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5-8 percent (see De Bondt and Thaler (1989)).

Bremer and Sweeney (1988) find that the above results also hold for very

periods. For example, for a â€˜loser portfolioâ€™ comprising stocks where the on

fall has been greater than 10 percent, the subsequent returns are 3.95 percen

days. They use stocks of largefirms only. Therefore they have no problem that t

0.2

a 0.1

a

0

0.0

-0.1

-0.2

Figure 8.3 Cumulative Excess Returns for â€˜Winnerâ€™ and â€˜Loserâ€™ Portfolios. Sourc

and Thaler (1989). Reproduced by permission of the American Economic Association

spread is a large percentage of the price (which could distort the results). Also

problems with â€˜the small firm effectâ€™ (i.e. smaller firms are more â€˜riskyâ€™ and he

a greater than average equilibrium excess return). Hence Bremer and Sweeney

to find evidence of supernormal profits and a violation of the EMH.

One explanation of the above results is that â€˜perceived riskâ€™ and actual risk m

That is the perceived risk of the â€˜loser portfolioâ€™ is judged to be â€˜highâ€™ hence

high excess return in the future, if one is to hold them. Evidence from psycholog

suggests that misperceptions of risk do occur. For example, people rank the

of dying from homicide greater than the risk of death from diabetes but proba

they are wrong.

The above evidence certainly casts doubt on the EMH in that it may be

make supernormal profits because of some predictability in stock prices. Howe

be noted that many of the above anomalies are most prominent among small

January effect and winnerâ€™s curse of De Bondt and Thaler (1985) and discounts

End Funds (Lee et al, 1990). If the â€˜big playersâ€™ (e.g. pension funds) do not trad

firm stocks then it is possible that the markets are too thin and information g

costly, so the EMH doesnâ€™t apply. The EMH may therefore be a better pa

the stocks of large firms. These will be actively traded by the â€˜big players

be expected to have the resources to process quickly all relevant information

access to cash and credit to execute trades so that prices (of such stocks) al

fundamental value. Of course, without independent confirmation this is mere

NOISE TRADERS

8.2

The EMH does not require that all participants in the market are â€˜efficien

informed. There can be a set of irrational or â€˜noiseâ€™ traders in the market w

quote prices equal to fundamental value. All the EMH requires is that there i

â€˜smart moneyâ€™ around who recognise that P will eventually equal fundam

r

Vt. So, if some irrational traders quote Pt < Vt, the smart money will qui

irrational investors are able to survive in the market (De Long et al, 1990).

If investors have finite horizons then they will be concerned about the pri

future time N . However, if they base their expectations of the value of E,P,+N o

+

future dividends from t N onwards, then we are back to the infinite horizo

tion of the rational investor (see Chapter 4). However, if we allow heterogene

in our model then if agents believe the world is not dominated by rationa

the price at t + N will depend in part on what the rational investor feels th

investors view of P t + will be (i.e. Keynesâ€™ beauty contest). This general arg

˜

applies if rational investors know that other rational investors use different

equilibrium asset returns. Here we are rejecting the EMH assumption that a

instantaneously know the true model, or equivalently that learning by market p

about the changing structure of the economy (e.g. â€˜shipbuilding in decline, ch

growâ€™) is instantaneous. In these cases, rational investors may take the view tha

price is a weighted average of the rational valuation (or alternative rational

and effect on price of the irrational traders (e.g. chartists). Hence price does

+

equal fundamental value at t N . The rational traders might be prevented by

from buying or selling until the market price equals what perhaps only they be

fundamental value. Bonus payments to market traders based on profits over a

period (e.g. monthly) might reinforce such behaviour. The challenge is to dev

models that mimic such noise-trader behaviour.

A great deal of the analysis of financial markets relies on the principle of arb

see Shleifer and Summers (1990)). Arbitrageurs or smart money or rational

continually watch the market and quickly eliminate any divergence between a

and fundamental value and hence immediately eliminate any profitable oppo

a security has a perfect substitute then arbitrage is riskless. For example, a (v

+

mutual fund where one unit of the fund consists of â€˜1 alpha 2 betaâ€™ shares sh

the same price that one can purchase this bundle of individual shares in the op

If the mutual fund is â€˜underpricedâ€™ then a rational trader should purchase th

simultaneously sell (or short sell) the securities which constitute the fund, o

market, thus ensuring a riskless profit (i.e. buy â€˜lowâ€™, sell â€˜highâ€™). If the sm

has unlimited funds and recognises and acts on this profit opportunity then

quickly lead to a rise in price of the mutual fund (as demand increases) an

price of the securities on the stock exchange (due to increased sales). Riskle

ensures that relative prices are equalised. However, if there are no close sub

hence if arbitrage is risky then arbitrage may not pin down the absolute pric

stocks (or bonds) as a whole.

