Question

eBook Problem 6-07 The following are monthly percentage price changes for four market indexes. Month DJIA S&P 500 Russell 2000 Nikkei 1 0.03 0.01 0.04 0.04 2 0.09 0.08 0.13 -0.02 3 -0.02 -0.01 -0.05 0.06 4 0.01 0.02 0.02 0.01 5 0.04 0.04 0.15 0.01 6 -0.06 -0.03 -0.08 0.07 Compute the following. Average monthly rate of return for each index. Round your answers to five decimal places. DJIA: S&P 500: Russell 2000: Nikkei: Standard deviation for each index. Do not round intermediate calculations. Round your answers to four decimal places. DJIA: S&P 500: Russell 2000: Nikkei: Covariance between the rates of return for the following indexes. Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers to six decimal places. Covariance (DJIA, S&P 500): Covariance (S&P 500, Russell 2000): Covariance (S&P 500, Nikkei): Covariance (Russell 2000, Nikkei): The correlation coefficients for the same four combinations. Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers to four decimal places. Correlation (DJIA, S&P 500): Correlation (S&P 500, Russell 2000): Correlation (S&P 500, Nikkei): Correlation (Russell 2000, Nikkei): Using the unrounded answers from parts (a), (b), and (d), calculate the expected return and standard deviation of a portfolio consisting of equal parts of (1) the S&P and the Russell 2000 and (2) the S&P and the Nikkei. Do not round intermediate calculations. Round your answers to five decimal places. Expected return (S&P 500 and Russell 2000): Standard deviation (S&P 500 and Russell 2000): Expected return (S&P 500 and Nikkei): Standard deviation (S&P 500 and Nikkei): Since S&P 500 and Russell 2000 have a strong -Select-negativepositiveItem 21 correlation, meaningful reduction in risk -Select-is not observedis observedItem 22 if they are combined. Since S&P 500 and Nikkei have a strong -Select-negativepositiveItem 23 correlation, meaningful reduction in risk -Select-is not observedis observedItem 24 if they are combined.

Answer 1

a]

Average monthly rate of return is calculated using AVERAGE function in Excel

b]

Standard deviation is calculated using STDEV.S function in Excel

c]

Covariance is calculated using COVARIANCE.S function in Excel

d]

Correlation is calculated using CORREL function in Excel

e]

(1) and (2)

Expected return of two-asset portfolio R_p = w₁R₁ + w₂R_2,

where R_p = expected return

w₁ = weight of Asset 1

R₁ = expected return of Asset 1

w₂ = weight of Asset 2

R₂ = expected return of Asset 2

standard deviation for a two-asset portfolio σ_p = (w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2)^1/2

where σ_p = standard deviation of the portfolio

w₁ = weight of Asset 1

w₂ = weight of Asset 2

σ₁ = standard deviation of Asset 1

σ₂ = standard deviation of Asset 2

All the calculations are below :

Since S&P 500 and Russell 2000 have a strong positive correlation, meaningful reduction in risk not observed if they are combined.

Since S&P 500 and Nikkei have a strong negative correlation, meaningful reduction in risk is observed if they are combined.