Question

You have classified the market in four portfolios as follows:

Small Value

Large Value

Small Growth

Large Growth

Suppose the risk-free rate is 2% and accordingly you have designed the following model:

Portfolio	Weight	Sensitivity to factor 1	Sensitivity to factor 2	Sensitivity to factor 3
Small Value Small Growth Large Value Large Growth	5% 5% 40% 50%	0.85 0.95 0.90 1.10	0.8 1.3 2.0 3.0	1 1 8 10
Risk Premium		8%	-2%	0.1%

a.           When using the APT, which portfolio has the highest expected return? Show your calculations. (5 points)

b.           Still using the APT, what is the expected return of the market and how does it compare with the returns of the other 4 portfolios? (5 points)

c.           In order to diversify his anticipated risk, another competitor wants to combine the Small Value and the Large Growth Portfolios. The new portfolio should have an overall sensibility to factor 1 of one. Show how much the competitor must invest in Small Value and how much in Large Growth. The portfolio must be fully invested. Short sales are not allowed. (5 points)

Answer 1