## Thursday, May 3, 2007

### 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.

John said...

Hal Varian misunderstood the paper. The paper's point is really that the simplistic stock price buy-and-hold analysis misses the dilution effects of companies making follow on public offerings when their price is high, and buybacks when their stock is low.

A stock may go from \$10 to \$20 to \$10, but if the company issued additional stock when it was at \$20, then the losers (among the investors) may outweigh the winners considerably.

Karl Smith said...

I'll look again but that didn't look like the point of the paper to me.

To me the arguement went like this -

Suppose I have a stock that is growing at 10% per year.

One investors buys and holds it for seven years.

Seven other investors each buy it for one year before selling it to the next investor.

The average annual return for the seven investors is 10% but the annualized return for buy and hold guys is 13%

Why?

Because the buy and hold guy is compounding his 10%. The market timers are not.

Another way to look at is that the 1st guy did worse than buy and hold because he did not stay in to see his gains multiply.

The last guy did worse than buy and hold because he had to put so much more money in to end up at the same place as the buy and hold guy.

Thus buy and hold is not a good proxy for the market as a whole.

John Thacker said...

FWIW, a commenter claiming to be Ilia Dichev, the author of the paper, has also commented on Arnold Kling's site and has supported my interpretation of the paper.

If you reread the paper, note that the first example the author offers is specifically about a subsequent public offering of stock. It makes sense-- additional offerings, buybacks, and option grants being exercised result in capital inflow or exit that a traditional buy-and-hold measure won't capture.

The buy-and-hold measure correctly captures the effects on someone who bought and held, but it doesn't measure how additional dollars might be entering or leaving the market without being the result of trades in the secondary market with other investors.

Anonymous said...

Seems to me that the calculation making Adam "in the middle" is odd. Don't you have to take time into account to understand real return?

Adam puts \$10 for 2 years to get \$30, a 73% compound two-year return.

Bill puts \$10 into the market for one year and sells for \$20 to get a 100% return for one year. But the second year his money lays fallow, so he has a 41% two-year compound return.

Chris is out of the market for a year then puts in \$20 to get a \$30, a 50% one-year return. But assuming he had \$20 in reserve from year 1 to employ in the year 2 purchase, then he has a 22% compound two-year return.

So this accords well with common sense: Adam did best, followed by Bill, then by Chris.

I find the discussion of 73%, 100%, and 50% to be misleading because it ignores time.

Am I missing something in the example?

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