Tuesday, June 14, 2016

market liquidity and price discovery

Two consequences associated by convention with market liquidity are a liquidity premium (the asset's price is higher than it would be if it didn't have a liquid market) and market efficiency (in many ways, but I have in mind at the moment price discovery — the price is more indicative of the correct "fundamental" price if the market is liquid than if it's not.  I've spent much of my life in the last couple of years formalizing the idea that the liquidity premium can be negative — if something is consumed regularly and can be stored, people may be willing to pay less if they trust their ability to buy it as they need it than if they worry that the market is unreliable — but it's worth noting a way in which market liquidity can also impede price discovery.

In [1], Camerer and Fehr note that a situation with strategic complementarity is more susceptible to irrational behavior than a situation with strategic substitutes; that is, if our action spaces can be ordered such that each of our best responses is higher the higher are others' actions, then I am likely to worry more about other people's actions than if it is lower the higher are others' actions.  For concreteness, consider a symmetric game in which actions are real numbers and my payoff is -(a-λ<a>)2, where <a> denotes the average of everyone's action and λ is some real number; for λ=1, any outcome in which everyone picks the same action is an equilibrium, and I care deeply what other people are doing, while for λ=0 my best response is 0 independent of what others are doing. For λ=0.9, the only equilibrium is one in which everyone chooses 0, but if I think there's a general bias toward positive numbers, I may be better off choosing a positive number — and thereby contributing to that bias. If λ<0, then if I expect a general bias, I'm better off counteracting that bias; even a relatively small number of agents who are somewhat perceptive to the biases of themselves and others will tend to move the group average close to its equilibrium value.

Now consider an asset with a secondary market; in general the value of an asset to a buyer is the value of holding it for the amout of time the buyer plans to hold it, plus the value of being able to sell it at the time and price at which the buyer expects to sell it.  In a highly liquid financial market, especially one in which a lot of the traders expect to hold their asset for a short period of time, an agent deciding whether or not to buy will base the willingness to pay very sensitively on the price at which the asset is expected to be sold some time later.  If the market becomes less liquid, it makes less sense to buy with the intention of holding for a very short period of time; the value of owning the asset is a larger fraction of the total value of buying it.  λ is still positive, but is much less close to 1; I still care what other people will pay for it when I sell, but at least as a relative matter the value it has to me as I hold it is rather more important.  More to the point, though, I expect the seller to whom I sell it to make a similar calculation; the price at which I am able to sell it will be more dependent on what I expect it to be worth to the next owner to own it, and less on what I think the next seller thinks the seller after that will pay for it.  The cycle in which we care more about 15th order beliefs than direct beliefs in fundamentals is more attenuated the harder the asset is to sell.

It's worth noting that James Tobin suggested a tax in the market for foreign exchange for reasons related to this.

Addendum: Scheinkman and Xiong (2003): "Overconfidence and Speculative Bubbles," Journal of Political Economy, 111(6): 1183--1219 seems to be relevant, too.

[1] Camerer and Fehr (2006): "When does ``Economic Man'' Dominate Social Behavior?," Science, 311: 47 – 52

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