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Early 1970’s, Fama & MacBeth did a famous study testing the CAPM.

They found weak evidence that portfolios of stocks with higher betas had higher returns, and found an intercept slightly higher than zero. (CAPM Assumes Alpha = 0)

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Beta

Return

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Early evidence basically supported both the weak and the semi-strong form Efficient Markets’ Hypothesis (EMH).

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Positive Serial Correlation: + returns follow + returns for a given

stock or - returns follow - returns for a given stock

Called “momentum” or “inertia”

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Negative Serial Correlation: + returns follow - returns for a given

stock or - returns follow + returns for a given stock.

Called “reversals”

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If we find (+) or (-) serial correlation, this is evidence against the weak-form EMH as it implies that past prices can be used to predict future prices.

(Technical analysis)

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In 1960s, studies indicated that:

1. Stock Prices followed a random walk

2. No evidence of serial correlation. The price of a stock is just as likely to rise after a previous day’s increase as after a previous day’s decline.

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Event studies in the 1960s & 1970s looked at stock prices around the release of new information to the public. This was an effort to see if the market quickly incorporated new information into the prices of stocks.

One famous event study (1981) looked at CARs of takeover firms around the announcement date.

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1980s & 1990s: Empirical evidence began to accumulate

that provided evidence first against the semi-strong EMH and later against the weak form EMH

Initially any evidence against EMH was called an anomaly.

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Are abnormal risk-adjusted returns possible if you trade after information is made public? (fundamental analysts)

General Equation for Abnormal (Excess) Returns:

Actual Rit – Predicted Ri,t

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Without a risk adjustment: Actual Rit – Actual Rm,t

With a risk adjustment:Actual Rit – [ai + Bi[Actual Rm,t]

Or,Actual Rit – [Actual Rmatch,t]

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Difficult to measure risk-adjusted returns

a) Is beta the proper measure of risk?b) CAPM is forward looking and you are

using historic data. c) Is your matched firm the best match?

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(Quarterly EPS Released – Forecasted Quarterly EPS)

Measure the abnormal risk-adjusted return after an earnings surprise.

Measure CAR: Actual Rit – Predicted Ri,t

(Using CAPM for the predicted return)

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Rank from highest to lowest by magnitude of earnings surprises and place stocks into decile portfolios.

See if trading on earnings surprises results in subsequent abnormal returns.

(Cumulative Abnormal Returns (CARs) are the daily abnormal returns summed up over time)

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For positive earnings surprises: The larger the earnings surprise the

higher the positive abnormal return.

The upward drift in the stock price continues a couple of months after the earning announcement!

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For negative earnings surprises: The larger the negative earnings

surprise the larger the loss as measured by the abnormal return.

The downward drift in the stock price continues a couple of months after the earning announcement!

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Markets are efficient. The evidence of abnormal risk-adjusted returns is due to various Measurement Errors when using the CAPM. Perhaps the betas are wrong.

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Markets are efficient. The evidence of abnormal risk-adjusted returns (evidence against market inefficiency) is inconclusive as the CAPM may not be the proper risk adjustment model.

[Joint or Dual Hypothesis Problem!]

If the CAPM is wrong, then abnormal risk-adjusted returns using this model are wrong.

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Markets are Not Efficient

Behavioral Finance: Psychological and behavioral elements lead to predictable biases.

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After share repurchase announcements (Ikenberry) After dividend initiations and omissions (Michaely) After stock splits (Ikenberry) After seasoned equity offerings & after

IPOs (Loughran and Ritter)

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Portfolios of small cap stocks earn positive abnormal risk-adjusted returns (+ alphas):

Grossman/Stiglitz: Professionals move prices to efficiency. Don’t buy at the small cap end of the market much due to limits on portfolio positions.

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Returns in January are significantly

higher than returns in any other month of the year.Primarily due to returns in the first two

weeks of JanuaryPrimarily due to returns for small firms

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Possible sources of risk for small caps

Neglected by analysts and institutional investors, so is less information, which implies higher risk.

Less Liquidity: Higher trading costs as bid-ask spreads are wider, and broker commissions are larger.

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Over the years, returns on Mondays have been consistently lower than returns on other days of the week.

The bulk of the negative returns come from the diference between Friday’s closing prices and Monday’s opening prices. The interday returns on Monday are not unusual

The Weekend Effect is worse for small stocks

There is no difference between two and three-day weekends

No apparent effect following holidays29

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Beta

Return

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In 1992, Fama & French re-examined the earlier tests of the CAPM forming size decile portfolios.

