Supp ose that there are two independent economic factors, Fi a 596, and all stoc

Question

Supp ose that there are two independent economic factors, Fi a 596, and all stocks have independent firm-specific components with a standard of 50%. The following are well-diversified portfolios d F2. The risk-free rate is deviation Portfolio Beta on Fi Beta on F2 Expected return 31% 21% -0.5 a) What is the expected return-beta relationship in this economy? b) Suppose that another portfolio, portfolio C, is well diversified with a 0.6 beta on Factor arbitrage opportunities exist? 1 and beta 2 on Factor2. What is the expected return on portfolio C if no

Explanation / Answer

E(rp ) = rf+ 1,p [E(r1 ) rf ] + 2, p [E(r2 ) rf ]

We need to find the risk premium [rp] for each of the two factors:

rp1 = [E(r1)-rf] and

rp2 = [E(r2)-rf]

To do so, the following system of two equations with to unknowns must be solved:

31 = 5 + 1 * rp1 + 2* rp2 . . . .. . (Equation (1)

21 = 5 + 2 * rp1 + (-0.5) * rp2 . . .. (equation 2)

31 = 5 + rp1 + 2rp2  
26 - 2rp2 = rp1 . . . . . . subsituting rp1 in equation (2)

21 = 5 + 2 rp1 + (-0.5) rp2
21 = 5 + 2 (26 - 2rp2) + (-0.5) rp2
-36 = -4rp2 - 0.5rp2
rp2 = 8

rp1 = 26 - 2 *8 = 10

The solution to this set of equation is

rp1 = 10% and

rp2 = 8%

Thus, the expected return-beta relationship is:

E(rp) = 6% + 1, p 10% + 2, p8%

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