7.3.3 Averaging Returns
When statisticians want to understand a set of data, they use statistics. If they want to get a representative value for the data, they look to measures of central tendency. When they want to get a measure of the variability within the data, they look at measures of variability. Investment advisers also look at measures of central tendency and variability to understand the returns on investments.
Central tendency is a single value that summarizes a set of scores. For investors, central tendency is often used to summarize a set of returns. For example, an investor may wish to know the most representative return from a set of annual returns. The mode, median, and mean are all measures of central tendency. The mode is the most common score in a set of data. If we look at the historical returns for Stock B in the table that follows, the mode would be 5%, because this is the most common return. The median is the middle score when all the scores are ordered from lowest to highest. We can find the median for Stock B by ordering the returns from lowest to highest: 3%, 4%, 5%, 5%, 5%. The middle return is 5%, so that would be the median. When there is an even number of scores, the two middle scores are averaged to get the median. Because the median is not influenced by outliers, the median is the most commonly used measure of central tendency if there are outliers in the data.
The mean is the arithmetic average of the scores. The mean return of Stock B is 4.4%, because if you add up all the returns and divide by the number of returns, it is 4.4%. For a set of returns that includes negative returns, however, the arithmetic mean is not an accurate measure of the most central tendency. Consider an investment of $100 that rises to $125 in the first year. The return on this would be 25% ($25 gain / $100). Then in the second year, the investment drops back to $100, resulting in a negative 20% annual return ($25 loss / $125). If we ave