Problem:

The Wall Street Journal reported that almost all the major stock market indexes had posted strong gains in the last 12 months. The one-year return for the S&P 500, a group of 500 very large companies, was approximately + 27%. The one-year return in the Russell 2000, a group of 2000 small companies, was approximately + 52%. Historically, the one-year returns are approximately normal. The standard deviation in the S&P 500 returns is approximately 20%, and in the Russell 2000 the standard deviation is approximately 35%.

Requirement:

1. What is the probability that a stock in the S&P 500 gained 30% or more in the last year? Gained 60% or more in the last year?

2. What is the probability that a stock in the S&P 500 lost money in the last year? Lost 30% or more?

3. Repeat (a) and (b) for a stock in the Russell 2000.

4. Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation.