lecture5_35151_2013 by tobias moskowitz empirical asset pricing.

8/19/2019 lecture5_35151_2013 by tobias moskowitz empirical asset pricing.

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Market efficiency means:

• prices are correct:

– they fully reflect all available information

P t = E t

dt+1

1 + rt+1+

dt+2

(1 + rt+2)2 + . . .

• people use all available information in forming expec-tations about future cashflows

• the discount rate is right for the riskiness of the cash-flows

• prices react to new information quickly and to theright extent

• there is no free lunch:

– the only way you can get higher returns is by takingon more risk

– there is no information out there that can be usedto construct strategies that earn returns higherthan required for their risk

– When we say ‘prices are correct’, we are implicitlystating what ‘correct’ is (i.e., we are assuming anasset pricing model).

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What information are we talking about?

• information in past prices

• public information

• private information

• we can characterize markets as:

weak semi-strong strong

-form efficient if all:

past price public private

information is incorporated in prices already.

Paradox : If markets are efficient, then does not pay tosearch for information. But, how then, can markets be ef-ficient if no one searches for information and incorporatesit into prices?

Transactions and trading costs play a key role here.Prices reflect information to the point where the marginal

benefits of acting on information do not exceed the marginalcosts.

Thus, need to determine if deviations from extrememarket efficiency are within information and trading costs.

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How can we tell if markets are inefficient?

• look for stock-picking strategies based on some past

information which have earned high returns with littlerisk

• unfortunately, we can never be sure of inefficiency:

– it is always possible that we are not measuring riskproperly

– i.e., we don’t know what the right discount rate is– this is the “Joint Hypothesis Problem”

• Thus, market efficiency itself is not testable. It must be tested jointly with a model of prices/expected re-turns.

Why would we expect markets to be efficient?

• the forces of arbitrage

– smart investors exploit the mispricing in securitiesuntil it disappears

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Now, let’s examine tests of the various forms of marketefficiency.

1. Weak form efficient: current prices fully reflectall information in past prices.

Fama (1991) denotes slightly broader heading of “pastreturn predictability” in general (e.g., including D/P,E/P, size, BE/ME, . . . predictability).

• ⇒ ‘technical’ analysis using past price patterns willnot produce profits.

ex:

do prices over or under-react?

are there seasonal patterns?

• prices should take this into account, but do they?

• are deviations within transactions and trading costs?

2. Semi-strong form efficient: current prices fullyreflect all past prices and all publicly available infor-mation.

• ⇒ ‘fundamental’ analysis (e.g., sorting through in-

come statements) will not produce profits.

• Public news announcements will be incorporatedinto prices quickly → no profitable trading rule.

Event study analysis.

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e.g. announcement of a takeover

∗ do an “event study” to look at the stock pricereaction to the news

∗ average over many companies

• are deviations within transactions and trading costs?

3. Strong form efficient: current prices fully reflectall information, public and private.

• ⇒ insider trading will not produce profits.

ex:

knowing a merger is going to take place before it

is announced publicly.Random Walks and Efficient Markets

• it is often thought that efficient markets ⇒ pricesmove randomly

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• Consider a Martingale, which is how researchersoriginally began thinking of price processes

• Can be thought of as a fair game , which does notfavor one side or the other

• A martingale is a stochastic process P̃ t which satisfies

E [ P̃ t+1|P t, P t−1,...] = P tE [ P̃ t+1 − P t|P t, P t−1, ...] = 0

• the best estimate of tomorrow’s price is today’s price.

• This also implies that price changes (e.g., returns)should not be serially correlated at all leads and lags.

• This implies returns should not be predictable! But,we know risk and expected return should somehow berelated.

• Since the martingale hypothesis does not account forrisk, it is neither a necessary nor sufficient conditionfor rationally determined prices in an efficient market.

• If there is drift in the process, then returns will bepredictable, but the drift could be due to risk.

The martingale led to a closely related model: TheRandom Walk hypothesis.

• Consider the simplest case where prices are iid.

P t = µ + P t−1 + t, t ∼ iid(0, σ2)

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where µ is the expected price change or drift.

• Note: the random walk is also a fair game, but ina stronger sense than the martingale: independenceimplies not only that increments are uncorrelated, butalso that any nonlinear functions of the increments areuncorrelated.

E [P t|P 0] = µt + P 0V ar[P t|P 0] = σ

2t

Note: the conditional mean and variance are linear intime.

• We can also employ weaker assumptions on the RWprocess

1. we can assume the process is not identically dis-

tributed, but still independent.– this allows for heteroskedasticity and non-stationary

price changes (more realistic).

– Still, any arbitrary transformation of future priceincrements is unforecastable using any arbitrarytransformation of past price increments.

2. we can assume the process has uncorrelated, butnot independent, increments, and is not identicallydistributed.

– this is the weakest RW hypothesis of all, andcontains the other two as special cases.

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– ex: Cov(t, t−k) = 0, but Cov(2t ,

2t−k) = 0.

• if the discount rate for an asset does not change overtime, then it is true that efficient markets ⇒ randomwalk

– e.g. over short time frames, returns should lookrandom

This means predictability tests run head-on into the joint hypothesis problem.

One of the most direct and intuitive tests of the RW andmartingale hypotheses is to examine serial correlation inthe time-series of an asset’s return.

Usually employ short-term returns to avoid the jointhypothesis problem.

Consider the autocorrelation coefficient :

r̃it = γ 0,t + γ 1,kri,t−k + ̃it

γ 1,k = cov(rit, ri,t−k)

σ2

(ri,t−k)ρ(rit, ri,t−k) =

cov(rit, ri,t−k)

σ(rit)σ(ri,t−k)

ρ2(rit, ri,t−k) = γ 21,kσ

2(ri,t−k)

σ2(rit)

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= Proportion of variance attributed to ri,t−k

If process is iid,

σ(rit) = σ(ri,t−k) = σ(ri) ∀k

⇒ ρ(rit, ri,t−k) = γ 1,k

Autocorrelation = autoregression coefficient for lag k.

When calculate this for individual stocks at shorthorizons (daily, weekly, monthly), find that γ 1,k is nega-tive .

When calculate this for portfolios of stocks at shorthorizons (daily, weekly, monthly), find that γ 1,k is posi-tive .

This means there are large positive cross-autocorrelations across individual stocks over time.

Consider the equal-weighted market portfolio, Rmt =n

i=1

1

nrit

cov(Rmt, Rm,t−k) = cov(n

i=1

1

nrit,

n

i=1

1

nri,t−k)

=

1

n

2 n

i=1cov(rit, ri,t−k) +

n

i=1

1

n

2 n

j=icov(r jt, ri,t−k

= 1

n2

n

i=1cov(rit, ri,t−k) +

1

n

n

i=1

n

j=icov(r jt, ri,t−k)

= own autocovariances + cross-autocovariances

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Does short-term predictability mean markets are inef-ficient?

No, could be driven spuriously by microstructure ef-fects.

Evidence:Predictable components of returns are a small part of thevariance of daily, weekly, or monthly returns.But, explains as much as 40% of the variance of long-horizon returns (2-10 years).

It could be that market inefficiencies are missed by testsof short-term returns?

Long-term returns are negatively autocorrelated (Famaand French (1988a)) over 3-5 year horizons.

• But, small sample issues mean these tests have lowpower (not so reliable).

• Could be consistent with irrational bubbles as well asmean-reverting expected returns (rational).

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The Market Anomalies

• Anomalies can be thought of as investment strategies

which seem to earn high returns without being veryrisky

• They improve the Sharpe ratio of the mean-variancefrontier

Recipe:

(1) form a portfolio based on observable characteris-tics, and measure its returns over time

(2) does the strategy give high returns on average?

