# Why does buying at market prices (ala index funds) automatically equal to the average investor?

It's a frequent assumption, here by Burton Malkiel:

It’s true that when you buy an index fund, you give up the chance to boast at the golf course that you picked the best performing stock or mutual fund. That’s why some critics claim that indexing relegates your results to mediocrity. In fact, you are virtually guaranteed to do better than average

Why is buying at the market price (ala index funds) "virtually guaranteed" to do average? Are there any cases where it doesn't hold true? I feel like the answer will be something based on the Efficient Market Hypothesis, but not sure where to look.

Edit: I know from fees, taxes, etc. that you'll do better than average, but I am unconvinced on the underlying "equal to average" statement.

• Welcome to Lake Wobegon, where all the children are above average. Commented Apr 17, 2019 at 11:56
• @PeteBecker: Of course, "all are above average" is universally (at least for a non-empty set) impossible, while "more than 50% are above average" is completely feasible depending on which average (arithmetic mean, geometric mean, median, mode, something else?) is being used. Commented Apr 17, 2019 at 17:56
• @Nolan: Are you claiming that the arithmetic mean investor equals the market average, or that the median equals the market average? Both cannot be true, since mean > median when the tail is long as it is for the population of investors. Commented Apr 17, 2019 at 17:59
• @PeteBecker - As a lifelong fan I corrected your mis-quote. Commented Apr 17, 2019 at 20:40
• The question is unclear: "Why is the average or median investor always the market price?" The average investor does not get the market return, if that's what you meant. The quote you included suggests the opposite, saying that by getting (close to) the market return you beat most investors. Commented Apr 17, 2019 at 21:19

This is a graphic from the Vanguard article @timday referenced.

The article itself uses the term zero-sum in a way that's not common, but I'm ok with it, once understood. Note, for the question Is it true that 90% of investors lose their money? I open by saying

The game is not zero sum. When a friend and I chop down a tree, and build a house from it, the house has value, far greater than the value of a standing tree. Our labor has turned into something of value.

In hindsight, I stand by this brilliant quip. But I'm also open to how others use the term. Here, what Vanguard is saying is that in any given year, the market as a whole will have a return. If you believe the S&P is not reflective of 'the market', use a broader index, such as the Total Market Index Vanguard offers. The random nature of tens of millions of investors produces a curve of returns. Some see a higher return, some lower.

The point that Jack Bogle ('father' of index investing) had was that the average investor in mutual funds saw a return that had a cost, typically 1% or more, and that meant that even a good fund manager would have a tough time even matching the market return.

His approach was to drive index investing down to where anyone could invest for a return of S&P less .05% or so. My own retirement plan (along with my wife's) is in VIIIX, which charges .02% per year. This is \$200 per million invested. vs \$10,000 for funds charging 1%. The graphic shows that in any given year, far fewer than 50% will match the average, as the 'zero sum' is total market return less fees, and fees over the year will drag the average investor return down below market return.

Lest anyone cite some fund that's beaten the market over X years, that's great, what about the rest of them? And what of the thousands of funds that lagged and are closed now?

• Great answer, but I am trying to focus just on on this part: The random nature of tens of millions of investors produces a curve of returns. Some see a higher return, some lower. Commented Apr 18, 2019 at 4:55
• Joe, I feel there is some confusion. Let's utterly set aside any trading costs. (And totally forget about any issues of what zero-sum means or doesn't mean.) A simple index fund (which is nothing more than "the biggest say 100 companies") thrashes 99.999% of human stock pickers, particularly in the long run. This is the reason why "index funds beat stock pickers" (ie, because observably stock pickers are useless). As I understand it this is what th OP is asking. Commented Apr 18, 2019 at 13:09
• Fattie - if trading costs were zero, and no manager fees at all for any money managers, it would seem the curves presented above would be identical, the left shift is the cost of transactions. There would be good traders/investors and bad, but take the average return and divide it over the population, and average is average. Commented Apr 18, 2019 at 13:21
• @NolanHergert - if you look at the returns of mutual fund in any given year you will see a range of returns clustered about the market return, but when averaged out, just a bit lower due to cost. Please help me understand what's not clear. Perfect bell curves don't quite exist in most real life situations, but they are the best way to illustrate the phenomenon for sake of discussion. Commented Apr 18, 2019 at 13:25

Your question starts with a wrong premise....

