We will review three common investment returns that are useful to understand and differentiate in analyzing performance.
Today we cover arithmetic mean investment returns. This is the most common measure and one that you use in daily life.
We will also compare mean versus median returns. Median being a term you may also encounter.
Next post will cover the other two important return calculations; geometric and dollar weighted average returns.
Mean versus Median Returns
The mean is the average of all the individual data points.
The mean is not the median, another term you may encounter.
The median return is simply the physical mid-point for all the individual results.
For example, you have 5 years of investment results: 10, 5, 22, 12, 11.
The arithmetic mean is the average of all results. Add the results and divide by number of years. In this case, 12.
To calculate median, you must rearrange all the data points from lowest to highest. Then find the exact mid-point.
In this example, we re-list the data in ascending order as: 5, 10, 11, 12, 22. The number at the mid-point is 11. That is the median. Do not forget to place the data in ascending order regardless of time period incurred.
Median Usefulness
The median is useful in letting you know that half the results are above 11 and half are below.
Medians are less sensitive to extreme scores (ie., outliers), so may be a better indicator for smaller sample sizes. Means can be impacted by a few extreme results, so provide better information in larger sample sizes.
In our example above, let us change the one data point from 22 to 220. The mean changes from 12 to 51.6. While it is indeed the arithmetic average, when compared to the other numbers in the sample, it appears unusual.
Does it really represent the “average” result from that time period?
If a mutual fund salesman tells you that his fund has averaged 51.6% over 5 years, you may expect that to be indicative of next year’s return. In reality, four of the five prior years had returns equal to or below 12%. Which do you think is more likely next year?
However, the median still remains at 11. The outlier had no effect on the median. If the fund salesman told you his fund had a median return of 11% over the five years, that is more representative of the prior years’ results.
However, if you are a fund salesman, what closes the sale better? Telling a potential investor that the 5 year average return is 51.6% or that the median return over that period is only 11%? I shall wait while you ponder this toughie!
Median Not Great in Real World Investing
That said, other than its relevance for small sample sizes and extreme results, I find the median of little real use in investing. But as you can see from the above example, knowing both the median and mean averages can provide better overall context.
Despite the potential impact of outliers, mean return can be quite useful in investing. Knowing the average results over a period of time or other criteria is important to the decision-making process.
There are a variety of mean calculations. Depending on the formula employed, the average returns can differ significantly.
Further, certain mean returns are good for some calculations, but are less relevant for others.
Arithmetic Mean Return
In our example above, I used the arithmetic mean calculation.
An arithmetic mean return is simply the sum of all the returns divided by the number of returns.
For example, you are analyzing an investment whose returns over the last three years were -10%, 20%, and 5%.
The arithmetic average return is 5% = [(-10+20+5)/3].
Pretty simple. Something you often calculate in everyday life.
Good for Independent Returns
Arithmetic mean returns are useful when data in the series is independent from each other.
For example, the arithmetic mean is relevant when calculating the average exam results for a class of students. The performance of each student is independent of the others (assuming no one is cheating by copying another student’s answers!). How you score is not affected by the students sitting around you.
Or when measuring the mean height of all the students in your class. The height of the student on your right should have no impact as to your own height.
But Investment Performance is Inter-Dependent
However, in investing, performance between periods is inter-related.
For example, if you invest $1000 and earn 100% in the first year, you start year two with $2000 in capital. But if you lost 50% in year one, you would only have $500 in capital at the beginning of year two.
In year two, let us say that you had a 20% return. In one scenario, your $2000 would grow to $2400. However, under the second scenario, your $500 would only grow to $600.
Same percentage gain of 20%, but significantly different monetary change.
You can see how the cumulative investment performance is inter-related to past results.
Negative Returns and Arithmetic Returns
A problem with using the arithmetic mean return for investment calculations is that negative returns skew average returns and sometimes make the results irrelevant.
For example, you invest $1000 on January 1, 2015. On December 31, the investment is worth $2000 and there were no cash flows during the year. Your annual and holding period return for 2015 is 100%.
You hold the investment throughout 2016 and at December 31, the value has fallen back to $1000, with no cash flows. Your holding period return for 2016 is -50%.
Your arithmetic mean return for the two years is 25% = [(100-50)/2].
But at December 31, 2016 you have exactly what you initially invested on January 1, 2015. Your return is 0%. It did not increase, on average, by 25%.
Always remember that negative returns skew arithmetic mean return calculations.
Also remember that arithmetic mean returns bias the average upwards.
To deal with the shortfalls of arithmetic means is where the geometric mean return becomes important. We will cover both geometric and dollar weighted returns next time.
