The problem with insider trading: a game theory perspective

I’m no expert at finance, so I can’t tell you in general how you should invest your money. What I can tell you, though, is why insider trading is such a harmful phenomenon, and why it should be curtailed to the best of the government’s abilities. To illustrate this, I’m going to use a simple Bayesian model.

To begin with, it is reasonably clear why someone would execute an inside trade. If some executive-honcho dude has some extra knowledge, not generally available to the public, which leads him (or her) to conclude that a particular financial asset (we’ll assume it’s a stock) is worth some amount different from its market value, he can use this to his or her advantage. If the stock is undervalued, he can purchase the asset and make money for nothing. If it’s overvalued, he can short it, again making money for nothing. Either way, he wins at the expense of other financial agents.

So far, pretty clear. But hold on a second: investors know that executives can do this, and so anticipate the relevant market moves. So, if the executive sells, the market for the stock responds by lowering the price; if he buys, it rises by a certain amount as well. Does this ability help the other investors to avoid the pitfalls of insider trading?

Unfortunately, it does not, for a few reasons. The first is pretty obvious from the definition of insider trading – though the market may expect the stock to be worth a certain amount more or less than  before, it can’t know the exact amount. Only the executive, with the inside scoop, knows this. Hence he will be able to capitalize on any difference between what the asset actually should be worth (based on all the information), and what investors expect it to be worth based on their more limited information (which includes the fact that the insider is taking action).

Second, it is important to take note of the advantage in timing that the executive has. Since the market can only correct itself in response to his or her moves, he or she gets to make the first move. So, if the asset is worth more, he can buy more shares before others realize what is going on. Similarly, he can sell before others notice that he or she thinks the stock is overvalued, still making a profit through these means as well.

Finally, we come to what I think is the most interesting problem: the executive can take advantage of investor expectations, even when the fundamentals of the company actually remain the same in as perceived in public. Thus, if investors believe that, say, a sale by the executive indicates that the stock is worth more than previously thought, they will reduce the price at which it trades. But if so, the executive, knowing that the other investors have this belief, can sell for no reason whatsoever, and then repurchase at a lower price, making a net profit without a loss of shares that he or she holds. Similarly, if investors expect the asset to be worth more if the executive buys more shares, then the executive can buy shares and resell at the higher price.

Combined, the first and last reasons demonstrate that there cannot be a perfect Bayesian equilibrium which allows for insider trading. For if the price falls with a sale (so the investors think the stock is worth less), the executive will take advantage of this investor belief through selling without reason (i.e. the stock is not worth less); a similar situation occurs if the investor believes that the asset is worth more, as then the executive will buy without fundamental reason. Hence the decrease in the market value for the stock will occur based on false beliefs due to the executive’s action. Meanwhile, if the investors respond to executive stock purchases by, say, lowering their expected values of the stocks (or keeping the price the same), the first reason above demonstrates that the executive can increase his or her payoff by purchasing when the stock is worth more than publicly thought. Thus, in the latter case, the investors also have false beliefs (undervaluing the stock).

In order to allow for the possibility of a perfect Bayesian equilibrium in the stock market, one must therefore eliminate the possibility of insider trading. Under a rigid enforcement mechanism, such an equilibrium does exist: the market does not respond to actions of the executive. Since the executive cannot use private information to purchase or sell stocks, he or she can’t take advantage of the first or second reason; and since the market does not expect a change in value based on his or her actions, he or she cannot take advantage of the third reason. From the other end, the investors know that the executive can’t use any information that they do not have, they are not taken aback by any executive stock moves, and so they don’t change their expected valuation of the stock. Thus we see the importance of an effective prevention of insider trading – otherwise, the stock market is open to the games of executives with too much information.