Market efficiency
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Market efficiency

  • The purpose of financial markets is to transfer funds between lenders (savers) and borrowers (producers) efficiently. “Efficiently” means funds that are supplied yield the highest return to savers given their risk preferences and fund the most profitable projects given their risks, at the lowest cost.

  • Perfect Markets

  • a. No frictions – no transactions costs, taxes, indivisibilities, regulations, or unmarketable assets.

  • b. Perfect competition – price-takers

  • c. Information is costless and simultaneously available to all

  • d. Individuals maximize expected utility.

  • 3. Market Efficiency is much less restrictive than market perfection. An efficient market allocates capital properly, given the costs of transactions, information etc.

Market efficiency three forms

  • Weak form

  • past prices hold no information about future prices

  • can't beat buy/hold strategy

  • much evidence to support including correlation

  • tests, filter test - fail

  • Semi-strong form

  • all publicly available information is immediately

  • reflected in price.

  • subsumes weak form since price data is publicly

  • available

  • assumes rational investors seek information

  • impound quickly.

  • result - prices may rise or fall with few trades - few

  • chances to make money

  • quite a bit of information such as stock split and earnings information is impounded quickly.

  • EXAMPLE: Yield curve misalignment in US. Treasury market - takes 15 seconds to correct.

  • Strong Form

  • all relevant information reflected in stock prices

  • due to insiders, specialists

  • evidence shows announcements of important

  • information often anticipated beforehand.

  • implies outside investors should buy and hold

  • the market portfolio.

  • 1. Rubenstein (1975) and Latham (1985) say that market efficiency with respect to a piece of information means that when the information is announced, prices don’t change and no trades occur. Fama (1976) suggests that trades can be made but prices do not change.

  • 2. The value (expected utility) of an information structure  (a set of messages m).

  • V() = m q(m)[ MAXa e p(e|m)U(a, e)] – V(0)

  • where q(m) = marginal probability of receiving a message m

  • p(e|m) = the probability of an event e, conditioned on receiving message m.

  • U(a, e) = the utility of the action a, if an event e occurs (the benefit function)

  • V(0) = the expected utility without the information

3. The MAX[.] part says that individuals choose among possible actions in a way that their utility is maximized given that message m is received.

Then, the maximized expected utility is weighted by the probability of receiving each possible message and summed over the messages.

Then compare this value to the expected utility without the information to see if the information structure has value.

4. Fama (1976) formally defines an efficient capital market as one where we have

m(P1t, … Pnt|mt-1) = (P1t, …, Pnt|t-1)

That is, the joint distribution of securities prices given the subset m of information the market uses, is the same as the joint distribution that would exist if all relevant information was used.

This also implies that, net of costs, the utility value of the gain from information structure m for individual I is zero.

V(i) = V(0)

Weak form =>  = past prices

Semi-strong form =>  = all publicly available information

Strong form =>  = all available information

Market efficiency properties
MARKET EFFICIENCY - PROPERTIES possible actions in a way that their

  • MARKET IS NOT ALWAYS CORRECT - just unbiased and usually close to correct


  • RANDOM - prices adjust rapidly to new information




  • It is difficult to prove market efficiency

  • Market variance is so large, superior investment

  • performance must be very large before it is

  • statistically significant.

  • Selection bias - those with profitable investment rules do not reveal them, hence, we can't be sure that some managers are profitable.

  • Luck - by chance some will have superior performance.

  • QUESTION possible actions in a way that their : Some stocks have very high returns and others very low returns even after adjustment for risk. Is this evidence of market inefficiency? No, because some firms may do surprisingly well for some periods.

  • 1. Efficiency implies that investors should

  • define risk level

  • hold a diversified portfolio that is a combination of the market portfolio and risk free assets

  • minimize trading transaction costs

  • Fully efficient markets reflect the full impact of all information, not just some average of the information. That is, if the true effect of the information implies a price of 4 and some interpret the information properly but others interpret the information to imply a price of 3, the price should still be 4. However, an averaging of information would give a price between 3 and 4.

  • Nevertheless, the action of the market in aggregating information can be illustrated by averaging.

  • Example: Guess the Number of Beans

3. possible actions in a way that their The effect of asymmetric information on market efficiency is often analyzed with a Trading Model. A Trading Model such as Kyle (1985) in Econometrica includes

a. Assumptions about the existence of or proportion of informed traders versus uninformed traders and the costs of trades. Assumption about whether trades are anonymous.

b. Requirements for equilibrium – zero expected net excess profits after costs. Informed and uninformed traders earn the same return after costs (assumes that the informed have costs to gather information and that they compete. If there is a single or non- competitive group of privately-informed traders, then they earn excess profits by trading at favorable prices with uninformed traders. Uninformed traders’ losses equals informed traders’ gains and market makers break even.)

c. For an interesting model, one needs to show that both informed and uninformed traders will find it rational to participate in the market, I.e., one does not totally dominate the market.

Statistical properties of stock prices and returns in an efficient market

  • A large and growing body of research shows that risk and expected returns for stocks change over time. Many studies explore the implications of these changing distributions for testing market efficiency and measuring performance.

  • Earlier work assumed that risk and expected returns were constant so efficiency would imply that there should be no pattern in asset prices or returns.

  • Theories of time series behavior of prices or returns.

  • Fair Game – describes the error in the return

  • j,t+1 = rj,t+1 – E(rj,t+1 | t)

  • A Fair Game implies Unbiased Expectations

  • E[j,t+1 ] = E[ rj,t+1 – E(rj,t+1 | t)] = 0

  • This says that, on average, the actual return equals the expected return.

