market efficiency: finance week 09

IPCOR421 FinanceAlex Kane 1

CLASS NOTES

WEEK IX

MARKET EFFICIENCY

Reading Assignment: BMA 13


How we think of time-series processes• The value of any RV (random variable) in a time series,

here price of a security, P(t), can be represented by: P(t+1) = E(P) + e(t+1),

where E(P) is the expectation at time t for the price at time t+1, and e(t+1) is a (zero-mean) surprise

• This useful decomposition is just a tautology -- it is true by definition of expectation, E(P), and tells us nothing about the process of prices

• In analyzing time series we ask: What do we know about E(P) and e(t+1)?


Two alternative time series• Consider two alternative time series of daily prices

1. P(t+1) = P* + e(t+1),where E(P)=P* is a known value that doesn’t change from day to day

2. P(t+1) = P(t) + e(t+1). Here, E(P)=P(t) is changing daily. The expectation for the next-day price is today’s price (this is called a random walk)


The two specifications tell vastly different stories

• With the first specification, no matter what the price today, we expect it to revert to P* tomorrow

• This means that if P(t)>>P*, we can say P(t) is abnormally high. Similarly if P(t)<<P*, it is abnormally low

• With the second specification, E[P(t+1)]=P(t), Declaring today’s price is “abnormal” would be insincere, since we expect it to stay where it is


More on P(t+1)=P*+e(t+1)• We call such a series “stationary” because its location

stays the same over time.• We say the price is “mean reverting” because it goes

back to the mean. Here we expect it to revert to the mean immediately (in one day)

• The series: E[P(t+1)] = P* + 0.5[P*–P(t)], is also mean reverting (stationary). Each day, yesterday’s surprise is expected to be cut in half. No matter how small the number in place of 0.5 is, sooner or later the price will revert to P*. Hence, still stationary


More on P(t+1)=P(t)+e(t+1)• This series is non-stationary (not mean reverting), as the

location changes each day permanently -- there is no indication the price will revert to any “normal” level

• By permanently we mean that at time t, E[P(t+h)]=P(t), no matter how far in the future (h) we look

• No matter how high or low the level P(t) has drifted to, we expect it to stay at that level

• Clearly, the notion of “high” or “low” prices is meaningless. If we were serious about such adjectives, we would expect the price to get back to what we think is “normal”


Which rule would we like prices to follow?• A stationary price is more pleasing. However slow

the mean reversion may be, it makes sense to us that, sooner or later, prices will revert to what we consider “reasonable”

• For example, if NASDAQ index drifts to very high levels (5000), its P/E ratio will become “irrational” and we would feel the index “must” come down soon to where P/E is “reasonable”

• The fly in the ointment is that any degree of mean reversion implies predictability


Why predictability trumps stationarity• Suppose prices are “pleasing” in that they are mean

reverting to some extent, and P(t)= NASDAQ is “high”• Investors know that, sooner or later, NASDAQ will drift

back to P*• How can we expect any rational investor to hold on to a

NASDAQ portfolio? Surely investors will sell it the moment they consider the index to be too high

• In such environment, rational investors won’t let the price drift away from “normal,” say a reasonable P/E, even for an instant. Therefore: P(t) = P* always. We must conclude that P* changes daily, and E[P(t+1)]=P(t) always. Conclusion: investor rationality => non-stationarity


Suppose investors are rational• We know already that prices will be non-stationary, that is, no

mean reversion. Hence, changes from P(t) will be unpredictable

• What else?

– Investors will bid on a stock no more than what they believe is the intrinsic value

– To arrive at the intrinsic value, investors will use all available information

• Conclusion

– market price, P(t), will reflect all available information– Any price change must be a surprise, driven by NEW

information


Market (informational) efficiency• We define an efficient market as one where prices

reflect all available information• In this market, prices are always equal to intrinsic

values (derived from all available information)P(t) = PV(future CFs, discounted at appropriate rate)

• Prices must be non-stationary• The expected rate of return on any asset is the

appropriate discount rate for future cash flows• No abnormal profits can be expected, that is,

NPV=0, since expected returns equal the appropriate rate


Do we care about market efficiency?• Most people see market efficiency as an issue of

distributive justice– No investor can expect a greater profit than any other

investor; everyone expects to earn the “appropriate” rate of return (that is, equal rate when adjusted for risk)

• The major reason efficient markets are valuable– Since capital will flow into industries with high expected

returns relative to risk, and out of industries with low risk-adjusted expected returns, then,

– when prices reflect all available information, the capital flows will make for the optimal allocation of capital to new investments


Stock price and capital allocation

• In general, as equity prices in an industry rise, more investment will take place and vice versa

• Hence, when stocks are overpriced, investment in these companies will be too high, so that marginal investments will have negative NPV. When stocks are underpriced, too little investment takes place, positive NPV will be lost

• In sum, inefficient capital markets lead to inefficient allocation of capital to new investments (see example last slides)


Can markets be perfectly efficient?

