Question

I need help setting up this question.

Background:

David Mark Peterson is considering his 401(K)-retirement portfolio and wonders if he should move some of her money into international investments. Up to now, he has simply put his retirement savings into a mutual fund with an investment strategy that matches the returns of the S&P 500 index (large company stocks). This fund has historically earned a return averaging 12 percent over the last 80 years or so years, but recently the returns were depressed somewhat, as the economy was languishing in a mild recession. David is considering an international mutual fund that diversifies its holdings around the industrialized economies of the world and has averaged a 14 percent annual rate of return. The international fund’s higher average return is offset by the fact that the standard deviation of its returns is 30 percent compared to only 20 percent for the domestic index fund. Upon closer investigation, David learned that the domestic and international funds tend to earn high returns and low returns at about the same time in the business cycle, such that the correlation is .75. Suppose David moves half his money into the international fund and leaves the remainder in the domestic fund.

Question:

What are the expected return and standard deviation of the combined portfolio?

Thank you in Advance

Answer 1

Expected return of the combined portfolio = weight of domestic fund * return from domestic fund + weight of international fund * return from international fund

= 1/2*12% + 1/2*14%

= 13%

Standard deviation of the combined portfolio = [ (weight of domestic fund^2*standard deviation of domestic fund^2) + (weight of international fund^2*standard deviation of international fund^2) + (2*weight of domestic fund * standard deviation of domestic fund * weight of international fund * standard deviation of international fund * correlation) ]^1/2

= [ (1/2^2 * 20%^2) + (1/2^2 * 30%^2) + (2*1/2*20%*1/2*30%*0.75) ]^1/2

= 23.45%

Thus expected return of the combined portfolio is 13% and standard deviation is 23.45%