6.51 At the end of the first quarter of 2006, all the major stock market indexes had posted strong gains in the past 12 months. Mass Mutual Financial Group credited the increases to solid growth in corporate profits ("Market Commentary: Economic Growth Characterizes Q1 2006," www.massmutual.com, May 1, 2006). The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was approximately 12%. The mean one-year return for companies in the Russell 2000, a group of 2000 small companies, was approximately 26%. Historically, the one-year returns are approximately normal, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the Russell 200 is approximately 35%. 2. What is the probability that a stock in the S&P 500 gained 25% or more in the last year? gained 50% or more? b. What is the probability that a stock in the S&P 500 lost money in the last year? Lost 25% or more? lost 50% or more? c. Repeat (a) and (b) for a stock in the Russell 2000. d. 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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6.51
6.51 At the end of the first quarter of 2006, all the major
stock market indexes had posted strong gains in the past 12
months. Mass Mutual Financial Group credited the
increases to solid growth in corporate profits ("Market
Commentary: Economic Growth Characterizes Q1 2006,"
www.massmutual.com, May 1, 2006). The mean one-year
return for stocks in the S&P 500, a group of 500 very large
companies, was approximately 12%. The mean one-year
return for companies in the Russell 2000, a group of 2000
small companies, was approximately 26%. Historically, the
one-year returns are approximately normal, the standard
deviation in the S&P 500 is approximately 20%, and the
standard deviation in the Russell 200 is approximately 35%.
2. What is the probability that a stock in the S&P 500
gained 25% or more in the last year? gained 50% or
more?
b. What is the probability that a stock in the S&P 500 lost
money in the last year? Lost 25% or more? lost 50% or
more?
c. Repeat (a) and (b) for a stock in the Russell 2000.
d. 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:6.51 At the end of the first quarter of 2006, all the major stock market indexes had posted strong gains in the past 12 months. Mass Mutual Financial Group credited the increases to solid growth in corporate profits ("Market Commentary: Economic Growth Characterizes Q1 2006," www.massmutual.com, May 1, 2006). The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was approximately 12%. The mean one-year return for companies in the Russell 2000, a group of 2000 small companies, was approximately 26%. Historically, the one-year returns are approximately normal, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the Russell 200 is approximately 35%. 2. What is the probability that a stock in the S&P 500 gained 25% or more in the last year? gained 50% or more? b. What is the probability that a stock in the S&P 500 lost money in the last year? Lost 25% or more? lost 50% or more? c. Repeat (a) and (b) for a stock in the Russell 2000. d. 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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