# Question: The typical standard deviation of the annual return on a

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?

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?

**View Solution:**## Answer to relevant Questions

You are ordering milk for Mr. D’s supermarket, and you are determined to please. Milk is delivered once a week (at midnight Sunday). The mean and standard deviation of the number of gallons of milk demanded each day are ...Have you ever watched the odds at a horse race? You might hear that the odds against a given horse winning are 9 to 1, meaning that the horse has a probability 1/(1 + 9) = 1/10 of winning. However, these odds, after being ...Scores on an exam appear to follow a normal distribution with µ = 60 and σ = 20. The instructor wishes to give a grade of D to students scoring between the 10th and 30th percentiles on the exam. For what range of scores ...It is widely known that many drivers on interstate highways in the United States do not observe the posted speed limit. Assume that the actual rates of speed driven by U.S. motorists are normally distributed with mean _ mph ...A production process manufactures items with weights that are normally distributed with mean 15 pounds and standard deviation 0.1 pound. An item is considered to be defective if its weight is less than 14.8 pounds or greater ...Post your question