EC371 Economic Analysis of Asset Prices
Topic #2: Predictability of Asset Prices & Market Efficiency
R. E. Bailey
Department of Economics
University of Essex
Outline
Contents
1
2
Using the Past to Predict the Future
1
1.1
Martingales and Random Walks . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Asset market efficiency
3
2.1
Methodology for assessing efficiency . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.2
Beating the market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
3
Patterns of Information
6
4
Asset Market Anomalies
6
5
Event Studies
9
Reading: Economics of Financial Markets, chapter 3
1
1.1
Using the Past to Predict the Future
Martingales and Random Walks
Unpredictability: martingales
• Objective: make precise the idea that asset prices fluctuations are unpredictable.
• Why may asset prices be unpredictable?
– Suppose not, i.e. asset prices are predictable.
– Investors will seek to profit from the predictions.
– How? Buy ‘cheap’, sell ‘dear’ assets.
– Collectively their actions drive expected profits to zero.
Note carefully: do not confuse this process with arbitrage. In EC371, ‘arbitrage’ refers
to riskless strategies. The process considered here is inherently risky, as it is based on
expected profits – expectations that may not be realised.
1
– Hence, price fluctuations become unpredictable.
• ‘Martingale hypothesis’ formalizes this process as
E[pt+1 | Ωt ] = pt
where Ωt = set of available information
(Always assume that Ωt includes pt , pt−1 , pt−2 , . . . )
• Rewrite as: rt+1 = µ + εt+1
where
E[εt+1 | Ωt ] = 0 , and µ is a constant
• Note: in the first form, µ = 0.
Most assets are assumed to have a positive return, on average. Hence, replace the martingale with:
E[pt+1 | Ωt ] = (1 + µ)pt
(1)
where µ is a constant. (In probability theory, if µ > 0, (1) is known as a submartingale. Typically it
is assumed that µ > 0.
Rearranging equation (1) gives
µ=
E[pt+1 | Ωt ] − pt
pt
(2)
so that µ can be interpreted as the expected rate of return from holding the asset, conditional upon
information set Ωt . In expression (2) it is assumed that the asset’s payoff at date t + 1 is equal to
pt+1 , that is, any dividends or coupons are absorbed in the price.
Martingales and Random Walks
• Martingale hypothesis is just a theory
– does not have to be ‘true’.
• In empirical tests, usually also assume (random walk):
– rates of return independent over time
– rates of return identically distributed.
Note carefully: for the purposes of EC371, you may use ‘martingale’ and ‘random walk
hypothesis’ to mean the same thing. Strictly, however, the random walk hypothesis is more restrictive because it requires additional assumptions (independently and identically distributed
rates of return). The martingale hypothesis is more general but is more difficult to test.
• Prediction:
cov(rt+1 , f (xt )) = 0 for any available info., xt
=⇒
cov(rt , rt−1 ) = 0 because rt−1 is available info.
1.2
Evidence
What’s the evidence?
• Estimated covariances are often non-zero:
2
– day-to-day negative correlation
– month-to-month positive correlation
– long term (months or years) “mean reversion”
Note carefully: these results are little more than commonly observed tendencies – contradictory evidence is often found.
• For individual assets, evidence is more supportive of r.w. than for portfolios of assets (stock
indexes).
• Are patterns in asset prices (‘technical analysis’) evidence of predictability? Not necessarily.
• Data mining often finds patterns that vanish out-of-sample.
• Beware of small sample sizes ⇒ unreliable statistical tests.
2
Asset market efficiency
Informational efficiency
• “A capital market is said to be efficient if it fully and correctly reflects all relevant information
in determining security prices.” (New Palgrave, v. 1, p. 739)
• What is ‘all relevant information’?
• Efficient Market Hypothesis: suggests that information should be ‘fundamental’.
Who says what is to be ‘fundamental’?
Note carefully: given that ‘fundamental’ is inherently ambiguous, it should not be surprising
that the EMH is controversial. Different researchers could reach genuinely different conclusions according to which information is treated as ‘fundamental’. Hence it is misleading to
claim that the EMH is ‘wrong’ – misleading simply because the EMH is incomplete.
• What does “fully and correctly reflects” mean?
• Implication: a model is always required.
Why? To provide the benchmark criteria for ‘efficiency’
• Which model?
