1. Use the following scenario analysis for Stocks X and Y: Scenario Description

Question

1. Use the following scenario analysis for Stocks X and Y:

Scenario

Description

Probability of Occurrence

Expected Outcome (HPR)

Stock X

Expected Outcome (HPR)

Stock Y

1

Bear Market

.25

-5.5%

-10.5%

2

Normal Market

.45

6.0%

8.0%

3

Bull Market

.30

11.5%

18.5%

Based on this information:

a. Calculate the expected returns for Stocks X and Y.

b. Calculate the standard deviations of returns on Stocks X and Y.

c. Which stock is riskier? Explain your answer. Hint: You may want to interpret and compare the standard deviation for each stock.

d. Assume that 90% of your $100,000 portfolio is invested in Stock X, while the rest (or 10%) is invested in Stock Y. What is the expected return of your portfolio?

2. Use the CAPM to calculate the required rate of return (expected return) to Stock X if: the risk-free rate of return is 4%, the expected return of the market is 12% and the stock’s beta coefficient is 1.25. What is the stock’s alpha if its actual return was 12.5%? Is the stock overpriced or underpriced? Explain.

Scenario

Description

Probability of Occurrence

Expected Outcome (HPR)

Stock X

Expected Outcome (HPR)

Stock Y

1

Bear Market

.25

-5.5%

-10.5%

2

Normal Market

.45

6.0%

8.0%

3

Bull Market

.30

11.5%

18.5%

Explanation / Answer

a.Expected returns for Stocks X and Y.

Stock X E(R ) = (0.25*-0.055)+(0.45*0.06)+(0.3*0.115) = -0.01375+0.027+0.0345 = 0.04775 or 4.775%

Stock Y E(R ) = (0.25*-0.105)+(0.45*0.08)+(0.3*0.185) = -0.02625+0.036+0.0555 = 0.06525 or 6.525%

b. Standard deviations of returns on Stocks X and Y.

Variance Stock X = 0.25(-0.055-0.04775)+0.45(0.06-0.04775)+ 0.3(0.115-0.04775) = 0.00263939+0.00006750+0.00135677=0.00406366

Standard deviation Stock X= (0.00406366)^0.5 = 0.06374684 or 6.37%

Variance Stock Y = 0.25(-0.105-0.06525)+0.45(0.08-0.06525)+ 0.3(0.185-0.06525) = 0.00724627+0.00009810+0.00430202 = 0.01164638

Standard deviation Stock Y= (0.01164638)^0.5 = 0.1079184 or 10.79%

c. Which stock is riskier?

Stock Y is more risker as it has Standard deviation of 10.79% compare to stock X 6.37%.

d. Assume that 90% of your $100,000 portfolio is invested in Stock X, while the rest (or 10%) is invested in Stock Y. Expected return of your portfolio =( 0.9 *0.04775) +(0.1*0.06525) = 0.0495 or 4.95%

2.Using CAPM

E(R) = Rf+Beta (Rm- Rf)

= 4% +1.25 ( 12%-4%)

= 14%

Stock’s alpha if its actual return was 12.5% = 12.5% -14% = -1.5%

Stock X is undervalued since forcasted return is higher than actual return.

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