Wall Street

New York City



                                        THE BEHAVIOR OF MARKETS

   This article suggests that the trading stock market has some tendency towards 
   equilibrium. Appropriate portfolio structure, however, is the primary means of 
   handling volatility. 
   I do not believe that a human system can ever be analyzed satisfactorily 
   In simple mechanical terms, and that at some point the complexity of the
   level of abstraction must begin to move towards the complexity of the 
   subject matter. In particular we cannot ultimately avoid economic models
   which take explicit notice of the nature of the economic system as an 
   information...process, very different from the simple dynamic system of            
   the physical world. 
                                                  Kenneth E. Boulding
                                                  Research in Economics




In a recent magazine article, a hedge fund manager wrote that on a bad trading day, he would break "...furniture and monitors and keyboards (the keys flying) and coffee mugs...."

We ask two questions: Since much stock trading is momentum inspired, how does the stock market result in economic efficiency? Furthermore, what is the likely behavior of a market comprised of value investors and momentum investors? The following comments first upon the relevance of economic theory to market behavior and discusses a complexly mathematical article written by J. Doyne Farmer of the Santa Fe Institute.

The concept of equilibrium, the state to which economic systems tend, defines standard economics. At economic equilibrium, the profits of each individual market participant and that of the economic system is maximized because:

1.      At the market clearing price, the amount supplied equals the amount demanded.

2.      Given the law of diminishing returns, all resources have been utilized to the points where their marginal costs equals their marginal revenues, and no further profits are possible.

Most crucially, it is furthermore assumed that information is perfect and that consumer preferences and the state of technology remain unchanged. Textbook economics is not literally applicable in a dynamic environment. Economics is useful for describing the structure of the system, tallying the risks and weighing those against the positives by judgment. This is why economists disagree. Tracy Clark says, "What economics is good for is not so much saying, 'We're going to have a recession starting next Thursday,' or that 'GDP will be precisely 3.26% next year. ' What economics is useful for is saying, 'Here are the risks, here's what to watch, here's what could go wrong based on what we know about the economy.' "

How is realized return determined in financial markets? To try to determine the price where supply and demand will intersect, we turn to Mr. Farmer's article titled, "Market Force, Ecology, and Evolution." (The author has revised this paper for publication; the following discussion pertains to the original.)

The Santa Fe Institute studies complexity, that is the behavior of non-equilibrium systems comprised of a large number of agents obeying simple and local rules. The Institute has been criticized for its reliance upon computer simulations and therefore the lack of empirical content in its studies. Nonetheless, to try to predict the path of a real market is to predict how a system evolves over time, at dates and levels certain. This can only be done by computer simulation.

We think this study is interesting because rather than assuming a simple and unrealistic uniformity among investors, it describes a dynamic of how investors with different strategies contend in markets and the result. We suggest that those whose utilities do not include mathematical formulations skip to the conclusion. For those who choose to proceed, the following describes observed market prices as the result of a complex dynamic between fundamentally driven value investors and momentum investors.

Mr. Farmer begins by writing equations describing the behaviors of three kinds of agents: the market maker, value investors, and momentum investors.


The Market Maker


The market maker uses an algorithm to calculate the price of an order, (w):

                         P t+1 = f(P t,w)
                              where: P t is the current price.

Function (f) is an increasing function of the order size; the larger the buy order, the higher the price must be to clear the market. This order has an impact upon the market approximated by the equation:

                         p t+1 ~ w/lambda + p t 
                               where: p t = log P t.
                                      For the sake of simplicity, all the                                                              
                                      following price and value calculations               
                                      are carried out in terms of logarithms. 
                                      w is the order size. 
                                      lambda is the market's liquidity.
                                      this is mainly of concern to market 
                                      makers and traders.

In the case of a whole market comprised of a market maker and many trading decisions, the future price of a security will be, summing the transactions:

   (1)        p t+1 = p t + (1/lambda) * SUM [w (i) (p t, p t-1, ...I t)] + N t+1                  
                                       i = 1
                   where:  lambda, as before, is market liquidity.
                           i is the ith market transaction.
                           w is the order size.
                           (p t ,p  t-1 ,...I t) is an investment                                                                                                 
                           strategy that utilizes the information available  
                           in the economy, I t. This is very well stated.
                           N t+1 is a random term; it can include 
                           unanticipated events.

The behavior of a market, even a simple one, is complicated. The following describes the market dynamics of value and momentum trading strategies based upon (I t), the information available in the economy at time (t).


Value Investors


Utilizing the investment strategy (p t, p t-1,...I t), value investors make a common assessment of value (V t) in relation to price.* They buy stock if the price is less than the estimated value and sell stock if the price exceeds this value. The amount of stock held is approximated by an equation related to the perceived mispricing:

                   X t+1 = c(v t - p t) 
                        where: X t+1 is the amount of stock held. 
                               c is a constant proportional to trading capital.                                     
                               v t = log V t. 