  • One type of Fair Game is a Martingale which just assumes

  • E(rj,t+1 | t) = 0 expected return is zero

  • Another Fair Game is a Submartingale which assumes

  • E(rj,t+1 | t) > 0 expected return is positive

Stock returns are assumed to be submartingales so in order to test for abnormal returns (return performance) for a stock or a portfolio of stocks we need a model of

E(rj,t+1 | t)

such as the CAPM, APT or Fama-French. Using the CAPM we have

j,t = rj,t – E(rj,t | t) = rj,t – [rf,t + (E(rm,t | mt) - rf,t )jt]

And so

E[j,t ] = E{ rj,t – [rf,t + (E(rm,t | mt) - rf,t )jt]} = 0

This says that the difference between the actual stock return and the return predicted from the CAPM is zero on average (Jensen’s alpha is zero). A test of market efficiency using the submartingale is a joint test of efficiency and the CAPM (only beta matters).

A joint test is problematic because if the data show E[j,t ] = 0, this may be due to the fact that the CAPM is wrong and markets are inefficient but the two offset one another. Thus, such a result does not prove either efficiency or CAPM individually, only in combination.

B. to test for abnormal returns (return performance) for a stock or a portfolio of stocks we need a model ofRandom Walk is a stronger model. It assumes that the whole distribution of returns conditional on an information structure is no different than the unconditional distribution.

(r1,t+1, … rn,t+1) = (r1,t+1, …, rn,t+1|t)

This says that unconditional returns already fully impound all information so conditioning on an information structure provides no advantage.

All return observations must be independent and taken from the same distribution because new information is always anticipated and fully reflected in a fixed distribution.

Because recent studies show that return distributions change over time, stock returns are not random walks.

4. One difference between a fair game and random walk:

A fair game can have correlated returns over time but a random walk cannot.

Example: Suppose you have a series of returns on a portfolio strategy that consists of buying stock X at the beginning of period 1, then selling it at the end of period 1 and reinvesting the money in stock Y at the beginning of period 2, and selling it at the end of period 2 and reinvesting the money in stock X at the beginning of period 3, and then selling it at the end of period 3 and reinvesting the money in stock Y and so on. If the mean returns of the stocks are Y = .10 and X = .15, what type of pattern will we observe in the return series?

Technical analysis
TECHNICAL ANALYSIS to test for abnormal returns (return performance) for a stock or a portfolio of stocks we need a model of

  • FUNDAMENTAL ANALYSIS – stock prices are determined solely by the expected discounted present value of all future cash flows based upon economy, industry, company information.

  • TECHNICAL ANALYSIS - use past price and trading

  • volume to predict future price.

  • Efficiency argument for studying Technical Analysis - Since market efficiency implies prices aggregate all information, then for an uninformed investor, prices may be used to infer what the market knows.

  • Technical Analysis is popular, perhaps because it is very visual and intuitive - analysts use charts

Dow theory best known technical theory
DOW THEORY - BEST KNOWN TECHNICAL THEORY to test for abnormal returns (return performance) for a stock or a portfolio of stocks we need a model of


  • primary trend

  • intermediate trend

  • short term corrections - day to day


  • bull trend - higher highs

  • bear trend - lower lows

  • 1. Problems with Dow Theory

  • Often late in identifying major trends

  • Not much help for short term trader - or which stocks to buy.

Volume analysis supply demand
VOLUME ANALYSIS - SUPPLY/DEMAND to test for abnormal returns (return performance) for a stock or a portfolio of stocks we need a model of

  • Large volume signals turning points followed by weak volume.

  • Volume goes with trend

  • Bull market - prices up on high volume

  • -prices down on low volume

  • Bear market -prices up on low volume

  • -prices down on high volume

Basis for technical analysis
BASIS FOR TECHNICAL ANALYSIS to test for abnormal returns (return performance) for a stock or a portfolio of stocks we need a model of

  • Supply-demand determine price

  • Both supply & demand are affected by rational and irrational factors.

  • Prices move in trends - trends persist because price adjustments to new information takes time

  • 1. Supposed Advantages of Technical Analysis

  • Aren't required to get good fundamental information and process quickly, this is difficult.

  • Just interpret price and volume movements to get information indirectly, don’t care about what a company does.

  • No need to decipher financial statements that are biased.

  • 2. Examples

  • Short interest - signals latent demand - not supported

  • Odd lot Theory - small investors trade incorrectly - not supported

  • Mutual Fund Cash Position to test for abnormal returns (return performance) for a stock or a portfolio of stocks we need a model of - latent demand - actually a concurrent indicator.

  • Call / Put ratio - usually more calls - increase in puts is

  • bearish.

  • Inside Information Indicators

  • - insider sell / buy ratio - since many companies pay in shares - expect some to sell, if none sell - bullish

  • - buy / sell differential by NYSE members

  • - short selling by specialists


  • resistance levels

  • support levels


  • hard to tell one from another

  • their use reflects individuals effort to see pattern in randomness, tests show people see patterns in random generated pictures general trends and sideways movements

Websites for technical analysis
Websites for Technical Analysis to test for abnormal returns (return performance) for a stock or a portfolio of stocks we need a model of

  • – has examples of formations and trendlines.

  • 2. – use Prophet JavaCharts for drawing in trendlines – interactive.

  • 3. Stockcharts – has MarketCarpets that give a visual of how sectors are doing day-to-day.