Efficient market hypothesis

Efficient Market Hypothesis

• A model predicts with great confidence that a stock currently at Rs.90 will rise in another 4 days to Rs.100

• What would investors with access to the model do today ?• There would be a flurry of buy orders to cash in on this prospective• No one holding the stock would be willing to sell• So price would start to go up

• And reach the target price of Rs.100 much earlier• So the price will immediately reflects the good news implicit in the

model • Forecast about favourable future performance leads instead to

favourable current performances • Why ?• Market participants try to cash in on the good news – Price Jump

• Information – stock under priced – investors flock to buy in the stock – take it to the fair level

• Only ordinary rates of return can be expected• If price is bid immediately to a fair level, what does it mean ?• All available information has been factored in• And any increase/decrease in price is only in response to new

information

Random Walk

• What does this mean ?• New information by its very definition is unpredictable • If it was predictable it would have been a part of today’s information• Thus stock prices change in response to new information, so they

move unpredictably • Random Walk • But if it was as simple as that, why are there so many analysts in the

market looking for stocks which are under priced, so that they can sell them at a profit

• This means that markets are not following random walk• Which means that markets are not efficient

Caveat in Random walk

• You see a pregnant women, you don’t know the Gender of the to be born child. It is random walk to you.

• But for the doctor, who is treating the women, the Gender of the baby to be delivered can be known for certainty. Hence it is not random walk to the doctor.

EMH

• Fama introduced various versions of the EMH• But Lets Digress for a moment and understand what Technical

Analysis and Fundamental Analysis is?

Technical Analysis

• Technical Analysts search for recurrent and predictable patterns in stock prices , so that an investor can ride that pattern and make a profit out of it

• Technical Analysts are also called chartists• Why ? • They study charts of past stock prices hoping to find patterns they

can exploit to make a profit

Fundamental Analysis

• Uses earnings and dividend prospects of firms, expectations of future interest rates and risk evaluation of firm to determine proper stock prices

• Ultimately it represents an attempt to determine the present discounted value of all payments a stockholder will receive from each share of stock

• If that price > market price the fundamental analyst will recommend purchasing of the stock

Fundamental Analysis Contd..

• Fundamental Analysis is usually started with the study of past earnings and an examination of company balance sheets. This is supplemented by further detailed economic analysis, an evaluation of the firm’s management, the firm’s standing within industry and the prospects of the industry as a whole

Fundamental Analysis

• Discovery of good firms does no good to an investor if the rest of the market also knows those firms are good

• No abnormal returns

• The trick is to find undervalued stocks before the market does

• Poor performance firms can be great bargains if they are not as bad as the market thinks they are

Versions of Efficient Market Hypothesis (EMH)

• Weak form hypothesis• Semi strong form hypothesis• Strong form hypothesis

Weak form hypothesis

• Stock prices already reflect all information that can be derived by examining market trading data

• History of past prices• Trading Volume • What does this mean ? • Technical Analysis is useless

Weak form hypothesis

• Past stock price data is publicly available and virtually cost less to obtain

• All the information generated by technical analysis has already been incorporated into the price

• So a signal has lost its value

Semi strong form hypothesis

• All publicly available information is reflected in the stock price • So technical analysis is useless• And so is fundamental analysis • Every body has access to publicly available information • And they have already traded on it

• So the information has already been incorporated into the price of the security

• There are many well informed and well financed firms conducting such research and in face of such competition it will be difficult to uncover data not also available to other analysts.

• But this does not happen all the time

Strong Form Hypothesis

• Stock prices reflects all information relevant to the firm even including information available to the company insiders

• Public and private information• Tests

Tests for weak form of efficiency

• Auto Correlation test• To check whether past price is influencing present price

• Pt = Pt-1 + ut

• What does this mean ? • All information has not been incorporated into yesterday’s price

• IS TODAYS price dependent on Yesterday’s Price?

• Price changes to be independent( Unpredictable or Random Walk) , Value of ‘r’ should be close to zero.

