Question

6. Consider the following data for two securities in the same industries.

Security	Beta	Implied Rate of Return
A	1.70	10%
B	.60	8%

I have answered part A but am struggling with part B,C,D

6. a.     What are the required rates of return for each of these securities when the average riskless rate is 3.5% and average return on the market is 8.5%?

For A:

12%

For B:

9.5%

6.b.         Show the amount of the risk adjusted excess return, alpha, for each security.

Security	Implied ROR	Minimum Required Return	Alpha
For A
For B

6c.       Which security would you select to buy? Why? Write 2 line for reasons in your selection.

6d.       Which security has more systematic risk? Why?

Answer 1

Answer 6

(a)  The required rates of return for each security A and B can be calculated using CAPM Model.

CAPM also known as Capital Asset Pricing Model predicts the relationship between the risk of an asset and its expected return. It gives the following equation for calculating the expected return on the securities:

E(R) = R_F + β (R_M - R_F)

Applying this formula on both securities we get,

For A, E(R)_A = R_F + β_A (R_M - R_F) = (3.5 + 1.7 (8.5 - 3.5)) % = 12%

For B, E(R)_B = R_F + β_B (R_M - R_F) = (3.5 + 0.6 (8.5 - 3.5)) % = 6.5%

(b)  Security alpha (α) is the difference between the implied rate of return and the required rate of return on the security. It is calculated as:

α = R_Implied - E(R)

For A, α = (R_Implied)_A - E(R)_A = (10 - 12)% = - 2% (negative)

For B, α = (R_Implied)_B - E(R)_B = (8.5 - 6)% = 2.5% (positive)

(c) A positive α indicates that the security is performing better than the market by providing higher returns than the minimum required returns. On the other hand, a negative α indicates that the security fails to generate the minimum required rate of returns for the investment to be profitable. Thus, one should select the security that has positive α value. Since, Security B has positive α, one should prefer this over security A.

(d) The systematic risk is the risk associated with the market returns. It is indicated by the β value of the securities. The higher the β, the higher the systematic risk. Since, β_A (1.70) > β_B (0.60), we can say that the Security A has more systematic risk than Security B.