Any model is only as good as the arguments in its favour
Here’s how Fama expresses the importance of a model in studying market efficiency:
“The theory [of asset market efficiency] only has empirical content . . . within the context of . . .
a specific model of market equilibrium when prices ‘fully reflect’ available information.” (Fama,
1970)
“. . . market efficiency per se is not testable. It must be tested jointly with some model of market
equilibrium, an asset pricing model.” (Fama, 1991)
3
Model of
asset prices
Set of
information
Q
Q
Q
Q
Q
s
Q
+
Criteria for Efficiency
?
Hypotheses
?
Evidence
?
Statistical test
Q
Q
Q
Q
+
Q
s
Q
Reject hypotheses
⇒ market inefficiency
Do not reject hypotheses
⇒ market efficiency
Figure 1: A Method for Appraising Asset Market Efficiency
Appraisals of market efficiency involve examining whether evidence about asset prices
is compatible with criteria for efficiency. A model of asset prices, together with an
assumed information set, generates the criteria. The criteria, in turn, provide testable
hypotheses that, when confronted with evidence, enable inferences to be drawn.
4
2.1
Methodology for assessing efficiency
How to appraise informational efficiency
• Start with a model, including available information set, Ωt .
• Derive model’s predictions (logical deduction)
⇒ criteria for efficiency
• Obtain evidence: test the predictions
• Possible outcomes:
– Evidence rejects model: inefficiency
– Evidence does not reject model: efficiency
• Are asset markets efficient?
– depends on the model
• Every inference about market efficiency is conditional on the assumed model.
What determines the model? – a priori ideas about what constitutes efficiency.
Example: testing market efficiency
• Model: random walk hypothesis
Information set: all past rates of return.
• Prediction: cov[rt , rt−1 ] = 0
• Collect data (e.g. sample of stock price returns 1990–2011).
• Estimate sample covariances
• Are the estimates significantly different from zero?
– Yes ⇒ evidence of inefficiency
– No ⇒ evidence of efficiency
• Remember: a different model may result in a different conclusion.
Summary
Tests of efficiency cannot be separated from the models and the information sets on which their
predictions are conditioned. Appearances can deceive: a test of efficiency is not model-free merely
because the model is left implicit. This does not mean that tests of efficiency are impossible or
worthless. It does mean that the conclusions about efficiency must be conditional on the model that
provides the criteria for efficiency — the conclusions can never be incontrovertible.
Hence, the bold question ‘Are financial markets efficient?’ should be treated with scepticism. Don’t
believe unequivocal answers.
5
2.2
Beating the market
Beating the Market
• Another approach to informational efficiency:
“A market is efficient with respect to a particular set of information if it is impossible to make
abnormal profits (other than by chance) by using this set of information to formulate buying
and selling decisions.” (W. F. Sharpe)
• Does this imply that a model is unnecessary? No.
• The model provides benchmark criteria for ‘normal profits’
• Which model? – Could be CAPM or APT, or some other model.
See Economics of Financial Markets chapters 6 and 8 for CAPM and the APT.
3
Patterns of Information
Patterns of Information
• Weak, Semi-strong & Strong Form Efficiency
– Weak Form Efficiency: information set: all current and past prices.
– Semi-Strong Form Efficiency: information set: all publicly available information.
– Strong-Form Efficiency: information set: all information, public or private.
• Grossman-Stiglitz Paradox: Suppose that information is costly to obtain. If prices reflect
information, no-one would incur the costs of collecting it. ⇒ asset prices cannot fully reflect
available information.
Hence: important role for asymmetric information.
4
Asset Market Anomalies
Asset Market Anomalies
• An anomaly violates conventional wisdom
– what is ‘conventional wisdom’?
• Conventional wisdom = prediction of ‘the’ orthodox model
• Some well known anomalies:
– Calendar effects
– Momentum in securities’ prices
– Weather and stock markets
– Sports results and stock price declines
– Small firm effect
6
– High earnings/price ratio effect
– Closed End Mutual Fund Paradox
– IPOs and SEOs
List of common anomalies:
1. Calendar effects:
(a) The January, or ‘turn of the year’, effect. The shares of many small companies (those with
a smaller than average market capitalization) tend to experience above average returns in
January, especially in the first half of the month.
(b) The September effect. It has been calculated that $1 invested in US stocks in 1890 would
have grown to $410 by 1994 if the month of September is excluded (i.e. sell in late
August and buy back in early October). This is about four times the increase if the $1
had been invested for the whole of each year.
