Explore BrainMass

# Calculating probability that a stock gained value and lost value

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

The major stock market indexes had mixed results in 2011. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was 0.00%. The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was -1.8% 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 2011?
b. What is the probability that a stock in the S&P 500 gained 10% or more in 2011?
c. What is the probability that a stock in the S&P 500 lost 20% or more in 2011?
d. What is the probability that a stock in the S&P 500 lost 40% or more in 2011?
e. Repeat a - d for a stock in the NASDAQ.
f. Discuss the risks associated with a large standard deviation.

© BrainMass Inc. brainmass.com March 5, 2021, 1:19 am ad1c9bdddf
https://brainmass.com/statistics/conditional-probability-distribution/calculating-probability-that-a-stock-gained-value-and-lost-value-580592

#### Solution Preview

For S&P 500, mean=0 and sd=20. SInce one-year returns are approximately normally distributed, z=(x-mean)/[sd]=(x-0)/.

a. P(a stock in the S&P 500 gained value in 2011)=P(X>0)=P(Z>0/20)=P(Z>0)=0.5 from standard normal table

b. P(a stock in the S&P 500 gained 10% or more in 2011)=P(X>10)=P(Z>10/20)=P(Z>0.5)=0.3085 from standard normal table

c. P(a stock in the S&P 500 lost 20% or more in ...

#### Solution Summary

The solution gives detailed steps on calculating the probability that a stock gained value and that a stock lost value.

\$2.49