Reference no: EM132484095

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.

Expected rate of return on Stock A = 0.3*12% + 0.7*(18%) = 3.6% + 12.6% = 16.2%

Expected rate of return on Stock B = 0.3*20% + 0.7*5% = 0.6% + 3.5% = 4.1%

ii) Find the standard deviation of each stock.

Variance of Stock X's returns = 0.3*(12% - 16.2%)² + 0.7*(18% - 16.2%)² =

Standard deviation of Stock X = square root of _______ = _________

Variance of Stoc Y's returns = 0.3*(20% - 4.1%)² + 0.7*(5% - 4.1%)² =

Standard deviation of Stock Y = square root of _____= __________

iii) Find the covariance between two stocks. 

Covariance between Stock X and Stock Y = = 0.3*(12% - 16.2%)*(20% - 4.1%) + 0.7*(18% - 16.2%) *(5% - 4.1%) = 28.8

Correlation between Stock X and Stock Y =

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