Prices Change (Pt-Pt-1) Lag1 Lag2 Lag3

650

665 15

665 0 15

685 20 0 15

685 0 20 0 15

705 20 0 20 0

708.5 3.5 20 0 20

707 -1.5 3.5 20 0

709.5 2.5 -1.5 3.5 20

707 -2.5 2.5 -1.5 3.5

706.5 -0.5 -2.5 2.5 -1.5

718.25 11.75 -0.5 -2.5 2.5

715 -3.25 11.75 -0.5 -2.5

710 -5 -3.25 11.75 -0.5

705 -5 -5 -3.25 11.75

698 -7 -5 -5 -3.25

691 -7 -7 -5 -5

705 14 -7 -7 -5

706.25 1.25 14 -7 -7

709 2.75 1.25 14 -7

715 6 2.75 1.25 14

- 6 2.75 1.25

Correlation Coeeficient -0.06047728 0.035792233 0.03577138

Runs Test

• What is a run ? • An uninterrupted sequence of same price changes.

• (++,_ _,00) would be three runs.• It is a test of randomness of share prices.

• a lower than expected number of runs indicates market’s overreaction to information, subsequently reversed,

• while higher number of runs reflect a lagged response to information. Either situation would suggest an opportunity to make excess returns.

Runs Test

1-Apr 881.52-Apr 856.5 -253-Apr 859.75 3.254-Apr 918.5 58.755-Apr 1010.25 91.758-Apr 1072.25 629-Apr 1074.5 2.25

10-Apr 1123.5 4911-Apr 1203.5 8012-Apr 1256.25 52.7515-Apr 1341.5 85.2516-Apr 1469.75 128.2517-Apr 1450.25 -19.518-Apr 1306.5 -143.7519-Apr 1258 -48.522-Apr 1332.75 74.7523-Apr 1315.75 -1724-Apr 1351 35.2525-Apr 1407.5 56.526-Apr 1547.75 140.2529-Apr 1521 -26.7530-Apr 1484.25 -36.75

Runs Test

• Runs Test

• N1 = number of + symbols i.e. every time the price increases

• N2 = number of - symbols i.e. every time the price decreases

• N = N1 + N2 = total number of observations

• Mean = (2 N1 N2 / N) + 1

• Variance (2 ) = 2 N1 N2 (2 N1 N2 - N)/ N2( N -1)

Runs Test

• Null hypothesis is that prices are random (i.e. unpredictable) • Prob [ Mean - 1.96 ≤ R ≤ Mean + 1.96 ] = .95• Lets take an example

• R = 3 , N1 = 19, N2 = 21

• Mean = (2 N1 N2 / N) + 1 = 10.975

2 = 2 N1 N2 (2 N1 N2 - N)/ N2( N -1) = 9.636

= 3.1134

Runs Test

• Mean - 1.96 = 10.975 – 1.96 ( 3.1134) = 4.8728 • Mean + 1.96 = 10.975 + 1.96( 3.1134) = 17.0722• R=3 does not lie between this interval• So the null hypothesis is rejected • So prices are correlated or dependent

Tests for Semi Strong Form

Steps in Event Studies

1. Collect a sample of stocks that had a surprise announcement ( Event)2. What causes a prices to change is an announcement that has a surprise.

– Positive surprises has +ve price changes– Negative surprises has –ve price changes– Stock splits, bonus, Earnings announcements, mergers etc.,

3. Determine the precise day of the announcement and designate this day as Zero.

4. Define the period to be studied( Event Period)– Usually -30 to + 30 days.

5. For each of the firms in the sample, compute the return on each of the days being studied

6. Compute the abnormal returns for each day in the event period.7. Compute for each day in the event period the average abnormal returns for

all the firms in the sample.8. Often the individual day’s abnormal return is added together to compute the

cumulative abnormal return from the beginning of the period.

Example

A Ltd has announced a stock split. A fund manager in order to test the consistency of the semi strong form of market efficiency, calculated the single index model taking into account the returns of A Ltd and the market index for a period of one year on weekly basis up to three weeks before the stock split decision was announced

Ri = 1.33 + 1.1 Rm

Example

Weeks Actual return Market Return-3 14.75 12.15-2 14.4 11.95-1 14.82 12.20 15.01 12.351 14.92 12.32 14.68 12.23 14.38 11.95

Example

• Ri = 1.33 + 1.1 Rm

• We need find out the abnormal return

• ei = Ri – (αi + βi Rm)

Example

Weeks Actual Return(AR) Market Return Expected Ret.(ER) Abnormal Ret.(%)-3 14.75 12.15 14.70 0.05-2 14.4 11.95 14.48 -0.07-1 14.82 12.2 14.75 0.070 15.01 12.35 14.92 0.091 14.92 12.3 14.86 0.062 14.68 12.2 14.75 -0.073 14.38 11.95 14.48 -0.09

Abnormal Return 0.04

Ri = 1.33 + 1.1 Rm AR-ER

Example

• Very close to zero so market is semi strong form efficient • But what is the problem with this example ?

