L2: Market Efficiency 1

Efficient Capital Market (L2)

• Defining efficient capital market• Defining the value of information• Example• Value of information and efficient capital markets• Rational expectation and market efficiency• Market efficiency with costly information• The joint hypothesis of market efficiency and the CAPM

– Materials from Chapter 10, CWS

Highlights

In an efficient market, security price contains all market information

To test the efficient market hypothesis, we check if investors obtain abnormal returns when investing

Then we need a formula for normal return, thus bad model issue arises

Rational expectation (regularity of the representative agent’s mindset) is typically required

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Defining Market Efficiency

• In an efficient capital market, prices fully and instantaneously reflect all available relevant information.

• Efficient market and perfect market differ• Necessary conditions for perfect markets

Markets are frictionlessPerfect competition in securities marketsMarkets are informationally efficient; that is, information is costless, and it is received simultaneously by all individualsAll individuals are rational expected utility maximizers

Operational Efficiency and Allocational Efficiency

• Allocational efficiency• Operational efficiency

• Efficient capital markets imply operational efficiency and asset prices being allocational efficient

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Definition of Value of Information

• Information: a message about various events that may happen

• The value of message differ across agents who receive the message– Whether they can take any actions based on the message

– What net benefits will result from their actions

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Definitions and explanations see page 356.

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The value of information consists of

• The payoff to the decision maker• Information about the event given the message• The action assumed to be taken by the decision maker

• The key: the agent chooses a given there are multiple messages m

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An Example• The analysis division of a large retail brokerage firm hires and

trains analysts to cover events in various regions around the world. The CIO allocates analysts and deals with the fact that the demand for analyst coverage is uncertain

• Suppose we need 300 analysts or 0 analyst with 50-50 probability for coverage in each of three countries

• CIO has three options (i.e., 3 policies)– Hire analyst and keep them on their initial allocations– Switch analysts at a cost of 20 thousand dollars when makes sense– Create a catalogue (CAT) that provides better information for matching

analysts to countries when they are switched

• We also know payoffs to the CIO – page 356• Probability for an analyst to be satisfied and not given a policy

– page 357

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Value of information and Market Efficiency

– Market efficiency -- Fama (1976)

– Value of information is determined net of costs.– In term of value of information, in an efficient capital market, the

utility value of the gain from information, net of costs, to the ith individual, must be zero.

– In an efficient market, information has no value to investors• Note: this is an ex-post result.

– Value of information is determined net of costs – the costs of undertaking courses of action and the costs of transmitting and evaluating messages.

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Rational Expectations and Market Efficiency

• How the individual’s decision making process, given the receipt of information, is reflected in the market prices of assets.– Naïve hypothesis – asset prices are completely arbitrary and unrelated

either to how much they will pay out in the future or to the probabilities of various payouts.

– Speculative equilibrium hypothesis – investors base their investment decisions entirely on their anticipation of other individuals’ behavior with any necessary relation to the actual payoffs that the assets are expected to provide.

– Intrinsic value hypothesis – prices will determined by each individual’s estimate of the payoffs of an asset without consideration of its resale value to other individuals.

– Rational expectation hypothesis – prices are formed on the basis of the expected future payouts of the assets, including their resale value to their parties.

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Experiment Result

• Conduct experiments to test among the hypotheses

• The result is generally consistent with rational expectation hypothesis, but refute the naïve hypothesis and speculative

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Market Efficiency with Costly Information

• Do we need security industries if the market is efficient?

• The key is market efficiency is a result

• Grossman and Stiglitz (1976, 1980) and Cornell and Roll (1981) show that a sensible asset market equilibrium must leave some room for costly analysis

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Cornell and Roll (1981) model His Opponent Analyzes? Yes No

Yes r-c2=-2% dr-c2=4% The trader analyzes? No r/d-c1=-1% r-c1=2%

R=normal return=6%

d=competitive advantage = 2x

c2=cost of analysis=8%

c1=cost of no analysis=4%

Mixed strategy equilibrium is identified.

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Statistical tests on market efficiency (I)

• Fair-game model– A fair game means that, on average, across a large number

of samples, the expected return on an asset equals its actual return.

– Expected return is zero. Mathematically, we have

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Statistical tests on market efficiency (II)

• Martingale or submartingale– A submartingale is a fair game where tomorrow’s price is

expected to be greater than today’s, implying a positive expected return.

– A martingale is a fair game that tomorrow’s price is expected to be the same as today’s price.

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Statistical tests on market efficiency (III)

• Random walk: there is no difference between the distribution of returns conditional on a given information structure and the unconditional distribution of returns

• Random walks are much stronger conditions than fair games or martingales because they require all the parameters of a distribution (e.g., mean, variance, skewness and kurtosis) to be the same with or without an information structure. The fair-game model makes no statement about the variance of the distribution of security return, thus nonstationarity of return variance is irrelevant to its validity.

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Joint Hypothesis Problem

• CAPM provides a theory that allows the expected returns of a fair-game model to be conditional on a relevant costless measure of risk.

• Any test of market efficiency that uses the CAPM to adjust the risk is a joint test of the CAPM that assumes market efficiency for its derivation and of market efficiency itself.

How to Test Market Efficiency?

• See Chapter 2 CLM

• Sequence and reversal: An example

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Exercises

• CWS, 10.1,10.2, & 10.4