The smart money may consider short selling a share that appears to be

relative to fundamentals. They do so in the expectation that they can purch

when the actual price falls to the price dictated by fundamentals. If enough o

money acts on this premise then their actions will ensure that the price does

all start short selling. The risks faced by the smart money are twofold. First

may turn out to be â€˜better than expectedâ€™ and hence the actual price of the shar

further: this we can call fundamentals risk. Second, if arbitrageurs know th

horizon. The smart money may believe that prices will ultimately fall to their fu

value and hence in the long term, profits will be made. However, if arbitra

either to borrow cash or securities (for short sales) to implement their trades

pay per period fees or report their profit position on their â€˜bookâ€™ to their s

frequent intervals (e.g. monthly, quarterly) then an infinite horizon certainly ca

to all or even most trades undertaken by the smart money.

It may be that there are enough arbitrageurs, with sufficient funds in the ag

that even over a finite horizon, risky profitable opportunities are arbitraged away

of the latter argument is weakened, however, if we recognise that any single ar

unlikely to know either the fundamental value of a security, or to realise whe

price changes are due to deviations from the fundamental price. Arbitrageurs

are also likely to disagree among themselves about fundamental value (i.e.

heterogeneous expectations) hence increasing the general uncertainty they perc

profitable opportunities, even in the long term. Hence the smart money ha

in identijjing any mispricing in the market and if funds are limited (i.e. a

perfectly elastic demand for the underpriced securities by arbitrageurs) or h

finite, it is possible that profitable risky arbitrage opportunities can persist in

for some time.

If one recognises that â€˜information costsâ€™ (e.g. man-hours, machines, build

be substantial and that marginal costs rise with the breadth and quantity of tr

this also provides some limit on arbitrage activity in some areas of the m

example, to take an extreme case, if information costs are so high that dea

concentrate solely on bonds or solely on stocks (i.e. complete market segment

differences in expected returns between bonds and stocks (corrected for risk)

arbitraged away.

Noise Traders and Herding

It was explained above why risky arbitrage may be limited and insufficient to k

prices of stocks in line with their fundamental value. We can now discuss wh

might contain a substantial number of noise traders who follow simple â€˜rules

or â€˜trendsâ€™ or waves of investor sentiment (herding behaviour) rather than act o

of fundamentals. In order that noise traders as a group are capable of influenc

prices their demand shifts must broadly move in unison (i.e. be correlated ac

traders).

General information on these issues can be had from psychological experi

Shleifer and Summers (1990) and Shiller (1989) for a summary) which ten

that individuals make systematic (i.e. non-random) mistakes. Subjects are foun

react to new information (news) and they tend to extrapolate past price trends

overconfident, which makes them take on excessive risk.

As the stock market involves groups of traders it is useful to consider some e

on group behaviour (Shiller, 1989). In Sherifâ€˜s (1937) â€˜autokinetic experimentâ€™

in total darkness were asked to predict the movement of a pencil of light. In the e

with individuals there was no consensus about the degree of movement (wh

with a group where all other members of the group are primed to give the s

answers. The individual when alone usually gave correct answers but when

group pressure the â€˜individualâ€™ frequently gave wrong answers. After the ex

was ascertained that the individual usually knew the correct answer but wa

contradict the group. If there is no generally accepted view of what is the

fundamental price of a given stock then investors may face uncertainty rathe

This is likely to make them more susceptible to investor sentiment.

Models of the diffusion of opinions are often rather imprecise. There is ev

ideas can remain dormant for long periods and then be triggered by some seemi

event. The news media obviously play a role here, but research on persuasion

that informal face-to-face communication among family, friends and co-wo

greater importance in the diffusion of views than is the media.

There are mathematical theories of the diffusion of information based on

epidemics. In such models there are â€˜carriersâ€™ who meet â€˜susceptiblesâ€™ and c

carriersâ€™. Carriers die off at a â€˜removal rateâ€™. The epidemic can give rise to

shape pattern if the infection â€˜takes offâ€™. If the infection doesnâ€™t take off (i.e.

either a low infection rate or a low number of susceptibles or a high removal ra

number of new carriers declines monotonically. The difficulty in applying su

to investor sentiment is that one cannot accurately quantify the behavioural de

of the various variables (e.g. the infection rate) in the model, which are like

from case to case.

