Consider a market where two factors arc sufficient to describe the returns on co

Question

Consider a market where two factors arc sufficient to describe the returns on common stocks. For an asset i, the asset's expected return is given by where P1 and P2 arc the factor premiums (expected return of the factors in excess of the risk-free rate). Both factors are independent. The following tabic gives the sensitivities of the stocks ABC and PQR to the two factors, as well as the expected returns of each stock: Consider a portfolio, C, made up by selling short $.50 of security PQR and purchasing $1.50 of ABC. How sensitive will this portfolio be to each of the two factors? Consider a portfolio, D, made up by borrowing SI .00 at the risk free rate and investing $1.00 in portfolio C. How sensitive will this portfolio be to each of the factors? What combination of securities ABC, PQR and the riskless security will move on a one-to-one basis with factor 1 and be insensitive to factor 2?

Explanation / Answer

a) Sensitivity of the portfolio to:

Beta_a : 0

Beta_b : 0.5

b) Sensitivity of this new portfolio to:

Beta_a : 0

Beta_b : -0.25

c) Short $2.7 of ABC, invest in $1.6 of PQR and the remaining $1.1 in risk-free.

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