Suppose the market portfolio\'s excess return tends to increase by 30% when the

Question

Suppose the market portfolio's excess return tends to increase by 30% when the economy is strong and decline by 20% when the economy is weak. A type S firm has excess returns increase by 45% when the economy is strong and decrease by 30% when the economy is weak. A type I firm will also have excess returns of either 45% or -30%, but the type I firm's excess returns will depend only upon firm -specific events and will be completely independent of the state of the economy. What is the Beta for a Type I and Type S firms?

Explanation / Answer

Excess return is given by

r = + *rm + e

Where, e is the residual error, of which expected value is zero.

For estimated value of and , r = + *rm

of stock S relative to market M is given by

= Cov(S, M) * Var(S)/Var(M) = Corr(S, M) * SD(S) / SD(M)

Or, when you have just 2 states of economies

r = *rm

= r / rm

of firm S = (45 – (-30)) / (30 – (-20)) = 75/50 = 3/2 = 1.5

As firm I is independent of state of economy, its correlation with market is zero.

Hence of firm I = 0

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