Question

What is the expected return for the following stock? (State your answer in percent with one decimal place.)
Outcomes Possible returns Probability
better 36% 13%
same 25% 39%
worse 18% 48%

	20.37%
	23.07%
	24.98%
	26.42%
	28.40%

You are holding a stock that has a beta of 2.12 and is currently in equilibrium. The required return on the stock is 12.49%, and the return on the market portfolio is 10.00%. What would be the new required return on the stock if the return on the market increased to 13.00% while the risk-free rate and beta remained unchanged?

	15.16%
	35.34%
	12.49%
	28.40%
	18.85%

You are holding a stock that has a beta of 1.67 and is currently in equilibrium. The required return on the stock is 15.38% and the return on a risk-free asset is 7.0%. What would be the return on the stock if the stock's beta increased to 2.12 while the risk-free rate and market return remained unchanged?

	15.38%
	32.48%
	17.64%
	26.23%
	16.33%

Answer 1

1). Expected Return = [Probability_i * Return_i]

= [0.13 * 36%] + [0.39 * 25%] + [0.48 * 18%]

= 4.68% + 9.75% + 8.64% = 23.07%

Hence, 2nd option is correct.

2). According to the CAPM,

Required Return = Risk-free rate + beta[Market Return - Risk-free return]

12.49% = Risk-free rate + 2.12[10% - Risk-free rate]

12.49% = Risk-free rate + 21.2% - 2.12[Risk-free rate]

12.49% = 21.2% - 1.12[Risk-free rate]

1.12[Risk-free rate] = 21.2% - 12.49%

Risk-free rate = 8.71% / 1.12 = 7.78%

New Required Return = 7.78% + 2.12[13% - 7.78%]

= 7.78% + 11.07% = 18.85%

Hence, 5th option is correct.

3). According to the CAPM,

Required Return = Risk-free rate + beta[Market Return - Risk-free return]

15.38% = 7% + 1.67[Market Return - 7%]

15.38% = 7% + 1.67[Market Return] - 11.69%

15.38% = 1.67[Market Return] - 4.69%

1.67[Market Return] = 15.38% + 4.69%

Market Return = 20.07% / 1.67 = 12.02%

New Required Return = 7% + 2.12[12.02% - 7%]

= 7% + 10.64% = 17.64%

Hence, 3rd option is correct.