R2

1
R2
2
Asset Pricing Perspective

• R-sq. is simply a measure of the performance of
  the asset-pricing model used
• Roll (1988)
• Perfect hindsight, Excludes firm-specific event
  dates, same low R-sq.
• Extensions Cornell (1990) small sample, R-sq?
  when highest 200 volume days are excluded Robin
  (1993) - large sample, only 30 high volume days
  Brown (1999) acct. study, R-sq. ? when only
  private info.
• Shiller (1981) and West (1988)
• firm-specific price volatility is too large to be
  associated with changes in firms fundamentals
• the excess fluctuation can have different sources
  such as bubbles or fads (i.e. noise)
• See http//people.few.eur.nl/smant/m-economics/sh
  iller.htm
• Shleifer and Vishny (1997) result is consistent
  noise trading causes prices to diverge from
  fundamentals
• Empirical evidence on R-sq. around index
  additions/deletions Barberis et al. (2005)
  SP500, betas ? of stocks added (investors treat
  SP stocks as belonging to one category),
  Greenwood (2005) Nikkei225

3
Campbell et al. 2001 JF - Summary

• Simple summary of historical movements in market,
  industry, and firm-level volatility
• Disaggregated approach (they mean individual
  stock level study)
• Decomposition of volatility that does not require
  the estimation of covariances or betas for
  industries or firms
• 1962-1997
• Increase in firm-level volatility
• Decline in correlations among stocks (R2)
• same as
• Decline in explanatory power of market model
• Higher number of stocks to achieve given
  diversification
• Volatility moves countercyclically

4
Campbell et al. (2001) ivol?

• Conjectured explanations by Campbell et al.
• A lot more new listings in US (Brown and Kapadia
  (2005))
• Earlier listings
• Breaking up conglomerates
• Exec stock options
• Betas more volatile
• NOT
• ivol? not just because CFs are now separately
  traded, but also because info about those CFs is
  disseminated more rapidly
• HOWEVER
• better price discovery changes the timing of
  information, not the quantity of information, and
  thus does not change volatility!
• (discounting will reduce the vol of returns since
  news enters prices earlier, even if price vol
  increases)

5
Campbell not price discovery

• 3-period model
• Time 2 future profits X are realized
• Time 1 info arrives and expected profits are
  E1X
• Time 0 expected future profits are normalized
  to 0
• Volatility form time 0 to time 1 is
• Var(E1X)
• Volatility form time 1 to time 2 is
• Var(X-E1X)
• Average volatility is
• Which is unaffected by the timing of info.
• More careful analysis in West (1988)

6
Campbell et al. 2001 JF - Motivation

• Aggregate volatility is not constant (market
  risk)
• Non-aggregate volatility is important because
• Not all investors can diversify
• number of stocks to achieve diversification
  depends on idiosyncratic volatility
• One-stock arbitrageurs
• Calculating abnormal returns for event studies
• Pricing individual stock options
• In some macro theoretical models, aggreagate
  output may be affected by changes in
  industry-level vol of productivity growth, and/or
  differential arrival rate of information about
  management quality among firms

7
Campbell et al. 2001 JF Existing empirical
evidence

• leverage effect
• the tendency for volatility to rise following
  negative returns
• Black (1976), Christie (1982), Duffee (1995)
• Reallocation across industries or firms
• Loungani et al. (1990), Bernard and Steigerwald
  (1993), Brainard and Cutler (1993)
• Effect on investment
• Leahy and Whited (1996)
• Market vol decomposed into country and industry
  effects
• Roll (1992) and Heston and Rouwenhorst (1994)
• Emerging markets
• Bekaert and Harvey (1997)

8
Campbell et al. 2001 JF Results

• Confirm no trend in market vol using monthly
  data
• No trend in market and industry vol using daily
  data
• Firm-level vol large and significant positive
  trend
• All vol measures are pos corr
• Market vol tends to lead the other series
• All vol measures tend to lead recessions
• All vol measures forcast economic activity

9
Campbell et al. 2001 JF Methodology

• Variance decomposition is difficult based on CAPM
  (requires knowledge of firm-specific betas)
• Use market-adjusted-return model as in
  Campbells 1997 textbook
• a restricted market model with ?i0 and ?i1
• Maybe the major criticism of this paper

10
Campbell et al. 2001 JF Methodology

• Relation b/w market-adjusted-return model and
  CAPM
• Aggregate (4) and (5) across industries and firms

11
Campbell et al. 2001 JF Methodology

• (15) and (16) show that cross-sectional variation
  in betas can produce common movements in the
  variance components ?mt2,??t2,??t2, even if the
  CAPM variance components est.??t2 and est. ??t2
  do not move at all with the market variance ?mt2

