Thursday, February 16, 2017

The Economics of Insider Trading: A Puzzle

The standard story on insider trading is straightforward. I have knowledge that implies that a stock is going to go up, so I buy it. The seller sells because, absent that knowledge, my offer is more than he, and presumably most of the rest of the market, thinks the stock is worth.

There is a problem for this story if we assume that all the players are rational. If there are a significant number of insider traders in the market, the fact that I offered more for the stock than the owner thought it was worth should be evidence to him that I know something about it he doesn't, and so a reason not to sell.

To put the point differently, if the insider traders are making a higher return on their invested capital than the market average, which is the point of insider trading, everyone else must be making a lower return than the market average. But anyone who wants can get the market average by buying the whole market, or an index fund, or a random selection of stocks. All he has to do to protect himself against insider traders is to avoid the strategy of estimating stock values for himself and selling when the price he is offered is above his estimate, buying when below.

One possible explanation is that some traders are insiders and some think they are, believe they have better than average knowledge or judgement but are wrong. But I am assuming, as economists often do, that all the players in the game are rational.

This puzzle first struck me when I thought I had an ingenious explanation of why, on average, stocks outperform bonds, as it is commonly asserted that they do. If buying stock and holding for ten years is practically guaranteed to give you a better return than buying bonds and holding for ten years, one would think that everyone investing for the moderately long term would buy stock and their doing so would drive the price of bonds down and their yield up until the two investments were equally attractive. 

One could avoid that by assuming that there was enough risk averse money looking for short term investments to drive bond prices up and the yield down to a point where the yield was below the return on stocks. That conjecture could lead to interesting empirical work testing it. But I am by nature a theorist not an empiricist, so I was looking for a different answer and thought I might have found it.

Imagine a market where everybody is an inside trader on a small scale. I know more than the market about the firm I work for. You know more than the market about a firm you have repeatedly had dealings with. He knows more than the market about a technology he has worked with extensively that will affect the performance of several firms.

Each person invests some of his money where he has an edge and, by the standard analysis of insider trading, makes an above market return. But because he is risk averse he wants to diversify his investment, so part of his money goes into other investments. His marginal return is the return he can get without inside knowledge, his average return is a suitably weighted average of that and his insider return. Bond investments only have to do as well as his marginal investments, so the return on bonds is lower than the average return on stocks.

I thought it was a lovely theory–until it was pointed out to me that an investor who wanted to get the average return on stocks could do so with no inside information by simply buying the whole market, or an index fund, or ... . And, if the average return on stocks was higher than on bonds, he would.

Which brings me back to my puzzle. Does anyone have a good solution? I have wondered if it has some deep connection with Robin Hanson's old puzzle of why each of us prefers his own opinion to that of others even if he has no reason to think he is better informed on the subject than they are.

17 Comments:

At 3:33 AM, February 16, 2017, Blogger Nothing said...

Is it possible that the explanation to his puzzle is that, in a perfect rational world, this puzzle would never exist?

 
At 3:53 AM, February 16, 2017, OpenID hudebnik said...

I'm inclined to agree and go with the obvious explanation: stock investors are not perfectly rational.

Or, if you prefer, they're perfectly rational under the modified assumption that some of their "payoff" from investing is the enjoyment of playing the market rather than tangible monetary gains. Thinking you're an insider makes you feel good, whether or not it actually gets you a higher-than-average return.

This applies most obviously to amateur individual investors, but it could apply to professional brokers too: from what I've read about Wall Street, there's a tendency towards adrenaline addiction, which skews the payoff matrix away from pure monetary returns. Obviously, one would rather say "I made $3 million today" than "I lost $3 million today," but the latter might be psychologically preferable to saying "I made $30 today."

 
At 4:12 AM, February 16, 2017, Blogger Miguel Madeira said...

"There is a problem for this story if we assume that all the players are rational. If there are a significant number of insider traders in the market, the fact that I offered more for the stock than the owner thought it was worth should be evidence to him that I know something about it he doesn't, and so a reason not to sell."

But, in this scenario, stock market transactions never happens, no? After all, ALL stock market transaction occur when buyers offered more for the stock than the owner thought it was worth (only in this case the owner sells).

 
At 7:57 AM, February 16, 2017, Blogger Rohan said...

Maybe approach the problem from the other side. If the insider has information that the stock is going to fall, she sells it to someone else. Maybe to someone looking to cover the entire market. The stock falls, reducing the buyer's return.

