What Causes Persistence of Stock Return Volatility One Possible Explanation with an Artificial Stock

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What Causes Persistence of Stock Return
Volatility? One Possible Explanation with an
Artificial Stock MarketRyuichi
YAMAMOTOBrandeis University
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0. Review What are about Persistence of
Return Volatility?

• A well-known feature
• Identified if ARCH process exists. (Engle (1982))
• Evidence (Pagan(1996)).
• Not investigated much about how the volatility
  clustering is created.

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0. Review What are about an Agent-based
Stock Market?

• Deals with stock market
• A set of interacting heterogeneous agents
• Learning/Adaptation/Evolution

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1. Motivation

• Why would be an Agent-based Stock Market useful?
• the evolution of the agents strategies
• the dynamics of the return series with a relation
  to the interaction of the heterogeneous
  investors.
• What is new?
• How volatility persistence is endogenously
  created.

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How is the volatility persistence explained with
an agent-based stock market?

• (Two Steps)
• Agent-based stock markets, which can and cannot
  produce the volatility clustering, are examined.
  (social and individual learning)
• The relation between the persistence and agents
  expectation is investigated.

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Review What are Individual Learning and
Social Learning?
Figure 1 Individual Learning
Figure 2 Social Learning
Imitative behavior
Privately distributed
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Results

• A social learning economy produces persistence of
  return volatility while an individual learning
  economy does not.
• Expectations cluster in social learning economy
  but not in an individual learning economy.

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Outline

• 0) Preview
• Motivation
• Market structure
• Computer Simulations
• Conclusion

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2. Market Structure (LeBaron et al. (1999))

• 2 tradable assets a stock and a bond.
• The risk-free bond 10.
• The stock pays a dividend
• of shares is 150 of agents in the market.

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How do events in this artificial market
proceed? 1. Information set

• At time t, agents observe the past price and
  dividend, and calculate technical indicators.
• where k5 and 10.
• Form an information set, .

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• The information set, , includes
• 1)
• 2)
• 3)
• 4)
• 5)
• At time t, dividend, , is revealed and paid.

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2. Prediction

• LeBaron (2002)

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• Permitting to range with the allowable
  bounds for and as in LeBaron
  (1999), that is, and ,
• Agents are heterogeneous in terms of their
  expectation.

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3. Strategy making

4. Price determination
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5. Updating wealth

• After revealing the price, wealth, , is
  recorded.
• Wealth, w, for individual i is evolved according
  to

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6. Updating Forecast Strategies

• Step 1-5 are repeated for 25 periods.
• Figure 4 Timing of the market
• The fitness criterion
• Individual and Social Learning

25 50 .. 500

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Figure 1 Individual Learning
Figure 2 Social Learning
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3. Experiments

• Simulations are conducted in each market
  separately and are repeated for 10 times.
• The series of stock price, dividend, and point
  estimates on future prices made by agents,
  , are recorded for the last 5,000
  periods.
• Two steps

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Step 1 Volatility Clustering in Individual and
Social Learning Economies

• Following LeBaron et al. (1999), the estimated
  residual series are analyzed.

Table 1 Summary Statistics
ARCH(1)
Note Means over 10 runs. Numbers in brackets are
the fraction of tests rejecting the no ARCH null
hypothesis at the 95 confidence level.
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Step 2 What Causes the Volatility Persistence?

• Why is it in the social learning economy but not
  in the individual learning economy?
• Difference?
• The important phenomena in social learning is the
  following the herd.
• Agreement on
• Figure.
• The changes in the expectations over time
• (18)

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Figure 4 Dynamics of the Variation of
Expectations and Return Series.
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Relation between dynamics of expectations and
return volatility

• GMM
• An Explanatory variable
• A Dependent variable

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There IS a Relation between dynamics of
expectations and return volatility

• Economics
• When the agents point estimates on future prices
  differ, some traders shift expectations up and
  others down.
• As a result, the trading volume additionally
  increases so that the price changes.
• A large swing of the expectations is related to
  the large change in returns.

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What Causes the persistence of Stock Return
Volatility?

• Volatility clusters in a social learning economy
  since expectations shows clustering.
• Volatility clusters in an individual learning
  economy since expectations doesnt show
  clustering.

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Conclusion

• A social learning economy produces persistence of
  return volatility while an individual learning
  economy does not.
• A social learning economy is more likely to show
  the agreement of the point estimates on future
  prices than in an individual learning economy.
• The changes in the expectations explain the
  variability of the stock returns in both
  individual and social learning economies.

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Conclusion

• If the expectations cluster, the volatility of
  the returns series would also show the serial
  correlation. This phenomenon is found only in a
  social learning economy.
• Those of the results indicate that the
  persistence of stock return volatility would be
  caused endogenously with the behavior of the
  heterogeneous investors.