(c) Week-of-the-month effect. Shares tend to show above average returns in the first half of
the month.
(d) Monday blues. Rates of return on many shares tend to be negative each Monday.
(e) Hour-of-the-day effect. On Monday mornings shares tend to show below average returns
in the first 45 minutes of trading but higher than average returns during the early trading
period for other days of the week.
2. Momentum in securities’ prices. Begin with the definition of ‘relative returns’: the rate of
return on a security (e.g., a company’s ordinary shares) minus the average rate of return on
comparable securities (e.g., the shares of companies in the same sector). ‘Momentum’ in this
context is the hypothesis that relative returns tend to persist, i.e., securities that outperform
(relatively high returns) tend to continue to outperform (securities that underperform tend to
continue to do so). Notice that the hypothesis is silent about how long the tendency will
continue.
There is substantial evidence for momentum, especially in stock markets – this observation is known as the ‘momentum effect’. ‘Momentum investing’ describes strategies that
seek to profit from exploiting the momentum effect. Notice the strategies (like practically all
investment strategies) are risky: the magnitude of the relative returns may change, ultimately
disappearing all together. For a recent discussion, see Asness, C.S., Frazzini, A., Israel, R. and
Moskowitz, T.J. (2014) “Fact, Fiction and Momentum Investing”, Unpublished but available
at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2435323##
The momentum effect is an anomaly in that many conventional models of securities prices
predict that the relative returns (as defined above) will not tend to persist over time. To the
extent that such models characterise ‘efficiency’, then the securities markets in question are
inefficient.
But some models in finance can account for momentum: (i) behavioural models are consistent with the persistence of investors’ decisions; (ii) momentum may reflect a trade-off
between expected return and risk (persistence may be reversed when it is least expected);
(ii) momentum may reflect a principal-agent relationship between the managers of investment
funds and their clients who hold the funds. Thus the issue for efficiency is, as always, whether
any of these models is to be regarded as expressing ‘informatonal efficiency’.
3. Weather and stock markets. There is evidence that asset prices are positively correlated with
sunny days. The magnitude of the price fluctuations is, however, sufficiently small that even
modest transaction costs tend to outweigh the gains from trading strategies designed to exploit
the effect of weather.
7
4. Sports results and stock price declines. Edmans, A., D. Garciá, & Ø. Norli, (2007) “Sports
Sentiment and Stock Returns” provide evidence that losses in international soccer (football)
matches tend to be followed by falls in stock market prices.
5. Eclipses and stock market performance. Lepori, G. M. “Dark Omens in the Sky: Do Superstitious Beliefs Affect Investment Decisions” (unpublished, Copenhagen Business School,
2009) documents evidence that eclipses (carriers of ‘bad omens’) are associated with declines
in trading volume and have a negative impact on stock market returns, especially during periods of higher than usual uncertainty (i.e. eclipses have a bigger impact when stock markets
happen to be particularly volatile). But the effect tends to be reversed in days following the
eclipse. As eclipses are perfectly predictable and because reactions to them are regarded as
superstitious (irrational), Lepori claims to have found evidence “inconsistent with the Efficient
Market Theory”.
6. The small firm effect, or size effect. Evidence has been produced that small companies earn
higher returns than predicted by models such as the Capital Asset Pricing Model, CAPM.
7. The high earnings/price ratio effect. Companies with a high ratio of earnings to stock price appear to have shares which earn excess returns (again, measured against a common benchmark
such as the CAPM).
8. The Closed-End Mutual Fund Paradox. A closed-end mutual fund is essentially a bundle of
other securities that could themselves be purchased and sold individually. The closed-end
mutual fund paradox stems from the observation that the market value of the funds often
diverges from the current market value of their net assets.
9. Initial Public Offerings (IPOs) and Seasoned Equity Offerings (SEOs). Distinctive patterns of
share price fluctuations have been documented following IPOs, when companies issue publicly traded equity for the first time. Initial returns on the shares, in the weeks immediately
following an IPO, tend to be high (though the size of the short-term gain is thought to vary
cyclicly across time). Over time-spans of several years, the shares of IPOs are observed, on
average, to underperform relative to conventional market benchmarks. The price patterns for
SEOs — shares issued to raise additional funds for an existing publicly traded company — are
not dissimilar though perhaps less pronounced.
