Refer to the following example for part a)

Suppose that you consider two stocks, X and Y with their probability distribution.

Scenario Probability Stock X’s return Stock Y’s return

Bull market 60% 15% 8%

Bear market 40% -5% 2%

Expected rate of return on Stock X = 0.6*15% + 0.4*(-5%) = 9% + (-2%) = 7%

Expected rate of return on Stock Y = 0.6*8% + 0.4*2% = 4.8% + 0.8% = 5.6%

Variance of Stock X’s returns = 0.6*(15% – 7%)2 + 0.4*(-5% – 7%)2 = 38.4 + 144 = 182.4

Standard deviation of Stock X = square root of 182.4 = 13.51%

Variance of Stoc Y’s returns = 0.6*(8% – 5.6%)2 + 0.4*(2% – 5.6%)2 = 3.46 + 5.18 = 8.64

Standard deviation of Stock Y = square root of 8.64 = 2.94%

Covariance between Stock X and Stock Y = 0.6*(15% – 7%)*(8% – 5.6%) + 0.4*(-5% – 7%)*(2% – 5.6%)

= 28.8

Correlation between Stock X and Stock Y = 28.8/(13.51*2.94) = 0.73

a) Use the following two stocks.

Scenario Probability Stock A Stock B

Boom 30% 12% 20%

Recession 70% 18% 5%

i) Find the expected return on each stock.

ii) Find the standard deviation of each stock.

iii) Find the covariance between two stocks.

b) What is the beta? Explain with its formula.

Refer to the following example for part c)

Risk-free rate of return = 3%

Market return (or market portfolio’s rate of return) = 10%

IBM stock’s beta = 1.2

Then, based on the CAPM (capital asset pricing model), IBM stock’s required rate of return (or minimum acceptable return or fair rate of return)

= risk-free return + beta*(market return minus risk-free return) = 3% + 1.2*(10% – 3%) = 11.4%

Also, the market risk premium (or market portfolio’s risk premium) = market return minus risk-free return = 10% – 3% = 7%

c) suppose that a stock’s beta is 0.7. If the risk-free rate of return is 4% and the market risk premium is 8%, what is the stock’s required rate of return?

d) Explain some issues on the CAPM.

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