Impressions on Glode et al (2012)

Title: Financial Expertise as an Arms Race. Link to the paper.

Authors: Glode, Green, Lowery

Year published: 2012

Journal: Journal of Finance

This paper is trying to model the acquisition of financial expertise as an arms race. The basic idea is like this:

• We hesitate to trade with others whom we know to be more informed than us. (This is similar to our hesitation to play games with an expert, if we happen to be a novice.
• This is because we are afraid to be taken advantage of. This is called adverse selection.
  • In particular, people have the impression that people who are better-informed than they are will only say yes to deals that favor them.
• When the tradeable items have values that are not so different, it won't be so bad (on average) for us to trade with very informed people.
• But when the tradeable items have very divergent values, knowing that our counterparty is very good will make us not even consider trading with them.
• So basically, this is another explanation of why trade freezes after a crisis.

The basic model

• One buyer (who is not an expert), one seller who is an expert with expertise level \(e_i\in(0,\frac{1}{2})\). Both want to trade a particular good whose value is high \(v_H\) or low \(v_L\).
• The buyer values the asset at \(v+2\Delta\), while the seller only values the asset at \(v\).
• Expertise means that seller gets some signal about the value of the asset. Naturally signal is more correct if seller is more of an expert. In particular, the probability that the signal is correct is \(\mu_i=\frac{1}{2}+e_i\)
• For the basic model they assume that \(e_i=0\) so that the signal is always uninformative and \(\mu_i=\frac{1}{2}\).
• Buyer makes a take-it-or-leave-it offer, sellers says yes only if the offer is higher than or equal to the signal he got.
• Two possibilities
• If buyer's offer is too low, seller will reject if his signal is high, which occurs half the time
• If buyer's offer is high enough, seller will always accept.
• Thus, the buyer has to condition on the signal realization: set the price to be equal to the expectation of value conditional on the signal received by the seller (which presumably is known by both parties)
• Two prices will emerge:
• When he conditions on a low signal, \(p^*=\mathbb{E}(v|s=L)=(1-\mu_i)v_H+\mu_i v_L \)
• When he conditions on a high signal, \(p^{**}=\mathbb{E}(v|s=H)=\mu_iv_H+(1-\mu_i) v_L \)
• Comparing the expected payoffs under each case yields a cap on expertise under which the buyer will never make any offer to the seller. That is, $$\begin{eqnarray*} \frac{1}{2}\left[2\Delta + \mathbb{E}(v|s=L)-p^{*}\right] &\geq& \mathbb{E}(v)+2\Delta-p^{**}\\ \Delta &\geq& 2\Delta - (v_H-v_L)\cdot e_i\\ e_i&\leq& \frac{\Delta}{v_H-v_L}\\ &=&\bar{e} \end{eqnarray*} $$
• This is when trade breaks down when the seller is too much of an expert for the buyer's taste.
• It is not that the buyer never makes an offer to the seller, but he will only ever offer the low price which will definitely be rejected by the seller, and so trade breaks down.
• Yet when the seller accepts the sale, he always has a surplus proportional to his level of expertise.

Later in a more complicated version of this model, the role of buyer and seller is randomized, and so all the agents need to invest in expertise (in stage 1), to be able to obtain surpluses (in stage 2).

Some thoughts

• This is a good application of an old story that even children know instinctively (choosing playmates, e.g.)
• But why do some people still invest in knowledge? It would appear that this is to be able to play "at the top of the leagues"
• Couldn't traders trade with traders at their own level? On that note, do noise traders only trade with other noise traders? Having experts trade with noise traders is like taking candy from a baby, but I guess otherwise they wouldn't be able to make any money.
• It seems that what drives the results are the changes in asset values.
• It is true that the choice of expertise level precedes potential asset value realizations
• But wouldn't trade still freeze when asset values diverge, even without excessive expertise?
• I guess this is why they say that acquisition of expertise produces no social value, even though this expertise allows obtaining more precise signals.
• It is not clear why the acquisition of expertise serves as a deterrent here. Deterrent to what? To shitty offers made by the buyer? (it seems so)
• So in the two-stage version of this game, all traders acquire expertise up to a point.
• But why is it that even in the low-probability high-volatility regime, expert traders don't want to trade with each other? It seems that whatever level of expertise they have chosen to acquire previously, it is still trumped by the divergent asset values. Which brings me back to my earlier point. It seems that the divergent asset values is exogenous.
• A personal rant: I don't know how this could have gotten in to JF with this backdoor exogeneity.

Interesting things to look at later

• Do this but with ambiguity