Event Study

• Examines the excess returns around a specific information event • Dividend announcement, earnings announcement , stock split • Steps

Event Study

• Step 1 : Identify the event• Pinpoint the announcement date• Markets react to the announcement of an event rather than the

event itself

Announcement Date

Event Study

• Step 2: Collect returns data around the announcement date

Announcement Date- n + n

Event Study

• Step 3: Calculate the abnormal return

• Abnormal return = Ri – E(Ri)

Event Study

• Calculate the Average Abnormal return for each company for each trading period

• Calculate the Cumulative Average Abnormal return (CAAR)• CAAR = ( Average Abnormal returns for all companies)• How we do it, we will see in the example

Event Study - Example

• Four companies , A Ltd., B Ltd., C Ltd. and D Ltd have increased their level of cash dividends for the year 2001. A financial analyst at a mutual fund wanted to test the consistency of the semi strong form of market efficiency. He calculated the characteristic lines for a period of six years on weekly basis upto four weeks before the announcement took place

• The four equations are

• rA = 1.70 + 1.05 rM

• rB = 1.53 + 1.08 rM

• rC = 1.92 + 1.02 rM

• rD = 1.42 + 1.09 rM


Period Actual Return Market Return

A B C D

-4 13.47 13.61 13.35 13.6 11

-3 11.9 12.04 11.82 12.03 10

-2 13.5 13.67 13.42 13.71 11.15

-1 12.97 13.12 12.88 13.13 10.88

0 13.43 13.6 13.31 13.59 10.9

1 12.5 12.62 12.41 12.63 10.05

2 13.09 13.25 12.99 13.27 11.05

3 14.51 14.71 14.37 14.76 12.15

4 14.8 14.99 14.65 15.02 12.67


rA = 1.70 + 1.05 rM

Period Stock A Market Return Expected Return Abnormal Return

-4 13.47 11 13.25 0.22

-3 11.9 10 12.20 -0.30

-2 13.5 11.15 13.41 0.09

-1 12.97 10.88 13.12 -0.15

0 13.43 10.9 13.15 0.29

1 12.5 10.05 12.25 0.25

2 13.09 11.05 13.30 -0.21

3 14.51 12.15 14.46 0.05

4 14.8 12.67 15.00 -0.20


rB = 1.53 + 1.08 rM

Period Stock B Market Return Expected Return Abnormal Return

-4 13.61 11 13.41 0.20

-3 12.04 10 12.33 -0.29

-2 13.67 11.15 13.57 0.10

-1 13.12 10.88 13.28 -0.16

0 13.6 10.9 13.30 0.30

1 12.62 10.05 12.38 0.24

2 13.25 11.05 13.46 -0.21

3 14.71 12.15 14.65 0.06

4 14.99 12.67 15.21 -0.22


rC = 1.92 + 1.02rM

Period Stock C Market ReturnExpected

Return Abnormal Return

-4 13.35 11.00 13.14 0.21

-3 11.82 10.00 12.12 -0.30

-2 13.42 11.15 13.29 0.13

-1 12.88 10.88 13.02 -0.14

0 13.31 10.90 13.04 0.27

1 12.41 10.05 12.17 0.24

2 12.99 11.05 13.19 -0.20

3 14.37 12.15 14.31 0.06

4 14.65 12.67 14.84 -0.19


rD = 1.42 + 1.09rM

Period Stock D (1) Market Return

Expected Return (3)

Abnormal Return (1-3)

-4 13.6 11.00 13.41 0.19

-3 12.03 10.00 12.32 -0.29

-2 13.71 11.15 13.57 0.14

-1 13.13 10.88 13.28 -0.15

0 13.59 10.90 13.30 0.29

1 12.63 10.05 12.37 0.26

2 13.27 11.05 13.46 -0.19

3 14.76 12.15 14.66 0.10

4 15.02 12.67 15.23 -0.21


• So we have abnormal returns for every period • We can calculate the average abnormal returns


(.22 +.20+ .21+ .19)/4

Week AAR(%)

-4 0.205

-3 -0.295

-2 0.113

-1 -0.150

0 0.286

1 0.244

2 -0.206

3 0.066

4 -0.208


Week AAR(%) CAR(%)-4 0.205 0.205-3 -0.295 -0.090-2 0.113 0.023-1 -0.150 -0.1270 0.286 0.1591 0.244 0.4042 -0.206 0.1983 0.066 0.2644 -0.208 0.056