(3) don’t forget to consider transactions costs: fric-tions to trading and exploiting the anomaly (bid-askspread, transactions costs, liquidity, taxes, etc.)

IF YES:

• the strategy may be risky and the high average re-turns are just fair compensation for that risk

– how do we measure risk?

• if risk does not explain the high returns, is it evidenceof market inefficiency?

– No, it may be spurious, the result of data-mining

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∗ if you try many strategies, some of them will dogreat in historical data

∗ doesn’t tell you anything about future perfor-

mance– poor risk measurement

Note: even if none of the above turn up a measureof risk, it could be:

∗ the risk is present, but just hasn’t surfaced within

the sample analyzed∗ Or, we’re just not looking at the right measureof risk

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The Size Effect

• small stocks have higher standard deviations and be-tas

• but not high enough to explain their returns

⇒ small stocks may be mispriced

⇒ or small stocks may be correlated with a missingelement of risk.

The January Effect

• much of the small firm effect seems to occur in January

3/4 of small firm premium occurs in first five days of January!

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• often explained by tax-loss selling

– however, effect is widespread in international mar-kets also, even when there’s no capital gains tax

– and, there still seems to be a size effect after con-trolling for this.

• may not accord with efficient markets

– why don’t people buy in December in anticipation?

• ‘Window dressing’ by institutional investors

• Infusion of capital at beginning of year

Other Seasonal Patterns

• Day of the week effect.

– returns are on average negative on Monday.

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– returns are on average positive Wednesday − Fri-day.

• Weekend effect.

– from Friday to Monday, return drops dramatically.

– volume and volatility are higher on Friday thanMonday, despite the fact that information is re-leased over the weekend that cannot be traded onuntil the market opens

• Turn of the month effect

• Holiday effect

– returns are much larger in the days preceding mar-ket closures for holidays

Lakonishok and Smidt (1988) provide an excellent re-view of these anomalies, and address the data miningcritique.

Contrarian Strategies

Losers and Winners (DeBondt and Thaler (1985, 1987),or Thaler chapter 9)

• take a three year period and rank stocks on the basisof their performance over that period

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– form a “winner” portfolio of the top 10% best-performing stocks

– form a “loser” portfolio of the bottom 10% worst-

performing stocks

• this is called a contrarian strategy

• look at their returns over the next few years

• the loser portfolio seems to outperform the winnerportfolio (DeBondt and Thaler (1985))

Two explanations:

overreaction: the winners are firms that peoplehave become too excited about

– subsequently, they realize that they were too opti-mistic

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– price falls and returns are low

risk: the losers are riskier firms

– their higher returns are just compensation for risk

How do we account for risk?

• Variance

• Use regression analysis and a pricing model

– CAPM• Examine when the strategy exhibits the highest and

lowest payoffs

(i.e., does the strategy do well when the market does?when we are in the peak of a business cycle? a reces-

sion?, etc.)• Catastrophe risk

Since variation through time in returns is only partlydue to variation in expected returns, past returns are anoisy proxy for expected returns and therefore lack power.

So, researchers began using other, less noisy, forecastingvariables for expected returns.

• D/P, E/P

• Is this consistent with efficient or inefficient markets?

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Value and Growth

• form portfolios of value stocks

– a value stock is one with low price relative to somemeasure of fundamentals, i.e. high

* book to market (B/M) ratios

cash flow to price (C/P) ratios

earnings to price (E/P) ratios

• also form portfolios of growth stocks, i.e. with lowvalues of these ratios

• find that value stocks dramatically outperform growthstocks

Why?

– rational: Represents a distress factor in the econ-omy. Value stocks are more prone to this source of risk than growth stocks.

⇒ higher average returns.

Value stocks are typically ‘fallen angels’

• irrational: Growth stocks are ‘glamorous’. Peo-ple tend to want to buy these and stampede towardsthem, pushing up the price, and depressing future re-turns.

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Value stocks have been neglected, causing their priceto fall, and expected returns to rise.

