Problem 1:

Recall the data from Problem Set #8, problem # 1.

StockExpected ReturnStandard DeviationMarket Beta

A.15.23.8

B.20.181.2

The covariance between these two stocks is -.001.The expected return on the market is .15 with a standard deviation of .15.The risk-free rate is .03.You can borrow and lend at this risk-free rate.

Also recall that the expected returns shown above deviated from those implied by CAPM (both expected returns exceed those implied by CAPM, which resulted in a higher Sharpe ratio for the portfolio that that associated with the market).

This problem has you consider whether the higher-than-CAPM expected returns might be explained by the market being a poor proxy for the factors (ala APT) that affect the returns on these securities.

Since CAPM may not be very good at measuring all risk, you have done some additional analysis to estimate the factor sensitivities (or "loadings") of these two stocks to two "factor" portfolios (F1 and F2) that you think cover most of the risks in the market.You have also estimated the factor loadings for the market portfolio (denoted M below).

Expected ReturnFactor Loading for F1 Factor Loading for F2

A.15 0.6000.900

B.201.6000.524

M.150.8000.700

Risk-free rate = .03

Questions:

1. Is there a set of factor risk premia (one for F1 and one for F2) that is consistent with the above data and APT?Note that you will need to solve for values of RP1 and RP2 (i.e., the risk premia for factor 1 and factor 2, respectively) so that

A: .15 = .03 + .6*RP1 + .9*RP2

B:.20 = .03 + 1.6*RP1 + .524*RP2

M: .15 = .03 + .8*RP1 + .7*RP2

Solution approach:use the first two equations to solve for RP1 and RP2 that satisfy both; i.e., solve two equations in two unknowns.Given those solutions, plug those into the third equation for M and see if that equation holds.If so, then they are all priced correctly relative to one another.If not, then the three are not priced consistently relative to each other.That is, the expected returns on one portfolio reflect different risk premia for the factor risks.

1. Is there an arbitrage opportunity given the market and these two securities?Why or why not?