or Problems 23 - 26, consider the following table, which gives a security analys

Question

or Problems 23 - 26, consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:

Market Return

Aggressive Stock (A)

Defensive Stock (D)

7%

3.1%

4.9%

20%

30%

15%

What is the beta of the stock A?Question 23 options:

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Question 24 (5.5 points)

What is the beta of the stock B?

Question 24 options:

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Question 25 (5.5 points)

What is the expected rate of return on each stock if the market return is equally likely to be 7% or 20%?

              Rate of return on A      Rate of return on D

Question 25 options:

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Question 26 (5 points)

If the T-bill rate is 8%, and the market return is equally likely to be 7% or 20%, what are the alphas of the two stocks?

              Alpha of  A      Alpha of D

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Market Return

Aggressive Stock (A)

Defensive Stock (D)

7%

3.1%

4.9%

20%

30%

15%

Explanation / Answer

(a)

The betas of the two stocks are :

Aggressive stock = 30% - 3.1% / 20% -7%

= 2.069

Defensive stock = 15% - 4.9% / 20% -7%

= 0.7769

(b)

The expect return of the two stocks are :

Aggressive stock = 0.5 × 3.1% + 0.5 × 30%

= 16.55%

Defensive stock = 0.5 x 4.9% + 0.5 × 15%

= 9.95%

c)

The expected return on the market portfolio is 0.5 × 7% + 0.5 × 20% = 13.5%

Since the risk-free is 8%, the market risk premium is 13.5% – 8% = 5.5%

So, the SML, is Required return i = 8% + ßi x 5.5%

The alphas of the two stocks are calculated below

Stock A; Expected return = 16.55%, Beta =2.069

Required return = 8% +2.069 x 5.5% =19.38%

Alpha = 16.55% -19.38% = -2.82%

Stock B; Expected return=9.95%, Beta = 0.7769,

Required return = 8% + 0.7769 x 5.5%

=12.273%

Alpha = 9.95% -12.273% = -2.32%

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