Question

1. Given the information below, answer the questions that follow : Market return Aggressive stick Defensive stock 6% 2% 8% 20 30 16 a. Calculate the betas of the two stocks.(3) b. Find outthe expected return on each stock if the market return is equally likely to be 6% or 20%? (3) c. If the risk free rate is 7% and the market rate is equally likely to be 6% or 20%, find out the SML. (6) d. Calculate the alphas of the two stocks.(3)

Answer 1

Answer -

Part 1 -

Step 1

The formula to calculate beta of stock is given below:

Return on stock in case 1 - Return on stock in case 2 Beta = Market return in case 1-Market return in case 2

Step 2

For aggressive stock beta substitute 2% for return on stock in case 1, 30% for return on stock in case 2, 6% for market return in case 1 and 20% for market return in case 2 in the above formula,

                                                       2%- 30%

                                            =     ________________

                                                       6% - 20%

Therefore, Beta = 2.00

For Defensive Stock

                                                       8%- 16%

_____________________

                                                       6 %- 20%

Beta = 0.57

Part 2 -

EXPECTED RETURN of the two stocks are –

Aggressive Stock = (0.5 * 2%) + (0.5 * 30%) = 16%

Defensive Stock = ( 0.5 * 8%) + (0.5 * 16%) = 12%

Part 3 -

The expected return on market portfolio is :

0.5 * 6% +0.5 * 20 % = 13%

Since the risk free rate is 7%, the market risk premium is 13% - 7% =6%

So, the SML is :

Required retrun = 7% + βi * 6%

Part 4 –

The alphas of the two stocks are calculated below –

Stock A

Expected Return = 16%

Beta = 2

Required return = 7% +2 * 6% =19%

Alpha = 16% - 19% = -3%

Stock B

Expected Return = 12%

Beta = 0.57

Required return = 7% +0.57 * 6% =10.426%

Alpha = 12% - 10.426% = 1.574%