Arnold Kling  

Investor Returns, Stock Returns, and My Intuition

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An Old Prediction May Come Tru... Kling vs. Lang...

Hal Varian writes,


An investor who bought a value-weighted portfolio of stocks in the New York Stock Exchange and American Stock Exchange in 1926 and held them until 2002 would have earned an average annual return of about 10 percent.

By contrast, an individual who bought in 1926 but moved his dollars in and out of the market in the same pattern as the average dollar invested in the market would have earned a return of only 8.6 percent a year.


He cites this paper by Ilia D. Dichev, which appeared in the American Economic Review in March. I remember seeing the paper, and I remember being completely baffled by it.

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.

UPDATE: Some commenters, including the author of the paper, help to clarify. It sounds as though firms float new stock when prices are high and buy back stock when prices are low.

My first reaction to the comments (and I admit to being heavily medicated at the moment, due to allergies) is to think, well, ok, companies earn trading profits against individuals. But, then, individuals own companies. If I own 100 shares of XYZ, XYZ floats 10 shares that you buy for $100, then XYZ buys them back from you for $50, your loss is in some sense my gain. The point may be that my gain gets counted in the return to shareholders, but your loss does not, unless we dollar-weight returns. In that case, unweighted returns overstate the rate of return.


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TRACKBACKS (1 to date)
TrackBack URL: http://econlog.econlib.org/mt/mt-tb.cgi/695
The author at Modeled Behavior in a related article titled Do Most Investors Underperform writes:
    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 [Tracked on May 3, 2007 10:43 AM]
COMMENTS (20 to date)
jon writes:

They are comparing two fundamentally different measures of return - time weighted return and dollar weighted return.

I haven't read the paper, but here is my take - dollar weighted return will necessarily be less than time weighted return if you buy after good returns and sell after bad returns. The paper takes 2002 as its end date (i.e. after a significant bear market). I am not surprised that the dollar weighted return is less than the time weighed return (I am also not surprised that the difference appears to be greatest for the NASDAQ).

I would be interested to see if the results would be different with an end dat of 1999 or maybe 2006.

Maybe if I had read the paper, my doubts would be answered, but until then, I'll go with my intuition.

spencer writes:

Just remember the old wall street bromide that everytime a stock changes hands someone is making a mistake -- either the buyer or the seller.

Don Lloyd writes:

Arnold,


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.

To initially have the shares to sell, you must either have purchased them earlier, received them as a founder, or borrowed them to sell short. You have not covered any of these possibilities.

Assume that only a single stock exists and that it goes up 10% every year. If no one shorts the stock, then each investor realizes the stock's return only during the time period in which he actually owns the stock, and all investors gain.

The returns of a buyer and seller of a given share of stock in a single given transaction are independent of one another. The transaction represents the beginning of an investment time period for the buyer and the end of a time period for the seller.

Regards, Don

Arnold Kling writes:

jon,

But if I buy after good returns and sell after bad returns, who do I trade with? And why don't their excess profits offset my shortfalls?

That's what I don't get about this whole "dollar-weighted" deal.

John Goes writes:

The trajectory of the average investment will be different from the average trajectory of all investments, no?

So if most investors are trading like it's Vegas, the average trade will be erratic, but this is made up for on the extremes by stable investors, lucky/perceptive investors, who take the losses gained from the average trader, or the average dollar.

I don't have access to the paper, so I'm just throwing something out.

Michael Sullivan writes:

Arnold -- I believe that the lesser return comes not from problems with investment in the stocks, but from investment *not* in stocks -- IOW, all of the times that the average investor pulled out of the market because it looked too risky and lost some gains.

So the problem is that the average stock investor was only 86% (or less) as invested in stocks as a similar "buy and hold" investor over that time.

Your intuition is perfectly correct from the point of view of the *stock*. But from the point of view of the people, there were times when they weren't invested in that stock at all, but in something else (or even cash in the mattress).

Don Lloyd writes:

Michael,

Arnold -- I believe that the lesser return comes not from problems with investment in the stocks, but from investment *not* in stocks -- IOW, all of the times that the average investor pulled out of the market because it looked too risky and lost some gains.

This is exactly right, and, the fact that being out of the market at certain times may have produced lower historical returns in no way means that being out of the market was necessarily a bad decision, even if looking backwards would seem to indicate such.

Regards, Don

jon writes:

Dr. Kling:

I agree that in a closed system, for every dollar of profit on a trade there is a corresponding loss to the other party. I was merely saying that the comparison of dollar weighted return and time weighted return is comparing apples to oranges.

I believe that Michael Sullivan has part of the answer correct. In the numerical example provided, for you to sell me the 200 shares, you must either have owned them or have sold them short to be repurchased later. If you own them, and by selling me the shares you then hold cash for some period, your dollar weighted return will not be the inverse of mine. If you had not owned them, but sold them short to me, then your return would be the inverse of mine – only in this scenario would the time weighted return equal the dollar weighted return – even though your profits offset my losses in dollar terms.

I admit that I could probably stand to give this some more thought, but I think my answer is reasonable - it's not that investors do worse than average, it's that we are comparing two different averages.