So essentially the insider makes money by avoiding the parts of the market which depress the market average.

 
At 9:56 AM, February 16, 2017, Blogger Patri Friedman said...

There are a lot of well-known ideas to explain the equity premium, none satisfactory as the sole answer, but in total seem sufficient. Wikipedia has a nice list: https://en.m.wikipedia.org/wiki/Equity_premium_puzzle

 
At 11:16 AM, February 16, 2017, Blogger Steve said...

Do we have good evidence that insider information is more reliable overall than other forms of information, or no information?

Suppose that some investors do have reliable information which in fact improves their returns in the long term. Necessarily, someone on the other side will take corresponding losses.

"But anyone who wants can get the market average by buying the whole market, or an index fund, or a random selection of stocks."

Index investors will get the average of what the market yields. This is not necessarily the average of what all individual investors earn.

As an analogy, if sports betting is zero-sum, the average result from any game will be to break even. Someone could try to guarantee breaking even by choosing teams with a coin toss. In practice, the coin-toss bettor will be unable to place even bets for teams that informed fans know are stronger. They will have to pay a premium for these bets. They might also get a discount when the coin says to bet on weaker teams. If expert fans are in fact able to extract profit by betting with their sports knowledge, then "index" betting on random teams at prevailing odds is on average a losing proposition.

 
At 5:27 PM, February 16, 2017, Anonymous Anonymous said...

1) There are lots of incentives to hold stock portfolios that earn less in absolute terms (in the long run, unleveraged) than the index, provided those portolios have returns that are uncorrelated with and/or have a higher risk-adjusted return than the index. This is because investors are risk averse, so the benefits of a higher sharpe ratio and/or another uncorrelated stream of returns.

2) It's true that any stock picking strategy must overcome the adverse selection problem that some fraction of your trades will be filled against counterparties who have information you don't. Insider trading is just a particularly salient example of this, but it applies more generally to types of information that aren't necessarily illegal. One way to think about this is that your average trade has a slightly lower expected utility because of this problem. But if your stock picking strategy is sufficiently profitable in general, it will still make a profit after this additional cost.

No puzzle, as far as I can see.

 
At 8:17 PM, February 16, 2017, Blogger The Skip Bureau said...

To me, it's a straightforward thing. Traditionally, bonds are lower risk and guaranteed payout. When you buy a stock, there's a substantial risk you may lose all your investment. When you buy a bond that has a high rating, theoretically, you have a much smaller risk of complete loss, as bonds are paid out before stocks in liquidation, and bonds are issued on the credit of the company, not the estimated promise of the company. With a bond, at some point in the future, the bond issuer will redeem it for a stated value. With a stock, at some point in the future, you will have to find someone to buy it from you.

 
At 11:07 PM, February 16, 2017, Blogger David Friedman said...

Miguel:

In this market, transactions still happen, but not because the seller thinks he has guessed the value of the company better than the buyer, unless he really does have insider information.

I could, for example, sell a random selection of my stocks because I want the money to buy a house or send my kid to school.

 
At 11:09 PM, February 16, 2017, Blogger David Friedman said...

I should perhaps have made it explicit that what I mean by insider trading has nothing to do with whether the trade is illegal, only whether the trader correctly believes he has relevant information available to few others.

 
At 1:13 AM, February 17, 2017, Blogger Justin Flannery said...

I might be approaching this too simply but I think the (very simple) answer is how stock markets are structured. Investors aren't buying and selling stocks between each other. They're buying and selling at a stock brokers bid and ask price, which for any individual at a point in time are essentially fixed by the market price of the stock at that time. There's no information to be gleaned by a seller in such a situation.

It's a different situation if a large institutional investor is trying to take over a firm and is in fact making an offer per share. It's only in that situation, which isn't the typical transaction in a stock market, that your story is valid.

 
At 9:30 AM, February 17, 2017, Blogger Bravin Neff said...

"To put the point differently, if the insider traders are making a higher return on their invested capital than the market average, which is the point of insider trading, everyone else must be making a lower return than the market average."

Mathematically and literally true, but in practice nearly completely insignificant. The "lower return than the market average" the non-insider traders make pushes toward zero as the ratio of non-insiders to insiders is large. Put another way, the group size of the non insiders dwarfs the insiders, and so does their aggregate investments. Which means their returns closely reflects the market average, despite the above average returns the insiders make.