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Beta

Return Small cap stocks

Large cap stocks

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See that small cap stocks have higher betas than large cap stocks. Fama and French concluded that size is driving the relationship between beta and return not beta!

Also see that within the small cap groupings, portfolios of stocks with lower betas have higher returns! The same is true within the large cap groupings.

Fama, once a strong proponent of the CAPM now claimed that beta was dead. Beta was a rough proxy for size in his earlier tests!!

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Average Monthly Returns (in Percent)

All Low-β β-2 β-3 β-4 β-5 β-6 β-7 β-8 β-9 High-β

All 1.25 1.34 1.29 1.36 1.31 1.33 1.28 1.24 1.21 1.25 1.14

Small - ME 1.52 1.71 1.57 1.79 1.61 1.50 1.50 1.37 1.63 1.50 1.42

ME-2 1.29 1.25 1.42 1.36 1.39 1.65 1.61 1.37 1.31 1.34 1.11

ME-3 1.24 1.12 1.31 1.17 1.70 1.29 1.10 1.31 1.36 1.26 0.76

ME-4 1.25 1.27 1.13 1.54 1.06 1.34 1.06 1.41 1.17 1.35 0.98

ME-5 1.29 1.34 1.42 1.39 1.48 1.42 1.18 1.13 1.27 1.18 1.08

ME-6 1.17 1.08 1.53 1.27 1.15 1.20 1.21 1.18 1.04 1.07 1.02

ME-7 1.07 0.95 1.21 1.26 1.09 1.18 1.11 1.24 0.62 1.32 0.76

ME-8 1.10 1.09 1.05 1.37 1.20 1.27 0.98 1.18 1.02 1.01 0.94

ME-9 0.95 0.98 0.88 1.02 1.14 1.07 1.23 0.94 0.82 0.88 0.59

Large - ME 0.89 1.01 0.93 1.10 0.94 0.93 0.89 1.03 0.71 0.74 0.56

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Within each size group, the higher the beta the lower the return.

Additionally, after controling for size, Fama and French found that value stocks (those with a high B/M ratio outperformed growth stocks (those with a low B/M ratio).

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Book-to-Market Portfolios

All Low 2 3 4 5 6 7 8 9 High

All 1.23 0.64 0.98 1.06 1.17 1.24 1.26 1.39 1.40 1.50 1.63

Small - ME 1.47 0.70 1.14 1.20 1.43 1.56 1.51 1.70 1.72 1.82 1.92

ME-2 1.22 0.43 1.05 0.96 1.19 1.33 1.19 1.58 1.28 1.43 1.79

ME-3 1.22 0.56 0.88 1.23 0.95 1.36 1.30 1.30 1.40 1.54 1.60

ME-4 1.19 0.39 0.72 1.06 1.36 1.13 1.21 1.34 1.59 1.51 1.47

ME-5 1.24 0.88 0.65 1.08 1.47 1.13 1.43 1.44 1.26 1.52 1.49

ME-6 1.15 0.70 0.98 1.14 1.23 0.94 1.27 1.19 1.19 1.24 1.50

ME-7 1.07 0.95 1.00 0.99 0.83 0.99 1.13 0.99 1.16 1.10 1.47

ME-8 1.08 0.66 1.13 0.91 0.95 0.99 1.01 1.15 1.05 1.29 1.55

ME-9 0.95 0.44 0.89 0.92 1.00 1.05 0.93 0.82 1.11 1.04 1.22

Large - ME 0.89 0.93 0.88 0.84 0.71 0.79 0.83 0.81 0.96 0.97 1.18

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Beta does not explain returns.

Small cap stocks have higher returns. Small cap stocks have higher betas, but it is size not beta driving higher returns.

Low P/E or high Book-to-Market of equity stocks have higher returns.

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The Market is Semi-Strong Efficient: Small cap stocks and low P/E (high B/M) stocks generate higher returns because they are riskier. However, this risk is not captured by Beta!

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Lack of a theoretical model to explain why size and style (value vs growth) are important risk factors. The CAPM had an elegant, logical theory underlying it, this has none!

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The Market Not Semi-Strong Form Efficient:

You can make abnormal returns using public information regarding market capitalization and P/E or B/M ratio.

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(Lakonishok, Shleifer and Vishney) These professors offer a different

interpretation. Markets are inefficient. People overreact with a lag. Overprice firms with good recent returns (growth) and underprice firms with poor recent returns (value).

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DeBondt and Thaler (1985):

Create Loser and Winner portfolios based on past 36 months of CARs. Top decile are Winners, bottom decile are Losers.

