Series
Average return
Standard Deviation
Large-company stocks 10.7 % 19.3 %
Small-company stocks 16.4
33.0
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
What range of returns would you expect to see 68 percent of the time for large-company stocks?
To calculate the range of returns you would expect to see 68 percent of the time for large-company stocks, you need to use the standard deviation.
First, calculate one standard deviation:
Standard Deviation = Average Return * (Standard Deviation / 100)
Standard Deviation = 10.7 * (19.3 / 100) = 2.0631
Next, calculate the range of returns within one standard deviation:
Lower Bound = Average Return - Standard Deviation = 10.7 - 2.0631 = 8.6369%
Upper Bound = Average Return + Standard Deviation = 10.7 + 2.0631 = 12.7631%
Therefore, you would expect to see returns for large-company stocks within the range of approximately 8.6369% to 12.7631% for 68 percent of the time.
To determine the range of returns you would expect to see 68 percent of the time for large-company stocks, we need to use the concept of standard deviation.
Standard deviation measures the spread or dispersion of a set of data or returns. In this case, the standard deviation represents the volatility or variability of returns for large-company stocks.
In the given information, the standard deviation for large-company stocks is 19.3%. To calculate the range of returns within which we can expect to see about 68 percent of the time, we can use the empirical rule or the 68-95-99.7 rule.
According to the empirical rule, for a normal distribution of data:
- Approximately 68% of the data falls within one standard deviation of the mean
- Approximately 95% of the data falls within two standard deviations of the mean
- Approximately 99.7% of the data falls within three standard deviations of the mean
Since we are looking for the range of returns within one standard deviation, we can apply this rule to the average return of large-company stocks (10.7%) and the standard deviation (19.3%).
To calculate the lower range, we subtract one standard deviation from the average return:
Lower Range = Average Return - Standard Deviation
Lower Range = 10.7% - 19.3% = -8.6%
To calculate the upper range, we add one standard deviation to the average return:
Upper Range = Average Return + Standard Deviation
Upper Range = 10.7% + 19.3% = 30.0%
Therefore, we can expect to see about 68 percent of the time the returns for large-company stocks to fall within the range of -8.6% to 30.0%.