Normal Based on the following information Calculate the expe

Normal

Based on the following information:

Calculate the expected return for each of the stocks?

Calculate the standard deviation for each of the stocks.

What is the covariance between the returns of the two stocks?

What is the correlation between the returns of the two stocks?

Solution

Solution:

Calculation of Expected Return for each of the stocks

The expected return of an asset is the sum of the probability of each state occurring times the rate of return if that state occurs. So the expected return of each stock is:

E(R_A) = .27(-.02) + .62(.136) + .11(.216)

          = .1021 or 10.21%

E(R_B) = .27(.032) + .62(.060) + .11(.090)

          = .0557 or 5.57%

Calculation of Standard Deviation for each of the stocks

To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected returns. We then multiply each possible squared deviations by its probability, and then add all of these up. The result is the variance.

The variance and standard deviation of Stock A are:

Variance of Stock A (?²_A) = .27(-.02 - .1021)² + .62(.136 - .1021)² + .11(.216 - .1021)²

                                                = .00630

Standard Deviation of Stock A (?_A) = .00630^1/2

= .0794 or 7.94%

The variance and standard deviation of Stock B are:

Variance of Stock B (?²_B) = .27(.032 - .0557)² + .62(.060 - .0557)² + .11(.090 - .0557)²

                                                = .00029

Standard Deviation of Stock B (?_B) = .00029^1/2

= .0171 or 1.71%

Calculation of covariance between the returns of the two stocks

To find the covariance, we multiply each possible state times the product of each asset’s deviation from the mean in that state. The sum of these products is the covariance. So, the covariance is:

Cov(A,B) = .27(-.02 - .1021) (.032 - .0557) + .62(.136 - .1021) (.060 - .0557)

+ .11(.216 - .1021) (.090 - .0557)

= .001314

Calculation of correlation between the returns of the two stocks

?A,B = Cov(A,B) / ?_A ?_B

         = .001314 / (.0794) (.0171)

         = .9683