• Unfortunately, they cannot. This can be proved mathematically

• The reason is that in perfectly efficient markets there is no incentive for anyone to conduct security analysis, since investors are better off choosing a passive investment rather than pay for an active one

• When none conducts security analysis, nothing holds down prices to intrinsic values

• The question is therefore: How near to efficiency are capital asset prices?


How markets come closer to efficiency• The first target of research into profit opportunities would

be “cheap” ways of discovery• Example: regress, P(t+1) = a + b*P(t) +e(t+1). Significant

deviations from a=0, b=1, imply opportunities for abnormal profits

• Next would come more expensive research• Example: conduct macro analysis to predict overall market

movements, resulting in profits from market timing • Once such methods become widely known and used, prices

will move to eliminate these profit opportunities and come closer to informational efficiency


When does this process stop• As analysts exhaust low cost, available to all

methods of analysis, what remains are research methods that require talent (intellectual property) and significant resources

• This aspect suggests there will be outfits (employed talent and resources) with abnormally high returns

• Such outfits will proceed as long as uncovered profit opportunities exceed marginal cost

• Remaining inefficiencies will be hard to uncover as, by design, only few know how to uncover them


Levels of efficiency• The idea that improved efficiency eliminates “cheap” profit

opportunities first, leads to segment the EMH (efficient market hypothesis) to three levels of information that can lead to abnormal profits– The weak form: information about past prices only

(technical analysis)– The semi-strong form: any publicly available info

(fundamental analysis)– The strong form: inside information (illegal in most

markets). However, when issuing new shares, this issue becomes legitimately relevant since management has inside info

• We expect markets to, at least, pass weak form EHM tests


Difference in efficiency across markets• As markets grow and become more transparent (e.g., better

accounting), it becomes easier and more profitable to conduct sophisticated analysis

• Hence, such markets will automatically be closer to efficiency than others

• Example: emerging markets used to be all the rage. However, as they grew, partly because of large capital flows resulting from discovered inefficiencies, and as transparency improved, they lost much of their luster

• Still, large differences in efficiency across markets remain


Discovering inefficiencies• Making profits from discovered inefficient prices requires

taking extra risk• By construction, you must reduce diversification in order to

tilt your portfolio to use mispriced securities• Therefore, you can evaluate an active strategy only if you

assume some model of asset pricing that predicts risk-return relationship

• An extra difficulty is created: any test of efficiency is a joint test: (1) is there inefficiency (2) is the model used to test the hypothesis valid and reliable

• It’s possible that we will reject efficiency because our model isn’t valid


Abnormal returns and CAR

• Joint normality of asset rates of return leads to a linear relationship (see Week 9 slides) ri – rf = alpha + beta*(rM–rf) + e, where rM is the benchmark Pf and rf the risk-free rate

• When the CAPM/APT are valid, alpha = 0

• Accordingly, if we take the difference, date-by-date: ri(t)–rf(t)–beta*[(rM(t)–rf(t)], we should get e(t). The CAR (cumulate abnormal returns) over successive dates: t=1,…,T: e(t), should approach zero (and so should their average = e(t)/T)


CAR and market efficiency

• The average CAR of returns on an asset over a sample period makes for the estimate of alpha

• A significant non zero alpha (average CAR) contradicts the joint hypothesis of CAPM/APT and market efficiency (EMH)

• The test is more powerful the smaller the variance of e(t)

• Therefore, tests with portfolios that diversify most of e(t) and reduce its variance, rather than individual assets with high Var(e), are preferred


Recorded anomalies• A number of anomalies were recorded over the

years. The major ones are:– Size: smaller stocks have positive average CAR– BE/ME: larger ratios (value) stocks have positive CAR

(negative for low-ratio stocks = growth or glamour stocks)

– IPOs (initial public offerings)– Turn of the year returns (returns in early January)– Momentum strategies (use the inadequate speed of

adjustment of stock prices to new information)


Inadequacy of beta as measure of risk• Size and BE/ME help explain rates of return• This is believed to result from inadequate

measurement of risk by beta (the market factor) alone

• This is believed to be an issue of CAPM/APT mis-specification, rather than market inefficiency

• The CAPM/APT specification can be improved by– Add factors (size and BE/ME Pfs)– Improve measurement of betas (econometrics) by

allowing the coefficients to vary over time– Separate betas for cash flows and capital gains


IPOs• For a long time, it was taken for a fact that investment in

IPOs leads to abnormal returns. Hence, IPO returns were considered a significant anomaly

• Part of this anomaly, early gains, is explained by market structure -- practices of investment banking. Recent auction-based IPOs seem to eliminate this phenomenon

• Long term losses on IPOs appear to be explained away by the BE/ME phenomenon of the return deficiency of growth stocks (Newly issued stocks are mostly growth firms)

• In general, it appears that anomalies tend to disappear over time, providing some evidence that “cheap” profit opportunities cannot last


The January effect: A weak-form anomaly!• Records show most of the market annual risk premiums

were achieved in early January• This was more so for small stocks. Hence, a Pf long small

and short large stocks would have earned abnormal returns• Rationale: Investors sell stocks for tax reasons prior to Jan.

