Consider the following table for the total annual returns for a given period of
ID: 2714520 • Letter: C
Question
Consider the following table for the total annual returns for a given period of time.
Series
Average return
What range of returns would you expect to see 68 percent of the time for large-company stocks?
What about 95 percent of the time?
Series
Average return
Standard Deviation Large-company stocks 11.9 % 20.3 % Small-company stocks 16.433.0
Long-term corporate bonds 6.2
8.4
Long-term government bonds 6.1
9.4
Intermediate-term government bonds 5.6
5.7
U.S. Treasury bills 3.8
3.1
Inflation 3.1
4.2
Explanation / Answer
The empirical rule states that, for a normal distribution nearly all of the data will fall within three standard deviations on either side of the mean.
The empirical rule can be broken down into three parts:
From the data given, the large company stocks have a mean of 11.9% and standard deviation of 20.3%.
Answers to the Requirements:
1. Range of return 68% of the time = Mean + 1* std deviation = between (11.9 + 20.3) and (11.9 - 20.3) = between 32.2% and - 8.4%.
2. Range of return 95% of the time = Mean + 2* std deviation = between (11.9 + 2*20.3) and
(11.9-2*20.3) = between 52.5% and - 28.7%.