FUTURES MARKETS AND PUBLIC POLICY
Fischer Black
Sloan School of Management
Massachusetts Institute of Technology
February, 1982
James M. Stone
Commodity Futures Trsding CommissIon
Summary .
Introduction
-The Equilibrium
FUTURES MARKETS AND PUBLIC POLICY
The Effects of Regulation
The Model
Market Efficiency
i
1
4
6
7
9
Summary. We feel that the volume of
trading in securities and futures
markets can be explained only by
assuming that there are many "noise
traders" in the market. This means
that "information traders" can buy
information and make money trading on
it at the expense of the noise
traders. The "economic efficiency"
of the market and the allocation of
resources will be improved if we can
find a way to restrict noise traders
without restricting information
traders.
Int roduction
1
How should we regulate futures markets? Should we regulate them at all?
Should we regulate futures markets and markets for stocks and bonds in the
same way? These are the questions that motivated this paper. They are not
the questions that are answered in this paper.
To answer these questions, we must ask another: why do people trade? In
futures markets, there is a short position for every long position. If
someone makes money by trading, someone else must lose money. Total trading
profits are always exactly zero.
If everyone behaves rationally, and takes into account the fact that others
may be trading on information not currently reflected in futures prices, at
least some people must expect to lose money by trading. If they expect to
lose money, why do they trade?
In some models, the answer to this question is that they trade because a
2
change in circumstances has made their existing portfolios non-optimal.
The trouble with this answer is that it seems too weak to explain the volume
of trading in securities markets and futures markets. It might explain a
certain amount of trading in mutual fund shares, but does not seem to explain
trading in individual securities or futures contracts. Moreover, almost no
one gives this as the main reason for trading.
Most trading seems to be on information. People with favorable information
buy, and people with unfavorable information sell. They do this even though
their information may already be reflected in prices. Tney do it even though
the people they are trading with may have information that is not yet
reflected in prices. In short, people seem to trade on information even when
they should expect to lose money doing it.
To model this kind of trading, we have to assume that people trade for some
reason other than maximizing a rational expected utility of wealth or
consumption. Either they are irrational or they enjoy trading. They are
fools or gamblers. Their utility functions depend on the amount of trading
- 2 -
they do as well as on their consumption of r10re conventional goods and
services.
Let's assume that some people are fools or gamblers, while some trilde only
to make profits. Of those who trade only for profit, some buy information
and trade on it, while others don't buy information and don't trade at all.
'We ignore "liquidity trading," or trading for non-information reasons,
because we feel there is not enough of it in the world to make much
difference. We assume that both kinds of traders are rational, so the fools
or gamblers expect to lose money, while the information traders expect to
make money.
We assume that information is costly. That's why not everyone has a given
piece of information at the same time. We assume that it is as costly to
transfer information to someone else as it is to buy it in the first place.
That's why the government doesn't buy all the important information and give
it away. It's why an individual doesn't resell information after buying it.
Moreover, we assume that the cost of information is higher for some people
than for others. (We obtain similar results when we assume that the cost of
some pieces of information is higher than the cost of other pieces of
information.) Thus the people who buy information are those who can buy it
at lowest cost.
Everyone is risk averse. That's why a person who buys information does not
take a larger and larger position until the price fully reflects the
information. In fact, we assume that people are so risk averse and have so
little wealth that no one person's trading has a significant effect on the
3
price.
For simplicity, we assume that everyone has the same wealth. All fools or
gamblers have the same utility function, and all information traders have
the same utility function. In fact, we assume that the fools or gamblers
act just like information traders, except that they trade on randOln noise
rather than on correct information. They do not pay for their noise, but
they decide how large a position to take based on their wealth. risk
aversion, and the value the noise would have if it were correct
- 3 -
information. Except for the fact that they li'<e to trade on noise, their
utility functions are the same as the information traders' utility functions.
The fools or gamblers must trade on noise if the information traders are to
make any money. If the fools or gamblers take predictable positions, there
is no equilibrium except one where the price reveals all that the
information traders know. But in that equilibrium, the information traders
don't make
positions.
the three
any money. Thus they don't buy information and they don't take
The only equilibrium is one with no trading at all. Let's call
kinds of traders noise traders, information traders, and
non-traders.
We assume that some information is available to everyone at no cost. Even
when there is no information bought and no trading, the price reflects that
information. At any other price, some people would want to trade, though no
one would want to take the other side. Thus there is an equilibrium price
even without any added information.
We assume that producers use the price to guide their decisions. The more
information the price reveals, the better those decisions are. The more
noise there is in the price, the worse those decisions are.
Thus noise traders have two kinds of effects on producers. They put noise
into the price by trading on it. But the fact that the price is noisy
induces other traders to buy information. Their trading causes that
information to be partly reflected in the price. Does the noise have the
largest effect on the price? Or does the information have the largest
effect?
If the noise effect dominates, investment decisions and thus the allocation
of resources are hurt. If the information effect dominates, investment
decisions and thus the allocation of resources are helped.
