Do Most Investors Underperform

Arnold gets in on one of my favorite topics. The question of what are “returns” and “capital gains” really.

So for a little background Arnold writes:

I rely a lot on intuition. I make up simple, numerical examples to illustrate problems, and sometimes I mess up. I get misled by my own examples, and then somebody needs to correct me. In this case, let us start with an example Varian uses.

To understand the difference between a stock’s return and an investor’s return, consider someone who buys 100 shares of a company at a price of $10 a share. A year later, the share price is up to $20, and the investor buys 100 more shares.
Alas, the investor’s luck has run out. By the end of the next year, the price has fallen back to $10 and the investor sells his 200 shares.
A buy-and-hold investor who bought at $10, held the stock for two years, and then sold at $10 would have had a zero return.
But our friend who tried to time the market did much worse: over the two years, he invested $3,000 in the stock and ended up with only $2,000.

Fair enough. But who did our friend trade with? If I sold to our friend 100 shares at $10, then sold another 100 at $20, then bought them all back at $10, then I made $1000. In the aggregate, our friend and I broke even, which is what the stock did.
My intuition tells me that for every buyer there is a seller. So I do not understand how trading profits and losses do not cancel out in the aggregate. If they do cancel out, then investors as a whole end up earning the market rate of return.
In this case, my intuition blocked me from understanding the paper. This is one of those cases where I need help straightening out my intuition.

Arnold is correct. Varian’s example misses the return to the guy who sold at twenty and presumably bought at some previously lower price.

Here is a better one. Suppose there are three investors Adam, Bill, and Chris

Adam and Bill buy on the IPO at $10 a piece for one share of stock.

One year later the price has doubled to $20 and Bill sells his stock his stock to Chris. Bill realized a 100% return.

The next year the price goes up to $30. Both Adam and Chris sell their shares for $30.

Adam gets an annualized return of 73%¹. Chris gets a return of 50%.

At first blush it seems that Adam did about midway between Bill and Chris. So Adam is a good proxy for how well an investor can expect to do in the market. But, that’s not quite right. Chris invested as much money in the market as Adam and Bill combined. But, he made a smaller return than either of them.

In other words Chris’s 50% gain on $20 counts for more than Bill’s 100% gain on $10. The average dollar invested in the market behaved more like Chris’s money than like Bill’s money.

There is a big wrinkle in all of this though - an assumption that is not made explicit. I am going to think on it a bit more before I post.

1: (1 + 73%)*(1 + 73%) = 1 + 200%

Update: Greg offers some good advice on the matter.