The Case For A Geometric Mean For Quoting Returns

[Bryan Hancock]

Return citations were getting thrown around on another thread a few weeks ago so I took the liberty of dusting off some old finance texts where people try to get quite specific about citing returns. The case is made frequently for using a geometric mean instead of an arithmetic mean. There are also frequently negative returns with large enough samples so people like to add one to each of the observations and subtract one from the output of the geometric mean using these observations to arrive at a return metric.

So in other words you would use:

=GEOMEAN(Range_of_Percentages + 1) - 1

This mean is always equal to or smaller than the arithmetic mean that most people use to cite returns over a period of years. Presumably this is why it is not used even though it is more accurate.

Does anyone use this when they analyze their portfolio's returns? If so, do you use the percentages annually or make it more granular? Are there any problems you see with using geometric mean instead of arithmetic mean other than the greater difficultly in arriving at the figure?

[Dion DePaoli]

Well, in assets such as real estate, which do not have mark to market capacity, the way it is accounted for is only dealing with the actual. As value is not true until liquidation is achieved.

Measuring your net worth only shows that you increased how many assets you own, it is not a bench mark of management. Consider the following:

T1 = 10
T2 = 50
T3 = 30

So in year two, what is illustrated that you acquired more assets, 40 more to be exact. So you had a 400% increase in your worth. So what? Perhaps someone gave you $1 Million to invest with. In year three you sold assets, 20 worth. So your net worth dropped by -40%. Again so what, you liquidated some assets. It is not reflective of what gains or loss you had, merely the fluctuations in your asset schedule.

You could have gone from 10 in year one to 30 in year three with millions in loss. Adversely you could have gone with millions in gains.

Financial institutions do the net worth calculation you are talking about in relation to AUM. Which is not relative to return in any manner. You can have 200 Billion AUM and have a return of -50%. In year one, say a fund opens and perhaps it only raises 500k and then in year two say it raises 10 million. It is important to understand the raise since it might reflect in the return if some of the money was not fully invested to generate a return. However, it is a footnote to the return number and is not a major talking point in the discussion. Return is return and yield is yield.

Including cash flow is what is suppose to be done. To not include the cash flow your just doing math on numbers. Return includes cash flow by definition. Yield includes cash flow by definition. Its not complicated, it is proper.

You can do what ever you want, it doesn't mean it is right. If you mentioned to me your NW was X, I would still ask you what returns you had. If you use the difference between year beginning NW and year end NW you simply would be wrong. It has nothing to do with distortion in accounting, what you are doing is just trying to create a meaning from something that doesn't mean what you intend it to mean.