Market Efficiency Lecture - Days 3 and 4 (1)

11/9/11

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Empirics of Financial Markets

Patrick J. Kelly, Ph.D.

Market Efficiency

Market Efficiency

•  Allocational

•  Operational

•  Informational (also Capital Market Efficiency)

© 2010 Patrick J. Kelly 3

Market Efficiency

•  Allocational –  When marginal rates of return for all producers and lenders are

equal

•  Operational –  Transactions cost of transferring funds is zero

•  Informational (also Capital Market Efficiency)


Aspects of Information Efficiency

I.  Type and Quantity of Information Created 1.  Past Price 2.  Public 3.  Private

II.  Information Incorporation 1.  Speed 2.  Correctness 3.  Completeness


Type and Quantity of Information

•  Information Generated by –  Exchanges –  Investors, Analysts, Companies

•  Public •  Private


Past Prices

Public Information

Private Information

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Wall Street Journal September 21, 2005

Information Incorporation


FedEx’s Share Price July – October 2005

Sept. 21, 2005


Market Efficiency and New Information

•  When news about the value of a security hits the market, its price should react and incorporate this news quickly and correctly. –  Quickly: stale information is of no value –  Correctly: price response should be accurate on average –  Completely. no systematic over- or underreaction

Market Efficiency Requires Rational Investors

•  Market needs at least some investors to be rational –  Learn and update their beliefs correctly

•  According to Bayes’ law

–  Make choices that are in accordance with our beliefs

•  Behavioral finance: Some phenomena are best explained if some agents are not rational –  But let’s stick with the rational for a little longer….


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Maurice Kendall (1953)

•  In the 1950’s a statistician from the London School of Economics set out to examine whether stock prices were predictable.

•  To the surprise of many economists prices “behave almost like wandering series.” –  Does this indicate that prices are driven by psychology or “Animal

Spirits”? –  Is there a more rational explanation?


Efficient Prices and Competition (assuming rational investors)

•  Suppose stock X is currently priced at $10 per share

•  But you’ve developed a model that allows you to predict with confidence that prices will rise to $15 per share in a week.

•  If you were alone in the knowledge that the price will go up, you’d slowly buy as much stock as you can so don’t affect the price and can earn the biggest profit.


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Efficient Prices and Competition (2)

•  Suppose other investors also had access to your brilliant model.

•  You’d have to buy the stock quickly before they did and push up the price.

•  Everyone else would realize the same thing and place a large number of orders and push the price up to (nearly) $15.

•  The more investors who know – the more orders and the faster the prices will change

© 2008 Patrick J. Kelly 13 © 2008 Patrick J. Kelly 14

Competition and Efficient Prices

•  Competition (arbitrage) assures prices reflect information

•  Because prices quickly adjust to new information prices appear to “behave almost like wandering series.” –  Key assumption: Information arrival is random.

•  Random Walk - stock prices are random –  Actually submartingale

•  Expected price is positive over time •  Positive trend and random about the trend


Security Prices

Time

Random Walk with Positive Trend How Quickly Do Prices adjust?


Forsyth, Palfrey and Plott (1982)


Forms of the EMH

•  Fama (1970) categorized Information Efficiency with respect to the type of information prices reflect

•  Weak form: Prices reflect all information contained in past prices

•  Semi-strong form: Prices reflect all publicly available information

•  Strong form: Prices reflect all relevant information, even if it is not in the public domain (private information)

Are Markets Efficient?

•  Strong Form Efficient?

•  Semi-Strong?

•  Weak?


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Tests of Weak Form efficiency

•  Do prices follow a random walk? –  Campbell, Lo, MacKinlay (1997)


Random Walk 2: Technical Analysis

•  Predict future stock price movements by looking at patterns in past prices: charting –  Example: Head and Shoulders, from: http://www.investopedia.com/terms/h/head-

shoulders.asp –  1. Rises to a peak and subsequently declines.

2. Then, the price rises above the former peak and again declines. 3. And finally, rises again, but not to the second peak, and declines once more.

