Question

You are given the following information:

  

State of Economy	Return on Stock A	Return on Stock B
Bear	.111	-.054
Normal	.106	.157
Bull	.082	.242

  

Assume each state of the economy is equally likely to happen.

  

Calculate the expected return of each of the following stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Expected return
Stock A	%
Stock B	%

Calculate the standard deviation of each of the following stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Standard deviation
Stock A	%
Stock B	%

What is the covariance between the returns of the two stocks? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.

What is the correlation between the returns of the two stocks? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)

Answer 1

Their are three events, so probability of each event = 1 / 3

Expected return

Expected return = sum of ( probability x return)

Stock A = 0.111 x 1 / 3 + 0.106 x 1 / 3 + 0.082 x 1 / 3 = 0.09966666 or 9.966666% or 9.97%

Stock B = -0.054 x 1 / 3 + 0.157 x 1 / 3 + 0.242 x 1 / 3 = 0.1149999 or 11.50%

Standard deviation (?)

or, ?_A = 1.27%

or, ?_A = 12.44%

Covariance

or, Covariance = (-)0.001298

Correlation (r)

r = Covariance / ( ?_A x ?_B )

or, r = (-)0.0012976666 / (0.0126578908 x 0.12443740) = (-)0.82385513623 or (-)0.8239