Economic Natural Selection David Easley Cornell University June 2007

The Stock Market Knows Best Argument “Ultimately, the economy always follows the stock market– so, somehow, the stock market knows.'' Ted Andros, Wall Street Plus “Every time you think a stock is undervalued, you should think, 'what does the market know that I don’t know' and stop. Obviously, the market is full of information based trading,...'' John Cochrane, University of Chicago

What Does it Mean to Say That the Market Knows? What the market knows or believes usually refers to using prices as predictors. For example, suppose an asset that pays 1 if it rains in Beijing tomorrow and 0 otherwise has a price of x. Then commentators would say that the market predicts that the probability of rain in Beijing tomorrow is x. From this point of view the market serves as an information processor. The market takes as inputs the demands of all participants and generates a predictor.

Why Does the Market’s Prediction Matter? It affects real investment decisions by firms. Individuals use the market to invest in the economy. It affects wealth flows between individual investors.

Is the Market Correct? Three possible mechanisms:  Individuals have correct beliefs.  Aggregation of possibly incorrect beliefs.  Smart money dominates the market.

Correct Beleifs If all traders have correct beliefs, and don't make mistakes, then prices will be good predictors.  This is the basis of the Efficient Market hypothesis. In principle, individuals could learn and eventually have correct beliefs. But learning is hard---chasing a moving target as what the market does depends on what individuals believe it will do.  Education?

Aggregation Prices reflect an average of traders beliefs. Does this averaging of possibly diverse and incorrect beliefs produce a good predictor? In some circumstances aggregation produces good predictors---the average of many independent observations is a good predictor. But are individuals beliefs independent draws?  Their beliefs are based in part on common information— past returns.  Herding.

Smart Money There is also a selection process taking place in the market. Traders who make mistakes lose to those who have better beliefs. Traders demands are weighted by their wealth, so prices are a wealth- weighted average of beliefs. This is the topic of my talk today.  Does this wealth dynamic eventually produce good predictions?  Under what conditions on the market does it work?

The Smart Money Argument First made by Milton Friedman and Eugene Fama. “Given the uncertainty of the real world, the many actual and virtual traders will have many, perhaps equally many, forecasts … If any group of traders was consistently better than average in forecasting stock prices, they would accumulate wealth and give their forecasts greater and greater weight. In this process, they would bring the present price closer to the true value.''  Cootner, 1967

Is the Smart Money Argument Correct? Yes, if traders are able to trade on (make bets on) any disagreement about future asset values or cash flows. That is, if asset markets are complete. No, or at least its not necessarily correct, if asset markets are incomplete.  Blume and Easley, Econometrica, 2006.

Horse Races as an Analogue of Complete Stock Markets Suppose two horses, A and B, run a race every day, t=0,... The probability that horse A wins on any day is p. Bettors:  Names are i=1,…,I  Wealths are w i t at date t.  Aggregate wealth is 1 (wealths are wealth shares).  The fraction of i’s wealth bet on horse A is a i.

Prices or Odds Equilibrium odds at date t, p t for horse A,  a 1 w 1 t p t + a 2 w 2 t p t +… +a I w I t p t =1. Inverse odds or state prices, q=p -1, are wealth share weighted averages of betting rules  a 1 w 1 t + a 2 w 2 t +… +a I w I t = q t. Inverse odds are the market’s predicted probability of horse A winning. The market aggregates possibly different beliefs.

Smart Money in Horse Races Can show, using the Law of Large Numbers, that if a i is closer to p (as measured by relative entropy) than any other betting rule, then w i t converges to 1. Prices converge to the betting rule closest to p.  Smart bettors (those whose betting rules are closest to the truth) profit at the expense of the dumb bettors and this causes prices to converge to correct predictions.

Complete Markets Horse races are examples of complete markets--- bettors can bet on any disagreement about winning probabilities. If asset markets are complete, then the investors whose beliefs are closest to the truth will take money away from all other investors. Prices will converge to correct prices.

Incomplete Markets If markets are incomplete then irrational traders can drive rational traders out of the market, and irrational traders can set prices.  How does this happen? Irrationally optimistic traders can cause stocks to be over-valued. If rational traders can short these stocks then rational traders will make profits at the expense of irrational traders. But if short sales are not possible, rational traders cannot take advantage of irrational traders. Instead rational traders may leave the market.

What Does This Say About China? If prices are eventually to be rational (efficient) need participation by rational traders; both individuals and institutions. Want to discourage irrational speculation. Economic theory says that completing the markets helps. This may require new trading opportunities:  Futures markets.  Short sales.  Options.  International investments