Question

A U.S. investor is considering a portfolio consisting of 50% invested in the U.S. equity index fund and 50% invested in a global equity index fund. The expected returns for the funds are 10% for the U.S. and 12% for the global, standard deviations of 20% for the U.S. and 25% for the global, and a correlation coefficient of 0.30 between the U.S. and the global funds. What is the standard deviation of the proposed portfolio?

Answer 1

Weight of U.S. equity fund (Weight A)= 50%

Standard deviation of U.S. equity fund (σA)= 20%

Weight of global index fund (weight B)= 50%

Standard deviation of global fund(σB)= 25%

Correlation between U.S. equity fund and global index fund = 0.3

(σp)= √((weigh A * σA ) ^2 + (weight B* σB )^ 2 + (2 * Weight A* Weight B*σA *σB* correlation))

=√((50%*20%)^2+(50%*25%)^2+(50%*20%*50%*25%*0.30))

√(0.033125)

=0.1820027472 or 18.2%

So, standard deviation of proposed portfolio is 18.2%

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