Question: The typical standard deviation of the annual return on a stock is 20% and the typical mean return is about 12%. The typical correlation between the annual returns of two stocks is about 0.25. Mutual funds often put an equal percentage of their money in a given number of stocks. By choosing a large number of stocks, they hope to diversify away the risk involved with choosing particular stocks. How many stocks does an investor need to own to diversify away the risk associated with individual stocks? To answer this question, use the above information about "typical" stocks to determine the mean and standard deviation for the following portfolios:
¦ Portfolio 1: Half your money in each of 2 stocks
¦ Portfolio 2: 20% of your money in each of 5 stocks
¦ Portfolio 3: 10% of your money in each of 10 stocks
¦ Portfolio 4: 5% of your money in each of 20 stocks
¦ Portfolio 5: 1% of your money in each of 100 stocks
What do your answers tell you about the number of stocks a mutual fund needs to invest in to diversify adequately?