find the portfolio weights that one must place on stocks A, B and C to construct pure tracking portfolios for the two factors (i.e. portfolios in which the loading on the relevant factor is +1 and the loadings on all other factors are 0).
3. If one was to introduce a new portfolio, D, with loadings of +1 on both of the factors, what would the expected return on D have to be to rule out arbitrage?
4. Explain the concepts of idiosyncratic risk and factor risk in the APT. What role does diversification play in the APT?