Shiller (1989) uses the above ideas to suggest that the bull market of the

1960s may have something to do with the speed with which general informa

how to invest in stocks and shares (e.g. investment clubs) spreads among indiv

also notes the growth in institutional demand (e.g. pension funds) for stock

period, which could not be offset by individuals selling their own holdings to

total savings constant. This was because individualsâ€™ holdings of stocks were n

evenly distributed (most being held by wealthy individuals): some people in oc

pension funds simply had no shares to sell.

Herding behaviour or â€˜following the trendâ€™ has frequently been observed in t

market, in the stock market crash of 1987 (see Shiller (1990)) and in the foreign

market (Frankel and Froot, 1986 and Allen and Taylor, 1989b). Summers (198

and Summers, 1990) also shows that a time series for share prices that is

generated from a model in which price deviates from fundamentals in a pers

does produce a time series that mimics actual price behaviour (i.e. close to

walk) so that some kind of persistent noise-trader behaviour is broadly cons

the observed data.

Survival of Noise Traders

If we envisage a market in which there are smart speculators who tend to set p

to fundamental value and noise traders who operate on rules of thumb, then

arises as to how the noise traders can survive in this market. If noise traders

when the price is above the fundamental value, then the smart money should

money should purchase such assets from the noise traders and they will th

profit as the price rises towards the fundamental value. Hence the net effect

noise traders lose money and therefore should disappear from the market leavi

smart money. When this happens prices should then reflect fundamentals.

Of course, if there were an army of noise traders who continually entered

(and continually went bankrupt) it would be possible for prices to diverge f

mental value for some significant time. One might argue that it is hardly likely

traders would enter a market where previous noise traders have gone bankru

numbers. However, entrepreneurs often believe they can succeed where others h

To put the reverse argument, some noise traders will be successful over a fin

and this may encourage others to attempt to imitate them and enter the marke

the fact that the successful noise traders had in fact taken on more risk and jus

to get lucky.

Can it be explained why an existing cohort of noise traders can still make

market which contains smart money? The answer really has to do with the p

herding behaviour. No individual smart money trader can know that all other sm

traders will force the market price towards its fundamental value in the peri

for which he is contemplating holding the stock. Thus any strategy that the so

traders adopt given the presence of noise traders in the market is certainly n

There is always the possibility that the noise traders will push the price even fu

from fundamental value and this may result in a loss for the smart money.

averse smart money may not fully arbitrage away the influence of the noise

there are enough noise traders who follow common fads then noise-trader r

pervasive (systematic). It cannot be diversified away and must therefore earn a

risk premium, in equilibrium. Noise trading is therefore consistent with an ave

which is greater than that given by the pure CAPM. If noise traders hold a lar

assets subject to noise-trader risk they may earn above average returns and sur

market. If there are some variables at time t which influence the â€˜mechanicalâ€™

of noise traders and noise-trader behaviour is persistent then such variables ma

expected returns in the market. This may explain why additional variables, w

to the CAPM, prove to be statistically significant.

Shiller (1989) presents a simple yet compelling argument to suggest tha

non-institutional investors are concerned, the smart money may not dominate

He notes that if the smart money investor accumulates wealth at a rate â€˜

per annum) greater than the ordinary individual investor (e.g. noise trader) th

bequest at age 50, he can expect to accumulate additional terminal wealth of

If n = 5 percent then the smart investor ends up with 2.1 times as much we

ordinary (noise-trader) investor. Thus if the percentage of smart investors in

is â€˜moderateâ€™ then they are unlikely to take over the market completely. Also i

money investor wishes only to preserve the real value of the â€˜family wealthâ€™, t

not accumulate any additional wealth, he will spend it. However, given that i

investors play an important role in the market it must be explained why no

influence institutional decisions on portfolio allocation.

volatile than indicated by the volatility in future dividends and discount ra

Shillerâ€™s variance bounds inequalities might not hold in a world which inc

traders. To see this, note that the stock price is now determined by its fundam

V, = E,(CSâ€˜D,+i) (i.e. the DPV of future dividends) formed by rational trad

influence of the noise traders denoted N,:

For simplicity assume cov(V,, N,) = 0 and hence from (8.1) cov(P,, N,) = v

before the perfect foresight price PT differs from the fundamental value by

forecast error (due entirely to rational traders):

+ qr

P; = v,

From (8.1) and (8.2)

+ qr - Nt

P: = P,

+ var(q,) + var(N,) - 2 cov(P,, N,)

var(P;) = var(P,)

= var(P,) + var(qt) - var(N,)

where it has been assumed cov(P,, qr) = 0 by RE and for simplicity we

q,) = 0. From (8.3) we see that if var(N,) is large enough then we expect the

P: to be less than the variance of P,. Hence, the variance bound, var(P:) - v

may not hold in the presence of noise traders. The intuition behind this resul

Noise traders directly influence the variance of actual prices (via (8.1)) but do n

the variance of future dividends and hence the perfect foresight price. Also

noise trader behaviour Nt is mean reverting at long horizons then price chang

be mean reverting and this is consistent with the empirical evidence on mea

in stock returns.