Anomalies and market efficiency
• Characteristics of anomalies:
1. Is the phenomenon genuine or just a one-off fluke?
A “one-off fluke” is something that occurred but seems unlikely to be repeated. It
could be the result of an environmental incident (e.g., an earthquake) or a political event
(e.g., election outcome). Perhaps the phenomenon has found no explanation – is “random”.
2. Is there a model to explain the phenomenon?
The reason for requiring an explanation is the phenomenon should be comprehensible,
i.e., not regarded as beyond understanding. Almost invariably, some explanation (model)
will be proposed. The issue is whether the most generally acceptable model of the
anomaly is interpreted as representing ‘efficiency’. There is, of course, scope for disagreement on this point.
8
3. Is the phenomenon substantive or just a curiosity?
In this context a ‘curiosity’ could just be a trivial discrepancy due to measurement error, or rounding error in calculation. Or perhaps it is a consequence of an identifiable
difference in definition of similar things.
• If yes is the answer to the three questions, then ‘conventional wisdom’ is undermined.
Why? Most importantly because the explanation of the anomaly diverges from what is considered to represent ‘conventional wisdom’.
• Does the ‘conventional wisdom’ reflect criteria for efficiency?
– Yes ⇒ anomalies are evidence of inefficiency.
– No ⇒ anomalies are silent about inefficiency.
5
Event Studies
Event Studies
• Event: a well defined incident about which predictions can be made, e.g. a take-over bid.
• Other examples: stock splits; sinking of the Titanic; Challenger crash.
• Event ⇒ observations ⇒ test predictions.
• Efficiency criteria =⇒ predictions.
• Evidence against predictions ⇒ inefficiency.
• “Event studies are the cleanest evidence we have on efficiency (the least encumbered by the
joint-hypothesis problem). With few exceptions, the evidence is supportive.” (Fama, 1991).
– Event studies ⇒ clear, unambiguous inferences applicable to a broad class of models.
– But sample sizes tend to be small.
Stock splits
A ‘stock split’ involves redefining of the units in which a company’s stock is measured — for
example, each existing share becomes two new shares in a two-for-one split. Most models of asset
prices predict that stock splits should have no effect on the company’s total market value. This
implication follows simply from the recognition that a stock split does not, in itself, change any real
asset of the company: it is merely a bookkeeping exercise (though one which is made for a purpose,
typically that it enables the equity of the company to be traded in smaller units).
Suppose that when a stock split occurs, the market value of the company is observed to increase.
(Such observations are, apparently, quite common.) Is this evidence of market inefficiency? The
answer depends partly on how carefully the test has been made. For it could be that the event (the
stock split) and the observations (higher share prices) are both consequences of a third influence, such
as improved profitability of the company. Of course, the tests can and should be designed to control
for the simultaneous occurrence of all relevant factors. Even so, the omission of potentially relevant
explanatory variables should be a warning against making careless and extravagant inferences from
event studies.
Crash of the Challenger space shuttle
9
The NASA Challenger space shuttle crashed, shortly after lift-off, on 28 January 1986. At
the time of the crash it was not known which, if any, of the several companies subcontracted to
manufacture the shuttle was primarily responsible, though it was immediately inferred that the crash
was the result of a technical fault.
Stock market prices responded to news of the disaster within minutes of its occurrence, all
of the major companies contributing to the shuttle experiencing falls in their share prices on the
NYSE. Interestingly, the share price of Morton Thiokol, eventually deemed culpable for the defective
component that resulted in the crash, fell the most (even to the extent that the exchange authorities
halted trading in its shares for a short while). While concerns had been expressed among engineers
at Morton Thiokol and NASA for the safety of the relevant component, that its failure was the cause
of the crash was confirmed only several months later in June 1986.
In their study of the implications of the crash for stock market prices, M. T. Maloney and J. H.
Mulherin find “broad support for market efficiency. Within an hour, the market seems to have placed
the blame for the crash on Morton Thoikol, the party ultimately judged by authorities to have been at
fault” (p. 469 in “The complexity of price discovery in an efficient market: the stock market reaction
to the Challenger crash” Journal of Corporate Finance, vol. 9, 2003, pp. 453–479).
Summary
Summary
• Random walk models predict that asset price changes are are unpredictable.
• Empirical evidence suggests that asset price changes may be predictable.
• Asset market efficiency often relies on random walk models.
• Appraisals of efficiency rely on a model of prices and on the information set.
• Anomalies highlight evidence contrary to conventional wisdom.
• Event studies provide a flexible way of testing predictions about efficiency.
10