# Schizofinance

Robert Waldmann

In this post, I mentioned something which I have been thinking about. It seems to me that many strategies of financial market participants are based on simultaneously believing that financial markets are efficient and inefficient. If financial markets are efficient, then the way to maximize risk adjusted returns is to buy and hold the market. If one is forced to bear some risk, say I bear the risk that I will get sick, then I might rationally hold another portfollio including health insurance, but I can’t gain by delegating management of my portfolio to someone who doesn’t know anything about my personal unavoidable risks.

Therefore much employment in the financial services sector must be based on the conviction that markets aren’t efficient.

On the other hand, many decisions seem to be made based on the assumption that financial markets are efficient. For example, incentive contracts for traders reward them for short term risk adjusted returns. Outsiders argue that it would be better to reward traders in restricted shares of the firm (which they can’t sell for a fixed period) so that they don’t sacrifice the long term interests of the firm in order to obtain high cash bonuses. Silly outsiders, say the financiers, Samuelson proved decades ago that the optimal trading strategy doesn’t depend on the planning horizon. Indeed he did under the assumption that the objective is the log of end of horizon wealth *and* that financial markets are efficient. The logarithmic assumption can be relaced to any CRRA function so long as assets are geometric brownian motions so returns over all horizons are log normal. The assumption that markets are efficient is absolutely necessary to the result.

But if markets are efficient, the optimal incentive contract for a trader is “Your fired” and, if necessary, “If you are not out of the building in 15 minutes I will call the police.”

A blindingly obvious example, a maybe less obvious example, and some effort to understand how we managed to get to this doubleplusungood blackwhite after the jump.

The example is the case of a speculative bubble which is bound to burst but has a small chance of bursting in any brief interval of time. Let’s say that each period there is a 99% chance that the bubble continues to inflate and returns on the asset are higher than the safe interest rate. In contrast 1% of the time the bubble bursts and returns on the asset are very large and negative so the expected return on the asset is always lower than the safe interest rate. A rational investor would short the asset, although a rational risk averse investor may take a very small short position.

Now let’s assume that there are professional traders who understand all this and investors who don’t.

An investor who rewards traders in cash equal to the greater of performance minus market performance and zero will with probability 99% pay a positive reward after 1 period to a trader who goes long the asset. If the investor fires the trader after 1 period in which the trader underperforms the market, then a rational risk averse trader will always buy more of the risky than its share of the market portfolio. This for two reasons. The return if she goes short has huge variance and the chance of keeping the valuable job is 99 times as high if she goes long. The same result holds If the investor fires the trader after a few underperforming periods in a row.

Hiring a sophisticated trader and writing a short term incentive contract is a worse strategy than buying the market.

Now this is not an obscure example, so why were investors willing to accept short term incentive contracts. Part of it, of course, is that the contracts are really written by managers, but why did people ever buy shares of investment banks ? Didn’t they notice how incentives changes when partners became managers ?

I think the reason is that many people manage to simultaneously believe that markets are efficient and that smart traders can beat the market.

How could such beliefs co-exist ? Well first it is really necessary to believe that the efficient markets hypothesis is a good enough approximation that incentive contracts which would be optimal if it were true are not horribly bad, but not a good enough approximation that the conclusion that all traders are inferior to buying and holding the market. This is not a logical contradiction, but people didn’t even feel the need to write down a model in which both are true and decide if it seemed reasonable.

My guess is that the cognitive dissonance is caused by the desire people have to believe that they are doing well and doing good. The claim that financial markets are inefficient is associated with the idea that speculators hurt non speculators. Speculators are therefore sympathetic to the idea that financial markets are efficient, even though they have to believe that they aren’t perfectly efficient.

More crudely, active investors are restrained by regulations and have a perceived interest in reduced regulation. Therefore they see efficient markets fanatics as political allies and take advice from them on, say, incentive contracts. Thus two groups with diametrically opposite beliefs who both, to put it crudely, vote Republican, imagine that they agree even though they don’t.

Another example of shizzo finance is the use of the Black and Scholes formula to detect miss pricing of options. One of the many assumptions needed for the original formula, and one that has not, to my knowledge, been relaxed, is that the price of the underlying asset is a martingale. This is a reasonable assumption if markets are efficient. The formula can be used to test the efficient markets hypothesis along with a bunch of clearly false auxiliary hypotheses. It can’t be used to find miss pricing under the assumption that financial markets aren’t efficient. This strategy makes sense if one assumes that underlying assets must be efficiently priced but that options might or might not be efficiently priced. That was a bold guess back when options were new. It has become a silly idea now that they aren’t.