If noise traders are more active in dealing in shares of small firms than for

this may explain why small firms earn an above average return corrected for

CAPM risk. Again, this is because the noise-trader risk is greater for small-

than for large-firm stocks, and as this risk is systematic it is reflected in the hi

on small-firm stocks.

The impact of noise traders on prices may well be greater when most inves

the advice given in finance text books and passively hold the market portfol

traders move into a particular group of shares based on â€˜hunchâ€™, the holders of

portfolio will do nothing (unless the movement is so great as to require a ch

â€˜market valueâ€™ proportions held in each asset). The actions of the noise traders

countered by a set of genuine arbitrageurs who are active in the market. In th

if all investors hold the market portfolio but one noise trader enters the mark

to purchase shares of a particular firm then its price will be driven to infinity

Arbitrageurs may not only predict fundamentals but may also divert their

anticipating changes in demand by the noise traders. If noise traders are optim

particular securities it will pay arbitrageurs to create more of them (e.g. j

the business. The arbitrageurs (e.g. an investment bank) can then earn a shar

from the â€˜abnormally high pricedâ€™ issues of new oil shares which are current

with noise traders.

Arbitrageurs will also behave like noise traders in that they attempt to pick

noise-trader sentiment is likely to favour: the arbitrageurs do not necessarily co

in demand by noise traders. Just as entrepreneurs invest in casinos to exploi

it pays the smart money to spend considerable resources in gathering info

possible future noise-trader demand shifts (e.g. by studying chartistsâ€™ foreca

arbitrageurs have an incentive to behave like noise traders. For example, if n

are perceived by arbitrageurs to be positive feedback traders then as prices

above fundamental value, arbitrageurs get in on the bandwagon themselves in th

they can sell out â€˜near the topâ€™. They therefore â€˜amplify the fadâ€™. Arbitrageurs

prices in the longer term to return to fundamentals (perhaps aided by arbitrage

in the short term, arbitrageurs will â€˜follow the trendâ€™. This evidence is cons

findings of positive autocorrelation in returns at short horizons (e.g. weeks or

arbitrageurs follow the short-term trend, and negative correlation at longer ho

over two or more years) as some arbitrageurs take a long horizon view and sell

shares. Also if â€˜newsâ€™ triggers off noise-trader demand, then this is consistent

overreacting to â€˜newsâ€™.

So far we have been discussing the implications of the presence of noise trad

general terms. It is now time to examine more formal models of noise-trader

As one might imagine it is by no means easy to introduce noise-trader behav

fully optimising framework since almost by definition noise traders are irratio

misperceive the true state of the world. Noise-trader models therefore contain

arbitrary (non-maximising) assumptions about behaviour. Nevertheless, the o

the interaction between smart money traders (who do maximise a well-define

function) and the (ad-hoc) noise traders is of interest since we can then ascerta

such models confirm the general conjectures made above. Generally speak

shall see, these more formal models do not contradict our â€˜armchair specu

outlined above.

8.2.1 Noise Waders and the Rational Valuation Formula

Shiller (1989) provides a simple piece of analysis in which noise-trader dema

as smart money influence the price of stocks. It follows that the smart mone

to predict the noise-trader demand for stocks, if it is to predict price correctly

attempt to eliminate profitable opportunities. The proportionate demand for sh

smart money is Q1.The demand function for the smart money is based (loos

mean-variance model and is given by:

If ErR,+1 = p then demand by the smart money equals zero. If Q, = 1 then

money holds all the outstanding stock and this requires an expected return E t R t

Hence 0 is a kind of risk premium payment to induce the smart money to hold al

substituting (8.4) in (8.5):

Hence the expected return as perceived by the smart money depends on how th

current and future demand by noise traders: the higher is noise-trader demand

are current prices and the lower is the expected return perceived by the sm

Using (8.6) and the definition

+ + 0). Hence by repeated forward substitution:

where 6 = 1/(1 p

Thus if the smart money is rational and recognises the existence of a deman

traders then the smart money will calculate that the market clearing price is

average of fundamentals (i.e. E,D,+i) and of future noise-trader demand, E

weakness of this 'illustrative model' is that noise-trader demand is completely

However, as we see below, we can still draw some useful insights.

