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The table below shows the expected returns and volatilities of two investment funds, a bond fund B and an equity fund E
The table below shows the expected returns and volatilities of two investment funds, a bond fund B and an equity fund E. Fund Expected Return Standard Deviation Bond B 6.0% 10.5% Equity E 12.0% 21.0% The correlation between the returns on the two funds is -0.25. Consider a portfolio that invests equal amounts (i.e. 50% each) in each of the two funds. What is the standard deviation of this portfolio? A. 10.50%. B. 11.03%. C. 11.74% D. 15.75%. E. 21.00%.
Expert Solution
Answer) Option A. 10.50%
Working
Variance of portfolio = [(Weight of Bond B)^2*(Std. Dev of Bond B)^2] + [(Weight of Equity E)^2*(Std. Dev of Equity E)^2] + [2*[(Weight of Bond B)*(Weight of Equity E)*(Std. Dev of Bond B)*(Std. Dev of Equity E)*Correlation]
Variance of portfolio = [(.50)^2*(.105)^2] + [(.50)^2*(.21)^2] + [2*.50*.50*.105*.21*-.25]
Variance of portfolio = .002756 + .011 - .002756
Variance of portfolio = .011
Standard Deviation of portfolio = Square root of variance of portfolio
Standard Deviation of portfolio = Square root of .011
Standard Deviation of portfolio = 10.50%
Other options are incorrect based on above mentioned working.
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