The change in the logarithm of price, caused by a market consisting only of value investors and the market maker is:

                                 change p t+1 = c/lambda * (change v t - change p t) + N t+1 


This price change has no explicit dependence upon the consensus value, V t , or log V t , but only upon the directional change in this consensus; thus stock purchases according to the formula above will not make market prices approach value. This equation furthermore shows that stock prices in such a market will, in fact exhibit a negative dependency between adjacent data points. For every market driven trade that causes prices to approach value, there is a corresponding exit trade that drives prices away.

In a more complicated case, which is included in the overall market model, prices will approach value if the expected price movement exceeds transaction costs by a certain threshold. Nonetheless, in the words of the author, even under those conditions "mispricings...can persist for thousands of iterations." Value convergence occurs but slowly.

*If there is a range of perceived values, say occurring within a range of (1:5), the amount of excess volatility increases only slightly. The following computer simulation assumes that investors perceive a range of values.


Momentum Investors


Momentum investors buy stocks if the price is going up and sell stocks if the price is going down. Momentum investors hold stocks according to the formula:

                X t+1  =  c(p t - p t-theta)
                      where: theta is the time scale used to measure a                   

A market consisting only of the market maker and momentum investors will exhibit a positive dependency between adjacent data points, at the first approximation. Oscillations occur as the time scale lengthens due to the different time lags of different investors.


Value Investors and Momentum Investors


If value threshold investors are included, how does this market behave? Utilizing a model consisting of 1200 value and and 1200 momentum investors, also with sixteen additional assumptions, Farmer reproduces some of the statistical properties of the U.S. stock market between the years 1889 and 1984. The calculated market, however, is less volatile than the real market which was furthermore influenced in part by large changes in valuation V t which results from changes in international events. Both markets have the following statistical properties:


1.      Market volatility and trading volume are correlated.

2.      Compared to a Gaussian (bell-shaped) distribution, the returns of this market have "a higher density of values at the extremes and in the center, with a deficit in between." This statistical property of leptokurtosis is typical of assets traded in the financial markets. The realized return from investments, over the short term, results not from uniform expectations; but from the interaction between value and momentum investors in a market. Over the long term, increases in company valuation occur from the realized trend in increasing dividends.

3.      Farmer's model is capable of producing a sequence of returns whose autocorrelation is zero. There being no mathematical dependency between adjacent data points, no predictive econometric model is possible. This is also a feature of the real stock market over the time period of this study.


The author, however, believes that it is possible to predict when value and momentum investors are the most likely to trade.

Mr. Farmer's article then goes on to show the price formation rule above and a capital allocation model results in population equations describing the market as an ecology.




With this analysis, we can say the following about markets:


1.      Pure trading markets converge only approximately to the values perceived by value investors, even if this is the only strategy and there is a consensus. These markets do not consider most relevant the level of valuation, only the directional changes in this level. This is why Wall Street is considered mainly with the current news affecting changes in a company's valuation (business model) rather than with the actual valuation itself. We suggest Keynes' The General Theory (1935), the chapter on "Long-Term Expectation" which describes how the news determines short-term market behavior.

2.      Momentum decisionmaking in the financial and real economies result in a statistical distribution with extreme outcomes. Markets can go to extremes until the news changes.

3.      Equal numbers of value and momentum investors, with some additional assumptions, trading in a mathematical market can produce a statistical distribution of returns for which there is no predictive econometric time series model over the short term. When nothing fundamental is happening, trading dynamics will be the major influences upon prices. This is why the trading in financial assets exceeds the levels required to adjust prices to changes in the fundamentals.

4.      The direction of the news affects the near term direction of the stock market. The S&P 500 is affected by domestic economic trends, Fed policy, international trends, also the level of valuation about which more later. These fundamental influences on the near term S&P 500 can be summed by totaling the pluses, neutrals, and minuses.

5.      From the standpoints of both social policy and investments, unbounded outcomes are not desirable. Alan Greenspan noted in (January 25, 2001) congressional testimony that there is a qualitative difference between slowdowns and recessions. In recessions, "marked declines breach consumer confidence." Taking this to the extreme, a large decline in the economy will affect confidence for many years. The goal of the Fed is therefore to foster an economy and a financial market that are in greater degrees of equilibrium than that to which unregulated markets tend.

6.      A portfolio structure that is appropriate to your temperament and circumstances is the simplest way to handle the volatility of markets.


Pluralist markets are the major means by which free societies coordinate the goals of their participants. There is therefore a trading uncertainty within the context of a general cyclicality that is modulated by Fed policy. Markets allocate capital by communicating a general economic direction that operating profits must prove out. Economic efficiency occurs mainly at the level of the company; operating profits enable companies to continue to do what they do and their stock prices to increase over the long term.

Markets are "directional rather than biblical;" this can also be said for social science research. Over the short term, the direction of the news affects the direction of the market; actual prices being set mainly by the interaction between value and momentum investors. Over the long term, prices increase as dividends (earnings) increase.