What regulatory scheme minimizes the amount of noise and maximizf;s the
amount of information in futures prices? While the answer to that ouestion
- 4 -
does not tell us everything we want to know about regulation, that is the
question we emphasize in this paper
The Equilibrium
To model the equilibrium in this world, we assume a single infinitesimal
interval. In a more general model, this would be just one i.n a series of
intervals. We assume that the payoffs from securities and futures contracts
follow a joint normal distribution.
We focus on the investor's position in a single futures contract. In a more
general model, we would look at the investor's entire port folio of
securities and futures contracts.
The payoff is the sum of two random variables with zero mean and equal
standard deviation. An investor who buys information learns the value of
one of these random variables.
An information trader learns the value of the first random variable. No one
learns the value of the second random variable. To an information trader,
the mean payoff for a futures contract is the value of the first random
variable minus the price. The standard deviation for a futures contract is
the standard deviation of the second random variable. The larger the lTIean
payoff, the more contracts an information trader takes on.
Once an information trader has bought information, the amou:lt paid is a sunk
cost. The size of. the trader's position does not dEpend on the cost of the
information. It depends only on the value of the random variable and the
futures price.
For a non-trader, the futures price must equal the mean payoff conditional
on the futures price. If it were different, investors without information,
who are numerous, would take positions. This potential forces the pI-lce to
be equal to the conditional mean for an investor without information .,ho can
observe the price.
- 5 -
Noise traders act like information traders, 2'.,t they act on noise rather
than on information. Those with positive noise values take long positions,
and those with negative noise values take short positions. Each trader has
a different piece of noise. Thus noise traders may trade with one anct~er,
and noise traders may trade with information traders. All information
traders have the same information, so they don I t trade with one another.
The price is set by the fact that the sum of all long positions must equal
the sum of all short positions. The higher the price, the more people want
to shift from long positions to short positions. There is a single price
that balances long and short positions for given numbers of noise traders
and information traders.
The number of noise traders depends only on the number of potential noise
traders and the kind of regulation we have. The number of information
traders depends on profit opportunities and the kind of regulation we have.
For a given regulatory scheme, the number of information traders depends on
the number of noise traders. Hore noise traders mea;]s more noise, which
attracts more information traders.
But the added information traders have higher information costs. They come
in only if the mean gain from their futures positions covers these higher
costs. Hore noise traders means higher mean gains for information traders.
Thus more noise traders means more noise, net of the impact of the added
information traders. The price reveals less of the information that the
information traders have.
This h;:ppens because the number of information traders is affected by the
extent of profit opportunities, while the number of noise traders is not.
There is a lack of symmetry between the impact of the two kinds of traders.
- 6 -
The Effects of Regulation
If the futures market is banned, producers must use zero for the mean
payoff, or must buy the information. Those producers with high information
costs use zero. The variance of the estimate error for a producer without
the information is twice the variance of the estimate error for a producer
with the information.
High variance means less efficient production decisions, so consumers suffer
along with producers that have high information costs. In a multiperiod
version of the model, a producer with high information costs for most
relevant information simply goes out of business, and the other producers
expand to take up the slack. But this process does not solve the problem if
information costs are constantly shifting between producers and over tinle.
Suppose, then, that the futures market is allowed. The price reveals some
of the information to producers who do not buy it. Fewer producers buy the
information. Production decisions are more efficient. The variance of the
estimate error for a producer without the information who looks at the price
is between the variance for a producer who has the information and the
variance for a producer who does not have the information and does not look
at the price.
Now imagine that there is a way to reduce the num~er of noise traders
without affecting the information traders. There is less noise in the
market. Fewer information traders buy information, but the price reveals
the information more fully. Production decisions are more Qfficient.
The noise traders may feel unhappy about being blocked. Others, though, may
feel that noise trading is unhealthy, and may feel happy that such t~aders
are partially taken out of the market. Making production decisions more
efficient need not in itself help all consumers, but there will always be a
way, in principle, to transfer wealth between consumers so they are all
better off.
- 7 -
Imagine also that there is a way to reduce the number of information
traders,
traders.
or the size of their positions, without affecting the noise
This means that the cost of information rises more quickly as
information traders are attracted to the market by noise in the price. The
process stops before the noise has been reduced as much as it is with no
restrictions on the information traders.
Taking information traders out of the market means there is more noise. The
price does not reveal as much of the information to producers who don't buy
it. Production decisions are less efficient.
This suggests that the government should allow futures trading, but should
also look for simple ways to increase the ratio of information traders to
noise traders. In the real world, professionals may be more like
information traders, and small investors may be more like noise traders.
The government might leave the professionals alone, but look for ways to
4
keep small, unsophisticated traders out of the market.
The Model
To be more specific, let us outline a simple model of the kind described
above, and show some of its qualitative properties.
Write x for the first random variable, and y for the second random
variable. The payoff to a futures contract is x + y. Each variable has a
normal distribution with zero mean. The standard deviation of y is d
Thus the standard deviation of the payoff for an information trader who
knows x is d.