CAAR 0.056

-0.400

-0.300

-0.200

-0.100

0.000

0.100

0.200

0.300

0.400

0.500

-4 -3 -2 -1 0 1 2 3 4

AAR

CAR


• Since the value of CAAR is close to zero we conclude that markets are efficient in the semi strong form

Strong form efficiency

• Not easy to test • All investors who own more than a sufficient percentage of

outstanding shares or at sufficiently higher levels of the organization are known as insiders

• Super strong form– Insiders of a company or specialists in stock exchanges– In NYSE it has been shown that specialists consistently make

abnormal profits.

• Near Strong Form– Performance of mutual fund managers.– Mangers on an average failed to deliver abnormal returns

consistently.

Are Markets Efficient?

• Magnitude Issue– Investment manager improving the performance by 0.1% on a

500 crore fund translates into increase investment earnings of 50 Lacs.

– Can we statistically measure his/her contribution? Probably not.• The selection Bias Issue.

– You know the technique/Investment scheme – You either publish it or keep it a secret.

– If you can really make money through the scheme you would like to keep it a secret. You will be publishing it only if you cant make money out of it.

Are Markets Efficient?

– You can test whether you can make abnormal profits based on the investment strategy or technique you know/publicly available. The fact that it is publicly available may make it useless.

– Selection bias- here is the outcomes we are able to observe have been pre-selected in favor of failed attempts.

• The lucky event Issue.– You could be fairly lucky

Research

• Overall we can say that Indian stock markets along with other emerging Asian markets is not weak-form efficient (Worthington

• H. Higgs(2005))

• However there are many studies in the developed markets which show that the developed markets are semi-strong form efficient.

• Academic world argues that Markets in US and other developed markets are usually efficient. They term all the evidence against market efficiency as anomalies.

• Most of the tests are Joint test of efficient market hypothesis and the risk adjustment procedure (CAPM). Usually it is the risk adjustment technique that is questioned rather than the EMH.

Evidence on Market Efficiency

Returns over short Horizon– Thomas and Patnaik(2002) found no serial correlation for nifty index. But for

individual stocks they observed serial correlation at 5 minute interval.– (3 to 12 month holding period) Jegadeesh and Titman(1993) found a momentum

effect in which good or bad recent performance of a particular stock continues over time.

• Returns over Long horizon– Debondt and Thaler(1985)

• Rank order the performance of stocks over a 5 year period and group stocks based on investment performance.

• Loser portfolio defined as 35 stocks with worst performance• Winner portfolio defined as 35 stocks with best performance.• Loser portfolio out-performed the winner portfolio by an average of 25% in

the following 3 year period.• Reversal effect- Losers win and winners fade back suggest overreaction

hypothesis


• Calendar Effects– January Anomaly– Positive abnormal returns in the month of January.

• Tax Effect– Weekday effect

• Weekend effect ( Friday close to Monday open) –ve Returns• Monday Effect (Monday open to Monday close) +ve Returns

– Intraday effect• U pattern in trading.

• Price earnings ratios and returns.– Returns for stock with lower P/E ratios were superior to those with

higher P/E ratios.– Investors overestimate the growth potential and thus overvalue the

growth companies.


• The size effect.– small firms have significantly higher risk-adjusted returns than

larger firms.– Portfolio of small firms outperforms the portfolio of large firms by

4% per month. Beta of small firms is 1.17 as against beta of 0.85 for a portfolio of large firms.

– Even when returns were adjusted for risk using CAPM. A premium of 3.6% existed in the market.

• The small firm in January Effect– Later studies showed that small firm effect virtually occurs in the

month of January and in the first two weeks of January. The size effect is in fact the “small firm in January effect”


– Neglected firm effect• Arbel (1985) show that the small firm effect is because they

are neglected.• Divides the firms into Highly researched, moderately

researched and neglected stocks based on the number of institutions holding the stock.

• The January effect is in fact largest for the neglected firms.

• Book value-Market value (BV/MV)– Significant positive relationship is found to exist between a firms

historical BV/MV and future stock returns.


• Amihud and Mendelson (1986)– Effect of liquidity on stock returns.– Investors will demand a premium in rate of return to invest in

stocks that entail higher trading costs.– Small and less analyzed stocks as a rule are less liquid.– Liquidity effect may partially explain the SIZE effect.

Efficient market hypothesis

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