Head and Shoulders in Actual Data

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Technical Analysis (con’t)

•  Technical analysts: Info about a company’s prospects is not useless, but unnecessary for successful trading

•  If technical analysis is successful, then prices are NOT weak-form efficient

•  Difficult to believe as price info is available to all investors at a minimal cost –  Everyone can try to exploit the patterns, which implies that they should not

arise –  Chartists believe otherwise

A filter rule proposed in the WSJ

•  Consider an investor with a $1 million portfolio on Dec. 24, 1998, the first time the Standard & Poor's 500-stock index was at its current level. If the investor had merely held on, he would have seen essentially zero appreciation through Nov. 11 of this year. But if that same investor instead had sold one-tenth of his portfolio every time the stock market gained 20% and allocated one-fifth of his cash to the market when stocks fell more than 10%, he would have gained about $140,000, according to a Wall Street Journal analysis. –  I actually got $86,892, assuming I invested the cash in 1 month T-

Bills and completely ignoring transactions costs.

From: “How to Play a Market Rally ” by Ben Jevisohn and Jane J. Kim, WSJ Nov. 13, 2010.

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WSJ Strategy Back Tested

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Do prices follow random walks? Is Weak Form efficiency violated?


Are markets efficient?

•  Asking whether markets are efficient is a bit silly.

•  Why?

•  Efficient Markets are essentially a Platonic ideal: a perfection toward which we can strive – but can’t actually be obtained.

•  What we can compare is whether –  Some stocks are more efficient than others –  Some markets in some countries are more efficient than others


A look at the evidence

Comparing Emerging vs. Developed Markets –  [Griffin, Kelly, and Nardari (RFS, 2010)]

•  Statistical Tests –  Variance Ratios

•  “Economic” test –  Mid-term momentum –  Short-term reversal


Efficiency Around the World Higher means more persistent returns/less weak-form efficiency and more

likely profits to one week strategies:

Average Absolute 5-Day Variance Ratios Small: High return persistence or reversal

Large: Low return persistence or reversal

Griffin, Kelly, Nardari (2010)


Weak Form Efficiency

•  Weak form: Prices reflect all information contained in past prices

•  Simple trading strategies based on past returns shouldn’t be profitable. –  Returns should not be predictable.

Is past price information incorporated correctly?

•  If information is incorporated correctly and completely, then prices should not systematically overshoot. –  Prices should just look random

•  If prices do overshoot, we ought to see reversals –  Prices that drop after just going up OR –  Prices that rise after just going down

–  In the next slide we look at the profits to simple strategies designed to take advantage of over reaction

•  Buy long past week losers and •  Short past week winners


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One week contrarian profits

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Note: In the U.S. the contrarian strategy earns 30 basis points per week

Contrarian Profits

•  Are these profits meaningful?

•  The long-short strategy in the U.S. earns only 30 basis points per week before accounting for the cost of buying and selling stock. –  Is 30 basis points of return per week enough to cover the cost of a

high turn over strategy that buys, sells, shorts and covers stocks each week?

–  With $1,000,000 in assets, 30 basis points generates $3000 in profit ignoring trading costs.

•  Limits to arbitrage –  If it is too costly to trade on an anomaly – a seemingly easy way to

profit – the anomaly will continue to exist


One week contrarian profits over time

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In the US (in Green) trading costs have decreased over time – and so have the “profits” to these contrarian strategies.


Tests of Market Efficiency - Momentum

Momentum predicts return –  Portfolios Long on past six-month winners and short past six-

month losers earn high returns. •  Winners are the 10% of stocks with the highest returns •  Losers are the worst 10% of stocks with the lowest returns


Six-Month Momentum

•  Buys past six-month winners, shorts past six-month losers

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Market Risk Premia in Recessions and Expansions

Henkel, Martin, and Nardari (2011)


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Do Fundementals Forecast Future Returns?

expands on our empirical approach and is followed by adescription of the data in Section 4. Section 5 reports ourempirical findings. Section 6 concludes.

