Question

Suppose there are two independent economic factors, M, and M2. The risk-free rate is 5%, and all stocks have independent firm- specific components with a standard deviation of 48%. Portfolios A and B are both well diversified. Portfolio Beta on Mi Expected Return (%) Beta on M2 2.3 -0.6 38 2.2 What is the expected return-beta relationship in this economy? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Answer is complete but not entirely correct. 5.00 % 11.26 $ 1 4 .43 Expected return-beta relationship E(rP) = BP2

Answer 1

The expected return-beta relationship is computed as shown below:

Portfolio A

Expected return = Risk free rate + Beta on M1 x RP1 + Beta on M2 x RP2

38 = 5 + 1.6 x RP1 + 2.3 x RP2

Portfolio B

Expected return = Risk free rate + Beta on M1 x RP1 + Beta on M2 x RP2

8 = 5 + 2.2 x RP1 - 0.6 x RP2

Solving these two equations we will get:

38 = 5 + 1.6 x RP1 + 2.3 x RP2 ( Multiply this equation by 6 )

8 = 5 + 2.2 x RP1 - 0.6 x RP2 ( Multiply this equation by 23 )

After doing multiplication the new equation will be:

228 = 30 + 9.6 RP1 + 13.8 RP2

184 = 115 + 50.6 RP1 - 13.8 RP2

Now we shall add these equation and will get

228 + 184 = 30 + 115 + 9.6 RP1 + 50.6 RP1

4.44% Approximately = RP1

and RP 2 will be:

= 11.26% Approximately (This comes by feeding RP1 value in the above mentioned equation i.e. in 228 = 30 + 9.6 RP1 + 13.8 RP2 )

So the expected return beta relationship will be as follows:

= 5% + 4.44% BP1 + 11.26%BP2

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