1

Extrapolating Expectations: An Explanation for Excess

Volatility, Overreaction and Limited Information Albany-MIT System Dynamics Colloquium

Mila Getmansky

Jannette Papastaikoudi

April 5, 2002

2

Efficient Capital Markets

• The efficient market hypothesis (EMH) has been one of the cornerstones of modern financial theory

• Price is a martingale, conditional on all available information

• Price changes are unforecastable if properly anticipated; i.e. prices fully incorporate the expectations and the information of all market participants

ttt PIPE 1

3

Yet Some Facts Speak Against EMH

• Excess volatility exhibited in financial markets, i.e. the variation of stock returns cannot be explained by the variation in fundamentals (earnings/dividends)

• Excess volatility is equivalent to predictability in stock price

• One form of return predictability is momentum

• Momentum in general refers to the tendency of stocks that had positive (negative) abnormal returns to continue to outperform (underperform). This implies a positive autocorrelation in returns

4

And What About Information Transmission?

• Financial analysts are information intermediaries in markets, influence informational efficiency

• Speed which prices reflect public information increases in analyst coverage

• Yet, evidence shows, analysts reports are systematically biased.

Why?

• Optimistic reports generate investment banking

• Biasing upwards allows for increased management access

• Inexperienced analysts overreact to good/bad news

5

Put Two And Two Together

• Combine all three research topics

• Explain excess market volatility by means of momentum and incomplete information

• Recognize behavior of market participants and its effects on investors wealth

• Effect of excessive price movements with respect to fundamentals can be caused either by “irrational” trend chasing behavior of investors, or by distorting the available information used to form fundamental prices

6

Related Literature

• Excess volatility:

– Shiller 1981

– Campbell & Shiller 1988

• Momemtun:

– Jegadeesh & Titman 1993, 2001

– Daniel, Hirshleifer & Subrahmanyam 1998

• Analyst coverage:

– De Bondt & Thaler 1990

– Easterwood &Nutt 1999

– Hong, Lim & Stein 2000

– Lim 2001

7

Goal

• Formulate a model of financial market volatility that is grounded in the system dynamics approach to modeling decision making

• Explain excess volatility and price oscillations (excess volatility = volatility of return – volatility in the trend in earnings)

8

Assumptions

• Two types of assets: risky and riskless

• Market making mechanism is built into the price formation process

• Two types of investors: value and momentum

• Inexperienced analysts

9

Pricing

Price

Initial Price

DemandSupplyBalance

<TotalDesired Buy

Rate>

<TotalDesired Sell

Rate>

ExpectedPriceChange in

expectedprice

Time to Adjustexpected price

Demand Supply table

Effect ofdemand supply

balance onprice

PerceivedDemand Supply

Balance

Time toperceive

demand supplybalance

Change indemand supply

balance

Maximum DemandSupply Balance

10

HistoricalEarningsChange in Historic

Earnings

Earnings

Duration Over Which toCalculate Earnings Trend

Trend in EarningsPerceivedEarnings

Time to PerceiveEarnings

ExpectedValue Change in Value

Cost of Equity

Indicatedfundamental value

Time toperceive

value

Table for DesiredEquity Weight F

DesiredEquity

Weight F

Change inPerceived Earnings

Price/Value

Cost of Equity LessExpected Growth

Effect of earningsgrowth on discount rate

Table for the effect ofearnings growth on

discount rate

Riskless RateRisk Premium

<Price>

Earnings Forecast

EarningsForecastHorizon

Average RiskPremium

Initial Earnings

Effective discountrate

<Volatility ofReturn>

Average SD ofReturn

Volatility Switch

Switch for PinkNoise

<Noise inEarnings>

Switch for Step

11

Momentum Investor Decision

HistoricalPriceChange in

HistoricalPrice

<Price>

PerceivedPriceChange in

PerceivedPriceTime to

perceiveprice

Duration overwhich to

calculate pricetrend

Trend in Price

DesiredEquity

Weight M

Table for DesiredEquity Weight M

<Initial Price>Price Forecast

Horizon

Forecast Price

<Time to perceiveprice>

Forecast Price Relativeto Current Price

12

Good news Bad news

Fundamental price

+-

Fundamentaldemand

Momentumdemand

+

Clearing Price+ +

Upward Trend inPrice

+

R1Momentum

Extrapolation

Downward Trendin Price

-

Absolute Changein Price

++

Volatility +

Risk Premium

+

-

B1Fundamental

Strategy

-

Unexp. AnalystForecast+

-

++

+

13

Change in Investors Type Fraction

Equal fraction: Investors Type Fraction = 0.5Fundamental dominates: Investors Type Fraction = 0.8Momentum dominates: Investors Type Fraction = 0.2

