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 (1958)


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 nonequilibrium 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:
n
(1) p _{t+1} = p _{t} + (1/lambda) * SUM [w (i) (p _{t}, p _{t1}, ...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 _{t1} ,...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 _{t1},...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 _{ttheta})
where: theta is the time scale used to measure a
trend.
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.
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.
Conclusion
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 "LongTerm Expectation" which
describes how the news determines shortterm 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.