2. Background and motivation

2.1. Dynamics of expected returns

Early empirical evidence of countercyclical risk pre-miums is in Fama and French (1989) and Ferson andHarvey (1991). The basic intuition for a link betweencountercyclical risk premiums and return predictability issimple and appealing. If investors demand higher riskpremiums in bad times, and volatility is higher in badtimes as well, then overall adjustments to discount ratesper unit of change in economic state are larger in badtimes. Crucially, price–dividend ratios become morevolatile and prices more sensitive to changing expecta-tions as conditions worsen. Predictability might, there-fore, be a countercyclical phenomenon.

The cyclical dynamics of risk premiums and of returnpredictability need not be synchronous, however. Usingthe framework of Campbell and Cochrane (1999), Li (2007)shows, counterintuitively, that changes in risk aversionalone are insufficient to induce any return predictability atall. In another example, Mele (2007) demonstrates thatcountercyclical risk premiums do not necessarily implyhigher return volatility in bad times.

Nevertheless, we account for the possibility of counter-cyclical return predictability in two ways. First, we decom-pose the sources of predictability to control for shifts inmarket volatility relative to predictor volatility. Second, wedesign tests based upon professional survey data to betterdistinguish the effects of current conditions from the effectsof expectations regarding future economic conditions.

Changes in predictability over time could also resultfrom infrequent, random structural breaks rather thanbusiness cycles. Under different assumptions, Pesaran andTimmermann (2002) and Lettau and Van Nieuwerburgh(2008) both identify 1991 as one such structural break.Since there have been further National Bureau of

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Random walkFama (1965, 1970)

Short rate predictsFama and Schwert (1977)Fama (1981)Geske and Roll (1983)

Dividend yield predictsRozeff (1984), Shiller (1981)

Term premium predictsCampbell (1987), Fama (1984)Keim and Stambaugh (1986)Harvey (1988)

Default premium predictsChen, Roll and Ross (1986)Keim and Stambaugh (1986)

Predictability debatableGoetzmann and Jorion (1993)Hodrick (1992)Kim and Nelson (1993)Richardson and Stock (1989)

Predictability illusory?Ang and Bekaert (2007)Cochrane (2008)Goyal and Welch (2003, 2008)Valkanov (2003)

Fig. 2. The time-series of predictability research. The literature on stock return predictability follows closely the availability of recession data as acumulative proportion of the total data in CRSP which originally started in 1962. Shown are the percentages of recession data as a percentage of theavailable data at a given date, as measured by NBER (solid line) and RSVAR (dashed line) dates. Both the NBER and RSVAR samples show similar profiles,although RSVAR recession probabilities represent a much larger proportion of the data. Many seminal, and first, papers on return predictability werepublished just after the peaking of the proportion of recession data to total available data in 1985 and are followed by a decline in the proportion ofrecession data thereafter. The citations are representative for expository purposes and are not intended to be indicative of initial research, nor acomprehensive literature survey (Ang and Bekaert, 2007; Campbell, 1987; Chen et al., 1986; Cochrane, 2008; Fama, 1965, 1970, 1981, 1984; Fama andSchwert, 1977; Geske and Roll, 1983; Goetzmann and Jorion, 1993; Goyal and Welch, 2003; Harvey, 1988; Hodrick, 1992; Keim and Stambaugh, 1986;Kim and Nelson, 1993; Richardson and Stock, 1989; Rozeff, 1984; Shiller, 1981; Valkanov, 2003; Welch and Goyal, 2008).

Please cite this article as: Henkel, S.J., et al., Time-varying short-horizon predictability. Journal of Financial Economics(2010), doi:10.1016/j.jfineco.2010.09.008

S.J. Henkel et al. / Journal of Financial Economics ] (]]]]) ]]]–]]] 3


Henkel, Martin and Nardari (2011)

•  Predictive explanatory power in good and bad times –  Using : Short Rates, Dividend Yield, Term Premia


DeBondt and Thaler (1985) 800 The Journal of Finance

Average of 16 Three-Year Test Periods Between January 1933 and December 1980

Length of Formation Period: Three Years

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MON4TH1S AFTEn PORTFOLID FOIRATION

Figure 1. Cumulative Average Residuals for Winner and Loser Portfolios of 35 Stocks (1-36 months into the test period)

While not reported here, the results using market model and Sharpe-Lintner residuals are similar. They are also insensitive to the choice of December as the month of portfolio formation (see De Bondt [7]).

