Suppose that the standard deviation of returns from a typical share is about 0.3

Question

Suppose that the standard deviation of returns from a typical share is about 0.38 (or 38%) a year. The correlation between the returns of each pair of shares is about 0.5.

PLEASE EXPALIN IN STEPS  

Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares. (Do not round intermediate calculations. Enter "Variance"as a decimal rounded to 6 places and "Standard Deviation" to 3 places.)

  

  

How large is the underlying market variance that cannot be diversified away? (Do not round intermediate calculations. Enter your answer as a decimal rounded to 3 places.)

  

  

Assume that the correlation between each pair of stocks is zero. Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares. (Do not round intermediate calculations. Enter "Variance" as a decimal rounded to 6 places and "Standard Deviation" to 3 places.)

  

Suppose that the standard deviation of returns from a typical share is about 0.38 (or 38%) a year. The correlation between the returns of each pair of shares is about 0.5.

Explanation / Answer

a.Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares. (Do not round intermediate calculations. Enter "Variance"as a decimal rounded to 6 places and "Standard Deviation" to 3 places.)

Covariance of each pair = correlation*SD*SD

Covariance of each pair = 0.5*38%*38%

Covariance of each pair = 0.0722

Variance of portfolio = (38%)^2

Variance of portfolio = 0.1444

Variance of portfolio = (Variance - Covariance)/n + Covariance

Variance of portfolio = (0.1444-0.0722)/n + 0.0722

Variance of portfolio = 0.0722/n + 0.0722

Where n = no of share

SD of Portfolio = Variance of portfolio^(1/2)

b.How large is the underlying market variance that cannot be diversified away? (Do not round intermediate calculations. Enter your answer as a decimal rounded to 3 places.)

Market Risk= ((Variance - Covariance)/n + Covariance)^(1/2)

where n = infinity

Market Risk= (Covariance of each pair )^(1/2)

Market Risk= (0.0722)^(1/2)

Market Risk = 26.870%

c.Assume that the correlation between each pair of stocks is zero. Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares. (Do not round intermediate calculations. Enter "Variance" as a decimal rounded to 6 places and "Standard Deviation" to 3 places.)

Covariance of each pair = correlation*SD*SD

Covariance of each pair = 0*38%*38%

Covariance of each pair = 0

Variance of portfolio = (38%)^2

Variance of portfolio = 0.1444

Variance of portfolio = (Variance - Covariance)/n + Covariance

Variance of portfolio = (0.1444-0)/n

Variance of portfolio = 0.1444/n

Where n = no of share

SD of Portfolio = Variance of portfolio^(1/2)

No. of Standard Shares Variance Deviation (%) 1          0.144400 38.000% 2          0.108300 32.909% 3          0.096267 31.027% 4          0.090250 30.042% 5          0.086640 29.435% 6          0.084233 29.023% 7          0.082514 28.725% 8          0.081225 28.500% 9          0.080222 28.324% 10          0.079420 28.182%

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