Investing in a mix of U.S. stocks and foreign stocks
Many advisers recommend using roughly 20% foreign stocks to diversify portfolios of U.S. stocks. You see that the 500 Index (U.S. stocks) and Diversi?ed International (foreign stocks) Funds had almost the same mean returns. A portfolio of 80% 500 Index and 20% Diversi?ed International will deliver this mean return with less risk. Verify this by ?nding the mean and standard deviation of returns on this portfolio. (Example 4.38, page 284, shows
R = a σW + b σX + c σY + 2abρWX σWσX
+ 2acρWY σWσY + 2bcρXY σX σY
A basic well-diversi?ed portfolio has 60% in 500 Index, 20% in Investment Grade Bond, and 20% in Diversi?ed International. What are the (historical) mean and standard deviation of the annual returns for this portfolio? What does an investor gain by choosing this diversi?ed portfolio over 100% U.S. stocks? What does the investor lose (at least in this time period)?