Economic Natural Selection

1
Economic Natural Selection

• David Easley
• Cornell University
• June 2007

2
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
  dont know' and stop. Obviously, the market is
  full of information based trading,...''
• John Cochrane, University of Chicago

3
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.

4
Why Does the Markets 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.

5
Is the Market Correct?

• Three possible mechanisms
• Individuals have correct beliefs.
• Aggregation of possibly incorrect beliefs.
• Smart money dominates the market.

6
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?

7
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
  informationpast returns.
• Herding.

8
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?

9
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

10
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.

11
Horse Races as an Analogue of Complete Stock
Markets

• Suppose two horses, A and B, run a race every
  day, t0,...
• The probability that horse A wins on any day is
  p.
• Bettors
• Names are i1,,I
• Wealths are wit at date t.
• Aggregate wealth is 1 (wealths are wealth
  shares).
• The fraction of is wealth bet on horse A is ai.

12
Prices or Odds

• Equilibrium odds at date t, pt for horse A,
• a1w1t pt a2w2t pt aIwIt pt 1.
• Inverse odds or state prices, qp-1, are wealth
  share weighted averages of betting rules
• a1w1t a2w2t aIwIt qt.
• Inverse odds are the markets predicted
  probability of horse A winning.
• The market aggregates possibly different beliefs.

13
Smart Money in Horse Races

• Can show, using the Law of Large Numbers, that if
  ai is closer to p (as measured by relative
  entropy) than any other betting rule, then wit
  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.

14
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.

15
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.

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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