1, depressing prices. These stocks rise to normal levels in early Jan. (The tax selling is indeed a good idea! Sell matched losers with winners to wipe out capital gain tax liabilities and obtain the allowed loss offset)

• Still, it appears this phenomenon is fading -- but small number of years (data) makes such inference difficult


Momentum strategies• The general idea is that investors do not adjust

portfolio demand promptly on the heels of new information -- sometime they over-react, other times they are too slow to react

• The most prominent example is earning announcements: investors have consistently under-reacted to surprise announcements and were slow to revise forecasts of earnings

• Portfolios that take advantage of these anomalies have consistently outperformed the market


Behavioral finance• For years, behaviorists (pioneers were the late Tversky,

and Nobel laureates Kahanman and Allais) showed that people confront risky prospects with irrational behavior (prospect theory)

• Discovery of momentum anomalies led behaviorists to declare they emanate from such behavior

• Counter arguments invoke the role of arbitrageurs (APT) in eliminating such easy profit opportunities

• The jury is still out, but the popularity of these ideas is evident by the curriculum of CFA programs that now prominently include behavioral finance


The true story of “irrational exuberance”• Date NASD 12/5/96

Irrational exuberance speech 1300 12/6/96A day later 1288

12/13/96 A week later 1285 12/5/97A year later (r=25.7%) 1634 12/6/99Three years later (irr=39.8%) 3546 3/10/00Highest NAD ever (irr=51.9%) 5049 10/9/02Lowest NASD since (irr= –2.5%) 1114 6/1/07Last Friday (3pm) (irr = 6.4%) 2613

• Soros: “The best gains come at the tail end of a boom”• From the speech to today, IRR still better than T-bills.

Predictions with no date are of little value


Event Studies• Suppose we can date (t) the arrival of a significant

packet of new information, one that we know should affect security prices

• We can calculate CAR from well before the event date (t–h), through t and well after (t+h)

• The chart of an efficient market will show about zero CAR up to t, a one time jump to a new level at t, and zero changes thereafter

• CAR changes prior to t suggest anticipation/leak• Slow response of CAR at t and after suggests under-

reaction• A large change of CAR at t and shortly after, followed

by a later retreat shows over-reaction


Results of three event studies (good news)

Time

CAR

t–h t t+h

Time

Time

efficient

slow reaction

leak

over-reaction


Measuring intrinsic values• The CAPM/APT suggests ways to estimate expected

return• The model doesn’t tell the dollar value of an enterprise;

it only provides one piece of the puzzle• To get intrinsic value we must use a discounted dividend

(or free CF) model• In addition to the required rate we need to estimate

growth rates of current dividends/cash flows• Intrinsic values are very sensitive to g, allowing for

difference of intrinsic values across investors and rapid price changes of stock, the source of high volatility in rates of return and difficulty in assessing efficiency


Summary of the lessons from EMH1. Prices have no memory, only P(t) tells about the future

(history adds nothing)2. Prices indicate intrinsic values3. (from 2), price changes reveal required rates and

suggest value of announced policies4. Prices are unaffected by “veils,” e.g., accounting

methods5. Assets will be priced to reflect information about value

creation only -- not opportunities investors can obtain by trading in financial markets

6. Financial assets (and portfolios) are perfect substitutes, providing the same risk-return tradeoffs (mean/beta)


A challenging example of capital allocation

• A corporation has 2 million shares outstanding, selling at $5/share. Hence, current market value of the firm is $10 million

• The corporation surprisingly identifies a project that will pay $12 million next year (only) for an investment of $8 million now

• Management believes the project risk requires 20%, that is, NPV=$2 mil. Hence, they believe share value is (10+2)/2=$6

• Management has no cash on hand, cannot borrow any more, and must finance the project by floating new shares

• Upon announcement of the project idea and required financing (before flotation), the share price goes up to $x/share

• Will the corporation invest in the new project?


Answer to question• With a price of $x/share, the corporation has to sell 8/x

million shares• Current shareholders will then own a fraction: 2/(2+8/x) =

x/(x+4) of the corporate shares• According to mgt’s assessment, the total value of the

company (when shares sold) will be 10+12/1.2=$20 mil• Equity of current SH will have value of $20x/(x+4) mil• Since current value is $10 mil, they will invest only if

20x/(x+4)>10, that is, x>$4. ($4 is the break-even price)• At $4 they must sell 2 mil shares. At higher prices, they

will have to sell less shares and retain more value


What’s in it for new investors?• A higher share price means lower expected return• At $4/share, 2 million shares must be sold (N=4 mil)

and each share buys value of4 = [10+12/(1+r)]/(2+2), implying: r=100%

• At $6 (the value management believes is right), 8/6 mil shares sold: 6=[10+12/(1+r)]/(8/6+2), r=20%

• Conclusion, the higher the expected return investors assign to new projects, the higher they will bid for share prices. When they bid higher prices, corporations will invest more (at less than $4 this corp will invest zero)

market efficiency: finance week 09

Documents

alternative time series

time

higher

alexkane

price

invest

expectation