Chapter 6, Problem 39PS

The major stock market indexes had strong results in 2016. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was $+9.54\%$ . The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was $\text{+7}\text{.50\%}\text{.}$ Historically, the one-year returns are approximately normally distributed, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the NASDAQ is approximately 30%.

a. what is the probability that a stock in the S&P 500 gained value in 2016?

b. What is the probability that a stock in the S&P 500 gained $10\%$ more in 2016?

c. What is the probability that a stock in the S&P 500 lost $20\%$ or more in 2016?

d. What is the probability that a stock in the S&P 500 lost $30\%$ or more in 2016?

e. Repeat $\left(\text{a}\right)\text{through}\left(\text{d}\right)$ for a stock in NASDAQ.

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