Why Some Market Gurus Have a Problem With Elementary Math

Posted by Alex Frey (@alexhfrey )

That more and more investors are turning to passive strategies that employ low-cost ETFs and index mutual funds such as those from Vanguard (which we recommend) is, on the whole, a great thing. No visitor to this website should be surprised that I hold such a view. It's hard to look at any of the data about mutual-fund or hedge-fund returns and not conclude that most people are best off in a low-cost passive portfolio.

It's also nice that passive investing makes things easy. If you don't want to think about your investments, you can put money into a Vanguard Retirement Date fund and do better than most over time. Or you can build your own simple ETF portfolio as I talk about in my book or in various places on this site.

But all this is not enough for the passive investing "guru". You know the type I'm talking about: that hearty soul who has figured out a way to continually repackage old and relatively simple concepts in a way that makes him seem wise and all-knowing.

Instead, the passive investing guru would like to add two further ingredients to the above story. Only these ingredients don't mix so well. In fact, when combined, they create an illogical and false argument.

The first ingredient that the passive investing guru would like to add is behavioral anomalies. It turns out that many individuals actually do far worse than the market due to mistakes. People are overconfident, they are overly emotional, they suffer from loss-aversion that makes them hold on to losing positions for longer then they should (in the hope of finally "breaking even"), and they anchor their future expectations too much on the recent past. This is all, by the way, true, and by itself another great reason for following a systematic or non-discretionary strategy (of which buy-and hold / passive investing is the simplest approach, but not the only approach). It's also a great reason to be suspicious of anyone's "intuition" about market movements (for more, read a tutorial on behavioral finance here). 

The second ingredient the passive investing guru likes to add to the story outlined above is that there is no way to reliably "beat" the market averages. Anyone that is able to do so in the past has just gotten lucky. If you think you can "time" things, you are a fool.

The guru probably adds this because people inherently want to believe that their way of doing things is the absolute best way, rather then simply "one of the better ways of doing things." But in fact, this argument belies an ironic lack of understanding of the simple mathematical principle that forms the foundation of passive investing.

Imagine the following elementary-school level math problem... The average of two numbers is 12. One of the numbers is larger then twelve. Is the other number smaller or larger then 12?

The fact that the average of two numbers has to be greater then one of the numbers and smaller then the other one is a basic "law of averages."

The same principle holds when we are talking about performance relative to the market. "The market" is composed of all the participants in the market. It is an average. So if some participants are beating the market average, other participants must be losing to the market average by a cumulatively equal amount.

The law of averages is the logical basis for why passive investing works. Once you add in the high fees of active management, it becomes mathematically certain that the average person is better of with a low-cost index fund (and, indeed, this is reflected in the data).

But the passive investing guru wants us to believe both that 1) Many people lose to the market average not due to bad luck, but due to investing mistakes, and 2) There is no way for anyone to beat the market average other than through luck.

This violates the law of averages. If the vast majority of people will perform worse than the overall market as a result of making behavioral mistakes, then some people must be able to beat the market by taking advantage of those mistakes. This is the basis for the tactical shifts that we make with the IvyVest Dynamic ETF Strategy.

Similarly, the fact that the average person cannot beat the average (particularly after subtracting fees) is in no way an argument that nobody can beat the average (as it is commonly purported to be). It is a simply a statement of a logical truth, since the average person is the average.

Some of these "passive investing gurus" are, I think, well-meaning and are just trying to get people to do the least harmful thing - which for many is indeed buying and holding a never-changing composition of various index funds. But the sanctimonious way in which they argue that their way is the only correct way rubs me the wrong way -- particularly so given that their argument is fundamentally illogical in a way that even an elementary school math student should be able to understand.


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By Alex Frey