Examine CAR’s for next 36 months.

“Loser’s outperform “winners” Is an overreaction followed by a correction.

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Evidence is due to market risk premiums varying over time. It is not overshooting & correction, but instead a rational response to changes in the discount rate.

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Lo and MacKinlay (1988) test to see if there is serial correlation of weekly stock returns for NYSE stocks.

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Stock Price

Period

1 2

+ momentum

- momentum

reversal

reversal

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If momentum is present, the variance of returns should increase as the number of periods used is increased.

If there is no momentum, gains or losses will tend to reverse, keeping the variance of returns from becoming wider.

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Lo and Mackinlay (1988) find positive serial correlation of weekly stock returns for NYSE stocks as the variance of returns increases as the return interval is lengthened. Implies there is inertia in the short run.

The effect is the strongest in the small cap stocks.

Not clear if abnormal returns are possible by exploiting this information.

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Other studies of weekly returns found different results

Lehman and Jegadeesh (1990) found evidence of negative serial correlation over short horizons

Gutierrez and Kelley (2006) find both: negaitve serial correlation followed by positive serial correlation

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Study by Jegadeesh and Titman.

1.Measure stock rates of return over the past 6 months.

2.Rank the stocks from highest to lowest past 6 month return and then divide the sample into deciles. “Losers” are the bottom decile and “winners” are the top decile

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3. For the next 36 months, every time one of the winners or losers reports quarterly earnings, record 3-day returns starting 2 days before the earnings announcement and ending the day of the announcement.

4.Observe the difference in 3-day returns between the winners and losers reporting earnings in each month.

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For the 1st 7 months, the market is pleasantly surprised by the earnings announcements of the winners and disappointed by the earnings announcements of the losers.

(momentum in the intermediate term)

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From months 9 - 36, the market is pleasantly surprised by the earnings announcements of the losers and disappointed by the earnings announcements of the winners.

(Reversals in the longer term) If the stock market is efficient, it

should be able to anticipate the good or bad reports in advance.

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Abnormal profit opportunities. Reversion to the mean. The market overreacts with a lag.

Consistent with “Representativeness and Conservatism.”

Intermediate Run: Inertia Long Run: Reversals

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If the stock market is not weak or semi-strong form efficient, then professional portfolio managers should be able to achieve abnormal risk-adjusted returns!

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WSJ Article, “Stock Funds Just Don’t Measure Up”. Oct. 5, 1999

After adjusting for size and survivorship bias, funds trailed the S&P 500 by 1.4% per year which is on average what they charge for annual expenses.

Other studies: 1970’s – 1990’s: After expenses & commissions, only 1/3 beat the market on a risk-adjusted basis.

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Are abnormal risk-adjusted returns possible if you trade using private information?

Corporate insiders are required to report their transactions to the SEC.

They are not supposed to trade when in the possession of “material” information.

Even with regulation, they achieve positive risk-adjusted abnormal returns.

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23% Drop in One Day??

No large release of news

Efficient Market explanation: Due to chance. Are outliers in the distribution. Just an outlier observation in a random process.

Panic & Crowd Psychology

(behavioral finance explanation)

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Some companies saw their stock price go up just by adding dotcom to their names

When 3-Com spun off Palm Pilot, but kept 95% of the shares, The 95% of Palm owned by 3-Com were worth more than the market cap of 3-Com. Implies negative value for the rest of 3-Com!

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It is obvious now that the 1998-March 2000 tech run-up was a bubble, but was this market inefficiency, or merely poor valuations?

How do you know a bubble when you are in it?

Should you try to short a bubble if you don’t know when it will burst?

“The market can remain irrational longer than you can remain solvent”

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Just because you know something is overvalued or undervalued, doesn’t necessarily mean you can make money off it

Classic Example: We know that someday the sun will explode, but you can’t short the Earth

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Most arbitrage is not carried out by small investors, but by large money managers.

They usually manage OPM (other people’s money)

Most arbitrage in the real world is actually “risk arbitrage” and requires capital

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If money managers observe a price discrepancy and commit capital to an arbitrage position based on convergence, the initial movement may be away from convergence, but that merely means there is a greater opportunity for profit, and more capital should be committed.

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But that is exactly when investors are most likely to pull out.

Investors invest based on PBA (Performance Based Arbitrage) rather than expected returns

This lack of capital prevents arbitrage from taking place

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This is often given as an explanation for the collapse of LTCM (Long-Term Capital Management).

Amazingly, the Shleifer and Vishny paper came out about a year prior to the LTCM collapse

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