Question

15. Consider the following two stocks, A and B. Stock A has an expected return of 10%, 10% standard deviation, and a beta of 1.20. Stock B has an expected return of 14%, 25% standard deviation, and a beta of 1.80. The expected market rate of return is 9% and the risk-free rate is 5%. Security __________ would be considered a good buy if we are building a portfolio because _________. A. A, it offers better Sharpe ratio B. A, it offers better alpha C. B, it offers better alpha D. B, it offers better Sharpe ratio

Answer 1

The correct answer is option C ⇒ B, it offers better alpha

Step-by-step explanation:

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for pricing risky securities and generating expected returns for assets given the risk of those assets and the cost of capital.

The rate of return can be calculated using the capital asset pricing model (CAPM).

CAPM = Rate of return=Risk free rate + Beta*(Expected market rate of return-Risk free rate).

CAPM of A= 5+1.2(9-5)= 9.8%

Stock A has an expected return of 10%

Therefore an expected excess return of (10-9.8)% = 0.2%

αA = standard deviation of A - expected excess return of A

αA = (10 - 0.2)% = 1.8%

CAPM of B= 5+1.8(9-5)= 12.2%

Stock B has an expected return of 14%

Therefore an expected excess return of (14-12.2)% = 1.8%

αB = standard deviation of B - expected excess return of B

αB = (25 - 1.8)% = 23.2%

Thus, the correct answer is option C.

Answer 2

Option A => A, it offers better Sharpe ratio.

Step-by-step explanation:

So, we are given the following data or parameters from the question;

Stock A has an expected return = 10%, stock A standard deviation = 10%, a beta of 1.20. Stock B has an expected return = 14%, 25% standard deviation, and a beta of 1.80. The expected market rate of return is 9% and the risk-free rate = 5%.

Therefore, the formula for Calculating the sharp ratio = zp - zx/standard deviation.

For stock A = sharp ratio = zp - zx/standard deviation = (10 - 5)% / 10%= 0.5.

Also, For stock B = sharp ratio = zp - zx/standard deviation = (14 - 5)% / 24

5%= 0.36.

Therefore, since the sharp ratio of A > B then, would be considered a good buy.

Hence, the Return according to CAPM = Rf - beta × (v -zx).

For the Stock A; the Return according to CAPM = Rf - beta × (v -zx).

the Return according to CAPM = 5% - 1.2 (9- 5) % = 9.8%

Therefore, the Apha stock A = (10 - 9.8) % = 0.2%.

For stock B, the Return according to CAPM = Rf - beta × (v -zx).

Return according to CAPM = 5% -1.8 (9 -5 ) % = 12.2%

Therefore, the Apha stock B =( 14 - 12.2)% = 1.8%.