Information trader i pays Ci to learn x. After learning x , the
trader's conditional expectation of the payoff is just A. The conditional
standard deviation of the payoff is d All information traders have the
same utility functions. They are risk averse.
- 8 -
Write p for the price. When x > p , the information trader will take a
long position. When x < p , the trader will take a short position. The
size of the position will depend on x - p, d, and the degree of risk
aversion. Since these are the same for all information traders, all
information traders will take the same position.
u - P I~~ ~Sd:t,
A noise trader will choose a position in exactly the wayan information
trader does, but instead of x - P , noise trader i will use a variable
z The zi 's are normally distributed with zero mean. All the
zi 's and x and yare independent.
A trader decides whether to be an information trader or a non-trader by
comparing the expected utility of buying information and trading on it with
the expected utility of not trading. When making this decision, the value
of x is unknown, but the trader can observe the price p The
conditional standard deviation of x given p is s The decision
depends on the utility function, and on s d and the trader's
information cost ci There will be a value of ci above which no
trader buys information.
The closer p is to x , the fewer traders will buy information. When
fewer traders buy information, the total positions of information traders
will be smaller. In equilibrium, net positions of noise traders and
information traders must add up to zero.
A producer who buys the information will use a conditional mean x and a
conditional standard deviation d A producer with higher information cost
will use a conditional mean p , and a conditional standard deviation that
is larger than d. The conditional variance will be s2 + d2 .
Increasing the number of noise traders will increase the amount of noise,
which means p will on average be farther from x. This will attract more
information traders, and existing information traders will take larger
positions.
- 9 -
Raising information costs for the information traders (or restricting them
in some other way) will also make p farther from x on average. This has
no effect on the noise traders, because their behavior does not depend on
p •
Closing the futures market completely will mean that producers cannot use
p at all as a source of information about x A producer will either buy
x or will use an estimate of zero for the payoff. That estimate is the
worst of all. Its variance is equal to the sum of the variance of x and
the variance of y •
t~arket Efficiency
In this model, the market is not efficient with respect to the first random
variable, because if the value of x were known to everyone, the price
would change.
Using this "financial" definition of market efficiency, the market is
perfectly efficient when everyone agrees and the price reflects the
information that they all have. The market can be perfectly efficient (in
principle) at various levels of information.
There is also an "economic" definition of market efficiency. Using this
definition, the degree of market efficiency is measured by the standard
5
deviation of the payoff conditional on the price. Using this
definition, the more information people have, the more efficient the market
is likely to be. A market that is perfectly efficient in the financial
sense can be more or less efficient in the economic sense.
Producers care about economic efficiency. The more efficient the market is
in the economic sense, the less they pay for infcrmat:.on, and the better
their investment decisions are.
Our conclusions, then, can be restated as follows: the economic efficiency
of a futures market is improved if we restrict noise traders, or if we
G .
. , remove restrictions on information traders.
- 10 -
Footnotes
IFor example, see Grossman and stiglitz (1980) and Diamond and Verrecchia
(1981). In their models, people may start with non-optimal proportions of
a risky asset and a riskless asset. This gives them a reason for tracing
even when they expect to lose because they will be trading with people who
have more information.
2This assumes that the market is organized in a way that makes corners
impossible. Some restrictions on sophisticated traders have the effect of
making corners less likely, which could improve the economic efficiency of
the market. A simple way to avoid corners is to allow settlement of
futures contracts in cash.
3Edwards (1981) has a general framework for analyzing regulation that is
consistent with the views in this paper.
'Edwards (1981, pp. 21-22) discusses this kind of efficiency, in the
context of a more general discussion of economic efficiency.
sSamuelson (1972) has a model in which traders with incorrect beliefs
harm others. A key assumption in his model is that some traders are
over-optimistic, and short selling by other traders is banned.
6Green (1973) has a model in which investment in information by some
traders causes prices to reveal that information more fully. However, he
assumes that investors start with differences in information, and do not
take full account of the fact that others have valuab18 information. As a
result, his uninformed investors trade on their beliefs.
- 11 -
References
Diamond, Douglas W., and Robert E. Verrecchia. "Information Aggregation in
a Noisy Rational Expectations Economy." Journal of Financial Economics
9 (September, 1981): 221-235.
Edwards, Franklin R. "The Regulation of Futures I~arkets:
Framework. " Columbia Business School IVorking
October, 1981.
A Conceptual
Paper CSn,1-23,
Green, Jerry R. "Information, Efficiency and Equilibrium." Harvard
Institute of Economic Research Discussion Paper 284, ~Iarch, 1973.
Grossman, Sanford J., and Joseph E. Stiglitz. "On the Impossibility of
Informationally Efficient Markets. " American Economic Review 70
(June, 1980): 393-408.
Samuelson, Paul A. "Proof that Unsuccessful Speculators Confer Less Benefit
to Society than their Losses." Proceedings of the National Academy of
Sciences 69 (May, 1972): 1230-1233.