For this question, assume that each stock has the same variance of return (sigma

Question

For this question, assume that each stock has the same variance of return (sigma^2), the correlation between all pairs of stocks is the same (rho) and stocks are equally weighted. Suppose the average variance of return of all stocks in a portfolio is 676 and the correlation between the returns of any two stocks is 0.35. Calculate the variance of return of an equally weighted portfolio of 25 stocks. Then state that variance as a percent of the portfolio variance achievable given an unlimited number of stocks, holding stock variance and correlation constant. Suppose that the risk-free rate is 5 percent and the expected return on the investor's tangency portfolio is 15 percent, with a standard deviation of 22 percent. Calculate the investor's expected risk premium per unit of risk. Calculate the portfolio's expected return if the portfolio's standard deviation of return is 28 percent.

Explanation / Answer

1)

In case of equal investment of all pair stock

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

676 = (Variance - SD*SD * Correlation)/N + - SD*SD * Correlation

676 = (Variance - Variance*0.35)/25 + Variance*0.35

676 = 0.026Variance + 0.35 Variance

Variance = 676/0.376

Variance = 1797.87 %2

If number of Stock is unlimited than

Variance of portfolio = Covariance

Variance of portfolio = 1797.87*0.35

Variance of portfolio = 629.25

Answer

Variance of return = 1797.87 %2

Variance of portfolio = 629.25

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