Question

Assume that both X and Y are well-diversified portfolios and the risk-free rate is 8%.

Portfolio	Expected Return	Beta
X Y	16% 12%	1.00 0.25

In this situation you could conclude that portfolios X and Y:

a. Are in equilibrium.

b. Offer an arbitrage opportunity.

c. Are both under priced.

d. Are both fairly priced.

Short answer

The Correct answer is: ‘b’.

Step-by-step solution

Given Information

r_F = 8% and

E( r_M ) = 16%

β_X= 1.0

β_Y= 0.25

Solution

E(r_X) = r_f +β_X[E(r_M) – r_f] = 8% + 1.0(16% - 8%) = 16%

E(r_Y) = r_f+β_Y[E(r_M) – r_f] = 8% + 0.25(16% - 8%) = 10%.

Therefore there is an arbitrage opportunity.