The Meaning of Average
The term ‘average’ occurs frequently in all sorts of everyday contexts – you may say ‘I’m having an average day today’ meaning your day is neither particularly good nor bad, it is about normal. Similarly, we may refer to people, objects and other things as ‘average’.
The Average is one of the measures of “central tendency” in a data set. Calculating an average involves determining the sum of a list of numbers and then dividing the sum by the number of numbers in the list. Averages don’t take process variation into consideration.
Disadvantages when relying on averages:
1. Sensitive to extreme values
The arithmetic average is extremely sensitive to extreme values. Imagine a data set of 4, 5, 6, 7, and 8,578. The sum of the five numbers is 8,600 and the mean is 1,720 – which doesn’t tell us anything useful about the level of the individual numbers.
Therefore, the arithmetic average is not the best measure to use with data sets containing a few extreme values or with more dispersed (volatile) data sets in general. A median can be a better alternative in such cases.
2. Not suitable for time series type of data
The arithmetic average is perfect for measuring central tendency when you’re working with data sets of independent values taken at one point of time.
However, in finance, you often work with percentage returns over a series of multiple time periods. For calculating average percentage return over multiple periods of time, arithmetic average is useless, as it fails to take the different basis in every year into consideration (100% equals a different price or portfolio value at the beginning of each year).
The more volatile the returns are, the more significant this weakness of arithmetic average is. Here you can see the example and reason why arithmetic average fails when measuring average percentage returns over time.
3. Works only when all values are equally important
Arithmetic average treats all the individual observations equally. In finance and investing, you often need to work with unequal weights. For example, you have a portfolio of stocks and it is highly unlikely that all stocks will have the same weight and therefore the same impact on the total performance of the portfolio.
Calculating the average performance of the total portfolio or a basket of stocks is a typical case when the arithmetic average is not suitable and it is better to use a weighted average instead.
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