Regards,

jon

jon writes:

...but I still believe that the two measures would be closer together if the end date for the study was, say, Dec 31, 1998 instead of 2002.

jon

Bob writes:

It appears that Michael Sullivan's idea suffers from the same problem - if investors are, on average, 86% invested in stocks, there is no way for everyone to become 100% invested. Who do they buy from?

The whole idea of "money flows" is weird in a secondary market. Perhaps the paper is tied to the IPO market and corporate buybacks? Even this is complicated because if firms provide some "equilibrium" amount of stock based on the demand for equity investments, the shifting capital structure changes the expected return on the equity investments. I guess I should read the paper.

Karl Smith writes:

o the problem is that the average stock investor was only 86% (or less) as invested in stocks as a similar "buy and hold" investor over that time.

I think you guys are on the right track here but the question is what happened to the average dollar invested in the market. Not the average investor.

The problem is that the average dollar in the stock market today came in when the price was high. Therefore the return on the average dollar is lowers

Ted Shepherd writes:

I quote this:

If they do cancel out, then investors as a whole end up earning the market rate of return.

More completely: If they do cancel out, then investors as a whole end up earning the market rate of return reduced by whatever expenses the investors incur for trading, management, and research costs, and for capital gains taxes. Those are substantial costs as we see by the take of brokerages, financial managers, and IRS. A buy-and-hold investor in a no-load broad-market index fund can minimize these costs, paying as little as 12 cents per hundred dollars per year for management and nothing for trading, research, or capital gains taxes. I could be more specific about how to achieve this but then my post would look like a promotion.

John Thacker writes:

But if I buy after good returns and sell after bad returns, who do I trade with? And why don't their excess profits offset my shortfalls?

Professor Kling, the paper gives examples of stock buybacks and additional offerings, and I think that makes some amount of sense.

The point is that some shares are created or destroyed by additional stock offerings or buybacks. There is, in that sense, capital inflow and exit. The buy-and-hold model doesn't capture this. It doesn't have a lot to do with timing the market, so I think that Professor Varian is incorrect. (Not timing the market is good for other reasons, such as fees, as pointed out.)

Consider the following:

The share price for a company is $10 a share. A year later, the price is up to $20, but the company needs to raise more capital. They sell additional shares at $20. Another year later, the price declines to $10.

From the buy and hold perspective, there's a zero return. The price was $10, and it remains $10. However, clearly from the average investors' point of view, there was a decline. There were many new purchasers of the stock at $20 who clearly lost when it went to $10. The "dollar-weighting" is weighting that there actually was more shares (and more dollars) injected into the company when the new follow-on public offering was made.

That's the story in the paper. Another way of putting it, it seems, is that the buy-and-hold analysis either doesn't take into account the dilution effects of issuing additional stock in the company.

Unsurprisingly, the tech-heavy Nasdaq, with many companies looking for rapid growth through additional public offerings of stock, saw the biggest difference in its aggregate return.

John Thacker writes:

Your intution is correct, then.

Take into account that most companies issue additional stock when the price is high, not low, and buyback when the stock is low, and we see how simplistic price analysis from a buy-and-hold view misses out. People and dollars actually are joining the market later, when new shares are added.

John Thacker writes:

Although, now that I think about it, it is an argument against a type of stock market investment-- the paper seems to say that buying follow on issues is a bad idea.

Ilia Dichev writes:

All right, I am the author. From the above comments, John Thacker has the story right. Several additional points:

1. Yes, most trades cancel in the aggregate, so they do not produce dollar-weighted effects. DW effects are produced by net equity inflows or outflows (issue stock, repurchase stock, options exercise, etc.)

2. Dollar-weighted effects exist at any level of aggregation and for any security. They have been known for some time for mutual funds.

3. Yes, DW results for Nasdaq are less pronounced if you take 2005 or 2006 as ending year.

4. It is best to see the paper, available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=544142

5. DW effects result from the fact that there is different capital exposure of investors at different points in time. Buy-and-hold returns completely miss that.

6. DW effects do not results from transactions costs, these are separate.

Thanks for your interest!

Matt writes:

Arnold got me to read the paper, and I was interested in how IRR was used.

What does it mean that over a long time the IRR from the security industry is positive?

If all the inflation were compensated and the IRR was positive, then I would say, over the long time, that the stock market represents a more efficient form of organization. So I would expect that from, say 1926 to 2007, the corporations have grown in their share of the economy relative to other forms.

I have a hard time understanding wealth other than economic share.

John Thacker writes:

Another way of thinking about it that I find useful is that the company itself is the ultimate "insider." The company knows when to buy and sell its own stock better than the average investor, so in general the company's "investment" in its own stock does better than the stock price. Then, intuitively, the secondary market does worse than the stock price.

People who already own the company stock still approve, in general, because they'd rather the company get money than the new investors. :)

conchis writes:
"...companies earn trading profits against individuals. But, then, individuals own companies."

But there's no reason those trading profits have to make it back to individuals is there? Could they not simply be squandered?

Hal Varian writes:

Yes, Thacker (and Dichev) are right. Dichev explains clearly in the paper that what matters is net sales of stock from the corporations to the investors. I don't think that I said anything contrary to this, but I wanted to make some additional points about small investors who trade too much (Terry Odean's work) and the impact of news items on small investors (the FAJ article).

Perhaps it would have been better to focus on one of these articles rather than try to discuss all 3 since they all make different (but related) points.

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