The overreaction hypothesis predicts that, as we focus on stocks that go through more (or less) extreme return experiences (during the formation period), the subsequent price reversals will be more (or less) pronounced. An easy way to generate more (less) extreme observations is to lengthen (shorten) the portfolio formation period; alternatively, for any given formation period (say, two years), we may compare the test period performance of less versus more extreme portfolios, e.g., decile portfolios (which contain an average 82 stocks) versus portfolios of 35 stocks. Table I confirms the prediction of the overreaction hypothesis. As the cumulative average residuals (during the formation period) for various sets of winner and loser portfolios grow larger, so do the subsequent price reversals, measured by [ACARL,t - ACARw,,] and the accompanying t-statistics. For a formation period as short as one year, no reversal is observed at all.

Table I and Figure 2 further indicate that the overreaction phenomenon is qualitatively different from the January effect and, more generally, from season-


Anomalies

•  Next cross-sectional differences in return –  Risk or mispricing?

–  From 1936-1975 Small Firms in the US earned higher returns than explained by CAPM

•  Banz (1981) and Reinganum (1981)

–  The January Effect – small losing firms have high returns in January

•  Keim (1983) and Reinganum (1983)

–  Value Effect (Banz, 1977, 1983) •  High E/P firms earn higher returns.



Tests of the EMH – Anomalies

1.  Small Firm Effects –  One of the best known anomalies –  Returns on small firms are higher than those on large firms

after controlling for risk –  Initial study, smallest 20% of NYSE stocks yield 19.8%

higher returns than largest -- huge premium!

1a. “Small Firm in January” Effect 1b. Neglected Firm Effect 1c. Illiquidity Effect

“Small Firm in January” effect

______ ____ © 2008 Patrick J. Kelly 42

1a. “Small Firm in January” effect –  Return difference occurs almost entirely in January

•  Anomaly or Rational Explanation? •  Explained by tax-loss selling

•  Selling losers in December (or earlier) in order to offset profits •  Buying back winners in January to re-establish desired portfolio

diversification

•  Some recent evidence suggests the January effect is a “pure anomaly”: •  in the UK says that after the small firm effect was publicized, the

pattern has reversed

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Small Firm and Turn of the Year Effects


Small Firm Effect – Neglected Firms

1b. The “neglected firm” effect –  Small firms are riskier, more uncertain investments –  Information about these companies is less available –  Small firms are neglected by large institutional traders –  and therefore command higher returns

•  Empirical tests: •  Variation among analyst earnings forecasts or amount of research available

about firms was significantly related to strength of small firm effect


Small Firm Effect – Illiquid stock

1c. The “liquidity” effect: –  Small firms have High Trading costs –  Investors demand a rate-of-return premium for holding

stocks which are less liquid –  Empirical evidence:

•  Stocks with high bid-ask spreads (% of price) exhibit abnormally high risk-adjusted returns

•  Why do these returns occur mainly in January?


Tests of the EMH – the Book to Market Anomaly

2. Book to Market predicts return: –  A seemingly powerful predictor of returns across securities (a

role that should be played by β) is book-to-market ratio

–  Fama and French (1992): build 10 groups of stocks by book-to-market ratio.

•  Group with highest ratio had return of 1.65% per month •  Group with lowest ratio had return of 0.72% per month

–  Puzzle: High book-to-market stocks seem underpriced •  Stronger relationship than with CAPM’s β

Value Stocks Earn Higher Returns


Week-end-Effects

•  Returns are reliably negative over weekends from 1953-77 in US (French, 1980)


Market Efficiency Lecture - Days 3 and 4 (1)

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