Price

400

200

0

0 180 360 540 720 900 1080Time (Day)

Price : Equal Fraction $/sharePrice : Momentum Dominates $/sharePrice : Eq $/share

Price

200

100

0

0 180 360 540 720 900 1080Time (Day)

Price : Fundamental Dominates $/sharePrice : Eq $/share

14

Change in Investors Type Fraction

Equal fraction: Investors Type Fraction = 0.5Fundamental dominates: Investors Type Fraction = 0.8Momentum dominates: Investors Type Fraction = 0.2

Excess Volatility

0.2

0.0995

-0.001

0 180 360 540 720 900 1080Time (Day)

Excess Volatility : Fundamental Dominates 1/DayExcess Volatility : Eq 1/Day

Excess Volatility

0.4

0.199

-0.002

0 180 360 540 720 900 1080Time (Day)

Excess Volatility : Momentum Dominates 1/DayExcess Volatility : Equal Fraction 1/DayExcess Volatility : Eq 1/Day

15

Momentum Investors Lose on Average

Fundamental Dominates: Investors Type Fraction = 0.8Momentum Dominates: Investors Type Fraction = 0.2

Value_Price

400

200

0

0 180 360 540 720 900 1080Time (Day)

Expected Value : Momentum Dominates $/sharePrice : Momentum Dominates $/share

Value_Price

400

200

0

0 180 360 540 720 900 1080Time (Day)

Expected Value : Fundamental Dominates $/sharePrice : Fundamental Dominates $/share

16

Momentum Listening to Inexp. Analysts Reduces Exc. Vol.

Value_Price

400

200

0

0 180 360 540 720 900 1080Time (Day)

Expected Value : Momentum Listens to UA $/sharePrice : Momentum Listens to UA $/share

Price

400

200

0

0 180 360 540 720 900 1080Time (Day)

Price : Momentum Listens to UA $/sharePrice : Momentum Dominates $/sharePrice : Eq $/share

Investors Type Fraction = 0.2Momentum Dominates: Momentum Weight = 1Momentum Listens to UA: Momentum Weight = 0.5,

UA Weight = 0.5

17

Reducing Excess VolatilityExcess Volatility

0.4

0.199

-0.002

0 180 360 540 720 900 1080Time (Day)

Excess Volatility : Momentum Listens to UA 1/DayExcess Volatility : Momentum Dominates 1/Day

Investors Type Fraction = 0.2Momentum Dominates: Momentum Weight = 1Momentum Listens to UA: Momentum Weight = 0.5,

UA Weight = 0.5

18

Fundamental Listening to Inexp. Analysts Increases Excess Vol.

Value_Price

400

200

0

0 180 360 540 720 900 1080Time (Day)

Expected Value : Fundamental Listen to UA $/sharePrice : Fundamental Listen to UA $/share

19

Increasing Excess VolatilityExcess Volatility

0.06

0.029

-0.002

0 180 360 540 720 900 1080Time (Day)

Excess Volatility : Fundamental Listen to UA 1/Day

20

Conclusions

• Excess volatility cannot be explained by EMH

• Excess volatility is primarily due to speculative investors who chase market prices

• Decision rules and bounded rationality of investors lead to the overall oscillations in prices and excess volatility

21

Conclusions

• Momentum investors are not driven out even if most of the traders are fundamental investors (80%)

• Excess volatility is higher when initially there are more momentum traders than fundamental ones

• Excess volatility is increased when fundamental investors listen to inexp. analysts

• Excess volatility is decreased when momentum investors listen to inexp. analysts