Therefore, when you say "All [the non-insider] has to do to protect himself against insider traders is..."

...is more or less ignore their existence. Which is exactly what nearly everyone does.

I think there is a problem when you say "There is a problem for this story if we assume that all the players are rational," and then suppose that when one offers a higher price than onesself is willing to pay, that the reason this presents not to sell is particularly strong, or substantially stronger than other reasons that might exist for selling. Not only is it fantasy that all players are rational (as every economist knows deep down inside), even if they were, everyone has different price elasticities, which are in constant flux, and reasons always abound for selling when the price is right, even just a little bit right.

"Does anyone have a good solution? I have wondered if it has some deep connection with Robin Hanson's old puzzle of why each of us prefers his own opinion to that of others even if he has no reason to think he is better informed on the subject than they are."

I think that's right. Also, the Stiglitz and Grossman paper ("On the Impossibility of Informationally Efficient Markets") showed its paradoxical to assume markets are informationally efficient. The fact people always have an incentive to discover more information tucks in nicely with the Hanson thing. I think.

 
At 10:47 AM, February 17, 2017, Blogger Kian Conteh said...

https://www.thestar.com/news/insight/2016/01/16/when-us-air-force-discovered-the-flaw-of-averages.html

I suspect the problem is the use of average as if it is something you can be. In reality I would expect the stock market investors to form a wider bell shape with a higher average than the bond investors. No one can decide where on the bells they will end up.

A more than average risk averse investor may rationally prefer to risk being on the looser end of the bond market bell, than on the looser end of the stock market bell. That choice comes with the cost of a lower expected average.

That explanation would predict that in a stock bull market, the cost of being on the looser end of the stock bell is much lower, making the risk averse investor more likely to choose stocks than before, thus causing falling prices of bonds. That seems på be exactly what happens.

 
At 11:12 AM, February 17, 2017, Anonymous Procrustes said...

Suppose that all investors are either completely uninformed or insiders, and that uninformed investors ONLY invest in index funds.

Then, the only trades in individual stocks will be (toxic) insider trades and (non-toxic) trades by the index funds (as there will still be index inflows/outflows, and maybe index rebalances). Let's also say that both groups always trade by crossing the market makers' posted bid/ask spread.

Assuming that market makers are unable to discriminate between insider and investor orders, they will have to set a bid/ask spread wide enough (/more aggressively adjust their prices against their inventory) that their gains from trading on unformed fund orders will compensate them for losses on informed orders. As the proportion of total trading that is informed rises, the spread widens, but as long as there are enough uninformed orders there's some level at which the market maker has non-negative profit.

So in the above, the insiders beat the market, and the market makers don't lose any money--so where is the insiders' profit coming from? It's being paid by the investors in the passive index, in the form of increased transaction costs and price impact.

The above isn't anything close to an accurate model of the real market, of course. But I don't think that you need to have anyone behave irrationally for insiders to beat the market, as long as you allow for transaction costs.

 
At 4:34 PM, February 17, 2017, Anonymous Max said...

I think market participants try to guess which trades are based on information, and which aren't. And to the extent that they can't distinguish, prices react to trading. For example, a large sell order can "permanently" depress the share price, just because it might be based on information. Meanwhile the seller will try to make his trade look as innocent as possible (maybe breaking it into small pieces, using many intermediaries, etc).

 
At 3:43 PM, February 18, 2017, Anonymous Anonymous said...

I should perhaps have made it explicit that what I mean by insider trading has nothing to do with whether the trade is illegal, only whether the trader correctly believes he has relevant information available to few others.

Then there's no reason to believe that "insider trading" is limited to the stock market, and therefore you can't explain the equity premium without doing more work.

 
At 4:40 PM, February 18, 2017, Anonymous Eric said...

See this 1963 Paul Samuelson paper. You're assuming that stocks are more risky short term yet less risky long term than bonds. This is a fallacy. Risk averse investors who prefer bonds in the short term will also prefer them in the long term.

https://www.casact.org/pubs/forum/94sforum/94sf049.pdf

Investing in a risky asset over a long time period doesn't reduce the risk. If the risk-free rate is 5% and stocks are 6.5% +- 20% each year, then after 25 years your bond return is ~125% and your stock return is ~162.5% +- 100%. Risk averse investors who prefer 5% to 6.5% +- 20% will also prefer 125% to 162.5% +- 100%.

 

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