If E,Y,+i and hence aggregate noise-trader demand is random around zer

moving average of E,Y,+i (for all future i ) in (8.8) will have little influence on

will be governed primarily by fundamentals. Price will deviate from fundam

only randomly. On the other hand, if demand by noise traders is expected to b

(i.e. 'large' values of Y , are expected to be followed by further large values)

changes in current noise-trader demand can have a powerful effect on curren

price can deviate substantially from fundamentals over a considerable period

Shiller (1989) uses the above model to illustrate how tests of market effici

on regressions of returns on information variables known at time t (Q,), have

to reject the EMH when it is false. Suppose dividends (and the discount rate) a

for all time periods and hence the EMH (without noise traders) predicts tha

price is constant. Now suppose that the market is actually driven entirely by n

and fads. Let noise trader demand be characterised by

and hence:

S3, etc. Because 0 < 6 < 1, price changes are heavily dominated by uf (rath

past U r - j ) . However as uf is random, price changes in this model, which by c

are dominated by noise traders, are nevertheless largely unforecastable.

Shiller generates a AP,+1 series using (8.8) for various values of the per

Y t (given by the lag length n) and for alternative values of p and 8. He the

the generated data for AP,+1 on the information set consisting only of Pt.

EMH we expect the R-squared of this regression to be zero. For p = 0, 0

n = 20 he finds R2 = 0.015. The low R-squared supports the EMH, but it res

model where price changes are wholly determined by noise traders. In additio

level can deviate substantially from fundamentals even though price changes

forecastable. He also calculates that if the generated data includes a constan

price ratio of 4 percent then the â€˜theoretical R-squaredâ€™ of a regression of the

on the dividend price ratio ( D , / P , ) is only 0.079 even though the noise-tra

is the â€˜true modelâ€™. Hence empirical evidence that returns are only very wea

to information at time t (e.g. Dt/P,) are not necessarily inconsistent with p

determined by noise traders and not by fundamentals.

Overall, Shiller makes an important point about empirical evidence. Th

using real world data is not that stock returns are unpredictable (as sugges

EMH) but that stock returns are not very predictable. However, the latter evide

not inconsistent with possible models in which noise traders play a part.

If the behaviour of Y , is exogenous (i.e. independent of dividends) but is sta

mean reverting then we might expect returns to be predictable. An above av

of Y will eventually be followed by a fall in Y (to its mean long-run level). H

are mean reverting and current returns are predictable from previous periodsâ€™

In addition our noise-trader model can explain the positive association b

dividend price ratio and next periodsâ€™ return on stocks. If dividends vary very

time, a price rise caused by an increase in E Y , + j will produce a fall in the divi

ratio. If Yt is mean reverting then prices will fall in the future, so returns Rt+

Hence one might expect a fall in the dividend price ratio at time t to be foll

fall in returns. Hence ( D / P ) , is positively related to returns Rr+l, as found in

studies.

Shiller also notes that if noise trader demand Y f + j is influenced either by p

(i.e. bandwagon effect) or past dividends then the share price might overreact

dividends compared to that given by the first term in (8.8), that is the fundam

of the price response.

8.2.2 An Optimising Model of Noise-â€™Ikader Behaviour

in the model of De Long et a1 (1990), both smart money and noise traders

expected lifetime utility. Both noise traders and smart money are risk averse

a finite horizon in the model so that arbitrage is risky. The (basic) model is c

so that there is no fundamental risk (i.e. dividends are known with certainty

noise-trader risk. The noise traders create risk for themselves and the smart

generating fads in demand for the risky asset. The smart money forms optima

- N ( P * ,a2)

Pr

If p* = 0, noise traders agree on their forecasts with the smart money (on a

noise traders are on average pessimistic (e.g. in a bear market) then p* < 0, an

price will be below fundamental value. If noise traders are optimistic p* > 0, th

applies. As well as having this long-run view (= p * ) of the divergence of the

from the optimal forecasts, â€˜newsâ€™ also arises so there can be abnormal but

variations in optimism and pessimism (given by a term, p - p * ) . The specific

is ad hoc but does have an intuitive appeal based on introspection and evid

behavioural/group experiments.

In the DeLong et a1 model the fundamental value of the stock is a cons

arbitrarily set at unity. The market consists of two types of asset: a risky a

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