7.41 The major stock market indexes had strong results in 2013. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was +29.6%. The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized compa- nies, was +38.3%. Historically, the one-year returns are approxi- mately normally distributed, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the NAS-

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7.41 The major stock market indexes had strong results in 2013.
The mean one-year return for stocks in the S&P 500, a group of 500
very large companies, was +29.6%. The mean one-year return for
the NASDAQ, a group of 3,200 small and medium-sized compa-
nies, was +38.3%. Historically, the one-year returns are approxi-
mately normally distributed, the standard deviation in the S&P
500 is approximately 20%, and the standard deviation in the NAS-
DAQ is approximately 30%.
a. What is the probability that a stock in the S&P 500 gained
value in 2013?
b. What is the probability that a stock in the S&P 500 gained 10%
or more in 2013?
c. What is the probability that a stock in the S&P 500 lost 20% or
more in 2013?
d. What is the probability that a stock in the S&P 500 lost 30% or
more in 2013?
e. Repeat (a) through (d) for a stock in the NASDAQ.
f. Write a short summary on your findings. Be sure to include a
discussion of the risks associated with a large standard deviation.
Transcribed Image Text:7.41 The major stock market indexes had strong results in 2013. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was +29.6%. The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized compa- nies, was +38.3%. Historically, the one-year returns are approxi- mately normally distributed, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the NAS- DAQ is approximately 30%. a. What is the probability that a stock in the S&P 500 gained value in 2013? b. What is the probability that a stock in the S&P 500 gained 10% or more in 2013? c. What is the probability that a stock in the S&P 500 lost 20% or more in 2013? d. What is the probability that a stock in the S&P 500 lost 30% or more in 2013? e. Repeat (a) through (d) for a stock in the NASDAQ. f. Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation.
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