In fact, you are virtually guaranteed to do better than average

That is fundamentally different from your question.

Why is the average or median investor always the market price?

The market price, according to your quote (and all the stats I've seen) is doing better than the average investor.

Your question is unclear, but I think the gist of it is why is everyone measured against the market. And the reason is that that's all anyone cares about.
So you got 10% ROI on your investments ? that's great, but the market rose 15%....
So you got 5% ROI on your investments ? That's amazing when the market went down 30% over the same time.

Because investing is a zero-sum game. For every investor beating the average market return (which is what the index gets you), there are others under-performing it by an equivalent amount. Cheap index funds let you invest in that average pretty much "for free" (or near enough) these days. Doing something else is usually more expensive in charges, and without a way of predicting which managers and/or strategies will outperform in future it's a coin toss whether you'll do better or worse than the average (and that's before those higher costs are considered).

See also Vanguard's "What's the zero-sum game?" article saying much the same thing.

• Uh, maybe you folks should put up your own answers? Commented Apr 17, 2019 at 16:56
• Yes. They should. No new comments on this answer, Please. Commented Apr 17, 2019 at 20:19
• The issue of whether the "market" is a zero-sum game is very confusing. (1) almost nobody even understand the phrase (2) when you talk about the local in time market that is utterly different from the macroscopic market. (3) There is vast, vast confusion between the issues of "stocks" which is one thing and "company 'values'" which is another. Regarding the macroscopic market (i.e. over decades), on the contrary to being a "zero sum game", the long-term market is very simply a ponzi: more and more people put in money every year, every generation. Commented Apr 28, 2019 at 13:35

The premise of market indexes beat 50% of investors is a way underestimate. The real number is well over 90% closer to 95%.

Where I am from that is more than good enough an answer, but I can see how that is less than satisfying.

So allow me to elaborate.

Actively managed funds (by professionals) rarely beat the market over the long term (5-7 years). In fact, they rarely beat a monkey with a dart board.

Why?

Warren Buffett actually explained it really well.

The simplest reason is, modern portfolio theory.

For an individual investor, having one great investment idea is HARD. Even with a team of professional, having 3 or 4 great ideas a year is very difficult. Warren Buffett said there were years he bought nothing because there was just nothing to buy.

And notice, the more positions you have, the more companies and business sectors you will need to follow.

It is essentially impossible to have that many great investment ideas, and even more impossible to track them all.

But modern portfolio management theory says, you MUST diversify.

Logic dictates, the more you diversify, the more duds you would have.

BUT unfortunately, your funds are limited. So no matter how diversify you are, you would never be as diversify as the market.

But wait, there is an even worse part of the theory, which says you should take profits just because it has gone up "too much" ... This leads to the bizarre scenario where people sell the winners too soon, and hold the losers too long.

As a result, by adhering to the modern theory of portfolio management... almost nobody beats the market.

And finally, the market is not the median of investors.. the market is all the stocks......

I want to thank the other answers for pointing me in the right direction.

I found Index Investing Makes Markets and Economies More Efficient on Philosophical Economics an excellent overview and a welcome improvement on Sharpe's terse article, The Arithmetic of Active Management. I will summarize below, but please refer to the original above for more details/caveats.

For an experiment lasting one year with many idealized assumptions, assume two groups of investors, passive and active. All passive investors will always get the market return (the real underlying change in price) because they are not offering their shares up for sale until the end of the year. Active investors as a group will also only get the market return because in the end, all their shares will have the same price on the open market. Therefore, the active investors are playing a zero-sum game (after subtracting the market return) because they have to buy and sell between themselves. For one active investor to outperform the market return, another active investor has to sell them those shares (at an eventual loss).

The market return (which every passive investor is getting by default) can then be thought of as the weighted (by investment size) average of the returns of each active investor, which sounds a lot more appealing than saying the "market return". E.g. "I beat half of the actively invested capital on the market by doing nothing, and that's even before management fees!"

The article also does a great job of explaining the caveats and showing how in practice they end up not mattering that much.