This is an overreaction story.

Momentum

• form portfolios of stocks that performed well on a rel-ative basis in the recent past (‘winners’)

– i.e. over the past 3 months to one year• similarly, form a portfolio of ‘loser’ stocks

• the winners outperform the losers

• contrast to the mean-reversion result

• source of inefficiency: underreaction to informa-

tion? Or, is it risk? (we will discuss next week)

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Others argue the evidence clearly supports an inefficientmarket.

To show that markets are inefficient, need to show

• that people make errors in setting prices

• that arbitrage fails to eliminate these errors

Shleifer (2000) claims there are three arguments formarket efficiency:

1. investors are rational and value securities rationally.

2. if some investors are irrational, they are randomly so,and thus their trades cancel each other out.

3. if irrational investors behave similarly, a few rationalarbitrageurs can eliminate their influence on prices.Moreover, irrational investors will lose money on av-erage, and therefore be driven out of the market.

He then argues that:

1. We can show people behave in a less than rational

fashion (via psychological experiments, anecdotal ev-idence).

2. We can also show people make similar (correlated) er-rors in their decision making (e.g., framing, loss aver-sion, overreaction, underreaction).

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3. Finally, in practice arbitrage is limited.

If these anomalies are inefficiencies, why doesn’t

arbitrage eliminate them?

• in practice, arbitrage is limited

• a close substitute for the securities is often not avail-able, therefore there is risk(what types of markets are likely to be more effi-

cient/have more arbitrageurs in them and why?)

• sometimes the strategy can do very poorly, and youlose a lot of money

• money managers and individuals may have short hori-zons (due to regular evaluations or psychological pref-

erences)– a mispricing can take a while to close

– in fact it may not close within the investor’s hori-zon

→ investor will restrict the size of position taken

– when see bad performance, clients of arbitrageursget nervous, pull their money out.

Hence, when mispricing is even more severe (im-plying higher expected returns) arbitrageurs maynot be able to get funding (from clients or banks),

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and may even have to liquidate some assets. Thus,when arbitrage is needed the most to bring pricesback in line, arbitrageurs may be most constrained

and can’t take advantage. (Shleifer and Vishny(1997) or Shleifer chapter 4).

• there can be high transactions and trading costs dueto turnover in these strategies

– liquidity can be low at times when you need it most

– monitoring can be high• there are short sales constraints

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Finally, all of these so-called anomalies may be subjectto, . . .

Data Mining . . . we will discuss in detail later.

• techniques of finding anomalies are often subject tothe data mining critique

– if you try enough variables, something will even-tually appear to predict returns

– but, the forecast power of this variable will be com-pletely spurious (i.e., it won’t work out of sample)

– e.g., generate 100 different data series of completelyrandom numbers

∗ run a regression of actual stock returns on each

of the 100 random data series.∗ some of the regressions will produce significantresults:

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– does this mean you can make money? NO!

– the data mining critique is very powerful:

∗ bear it in mind when people try to impress youwith strategies that worked great in the past.

∗ they probably won’t work in the future!

So, how efficient is the market?

When confronting evidence on predictable return be-havior,

1. Does return predictability reflect rational variationthrough time in expected returns?

• could be tied to CAPM β risk. Maybe represents

important conditioning information.• could represent an omitted risk factor from the

APT – should explain common variation in re-turns.

• could be correlated with consumption growth – may represent consumption states investors care

about in the ICAPM or consumption-based mod-els.

2. Or, does it reflect irrational deviations of price fromfundamental value?

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• need to tie to psychological evidence, model of in-vestor sentiment.

• need to show that these irrational investors matter

and can influence prices.

• need to show how arbitrage fails to eliminate theseerrors.

3. Or, is it due to chance, the result of data-mining orsample-specific conditions (e.g., spurious predictabil-

ity)?• testing out of sample is the key—use new data.

lecture5_35151_2013 by tobias moskowitz empirical asset pricing.

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