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Campbell et al. 2001 JF R2 result
equally weighted average R2 statistic of a market
model, estimated using the past 60 months of
monthly data (solid line) or the past 12 months
of daily data (dotted line). Stocks included in
the calculation at each point in time are
required to have a complete return history over
the past 60 months (solid line) or 12 months
(dotted line).
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Pro and Con Campbell et al. results

• Finance
• Wei and Zhang (2006) follow up on Campbell
  (2001)
• Bekaert et al. (2005) no trend in ivol across
  OECD markets
• Accounting
• Rajgopal and Venkatachalam (2006)
• earnings quality and forecast dispersion explain
  differences in firm specific idiosyncratic
  volatility
• temporal link between idiosyncratic volatility
  and the two information quality proxies persists

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Con Morck et al. results finance, country-level

• Griffin et al. (2007) main result emerging
  markets do as well or better than developed
  markets at incorporating simple forms of public
  information into prices
• within country smaller stocks have much lower R2s
  on average - consistent with Roll (1988)
• no evidence that better legal, regulatory, and
  governance climates are related to higher levels
  of stock market efficiency
• investor protection measures are ever
  significantly related to R2 after controlling for
  market volatility and the number of firms
• longer and more recent 1994 to 2005 sample period
• Kelly (2006)

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Con Durnev et al. (2003) results firm-level

• Accounting
• Teoh, Yang and Zhang (2006) relationship b/w R2
  and 4 accounting anomalies, US data
• accruals, net operating assets, post-earnings
  announcement drift, and V/P anomalies all reject
  the information interpretation earnings response
  coef.
• for firms with lower R2 values, future earnings
  are less correlated with current returns
• Ashbaugh-Skaife et al. (2006) 6 developed
  markets, cross-sectional design, show that
  results are sensitive to sample selection
• Alves et al. (2006) US and UK data
• Confirm declining trend in R2
• R² and its components are poorly correlated with
  information-related measures such as market
  value, bid-ask spread, market-to-book ratio and
  analyst following
• Finance
• Hou et al. (2006) R2 and momentum
• investors overreaction to their private
  information can help explain the negative
  relationship between R2 and assets price
  informativeness.

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Support for info interpretation of ivol -
Ferreira and Leux (2007) JF

• Shows how governance provisions and informed
  trading interact to influence the incorporation
  of information into stock prices
• The absence of anti-takeover provisions creates
  incentives to collect private information, which
  is a central determinant of idiosyncratic
  volatility
• Grossman and Stiglitz (1980) predict that
  improving the cost-benefit trade-off on
  information collection leads to more informed
  trading and more informative pricing
• To take into account the fact that limits to
  arbitrage, pricing errors, and noise also
  manifest in volatility, FL verify their
  conclusions using other measures of information
  flow
• Alternative measures of private information flow
  PIN, private info
• IRRC dataset 1990-2001, daily data for ivol, mkt
  model, FF, and industry factors model
• Validity of this study is questionable if the
  G-Index is not a pure anti-takeover measure
• Sokolyk (2006) shows that the G-Index is not
  related either to likelihood of being acquired or
  the magnitude of takeover premia

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Support for info interpretation of ivol

• Qin Yafeng (2006)
• higher commonality in liquidity in emerging
  markets than in developed markets
• time-series analysis at individual security level
  shows that individual liquidity is more affected
  by market uncertainty than by individual security
  idiosyncratic uncertainty, which is in contrast
  to securities from developed markets
• Other papers
• Core, Guay, and Rusticus (2006)
• Goyal and Santa-Clara (2003)
• Cremers and Nair (2005)
• Chen, Goldstein, and Jiang (2005) provide
  independent evidence that idiosyncratic
  volatility and PIN
• Wei and Zhang (2006)

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Corporate Governance Perspective

• R-sq. contributes to understanding a countrys
  information environment
• Country level (R-sq. seems to perform well as an
  inverse proxy of firm-specific info being
  reflected in prices)
• Morck et al. (2000) R-sq. ? in poor inv. prot.
  countries (Art talked about their results last
  time)
• Li et al. (2003) extend to emerging markets,
  openness
• Jin and Myers (2006) opaqueness positive
  relationship b/w info and ivol.
• Chan and Hameed (2006) analysts greater
  analyst coverage increases stock price
  synchronicity (R2), i.e. analyst info has more
  market-wide content
• Firm-level
• Durnev at al. (2001) R-sq. captures the degree
  to which share prices reflect info about
  firm-specific fundamentals
• Piotroski and Roulstone (2004) sophisticated
  investors and R-sq., analysts and institutions
  R?, insiders R?

19
Lee and Liu (2006) reconcile the debate

• ivol has a information and a noise component
• In good (poor) info environment (the info
  production cost is low (high)) the dominant
  component of ivol is info (noise) and thus there
  is a positive (negative) relationship b/w ivol
  and price informativeness
• US data, confirms U-shaped relationship b/w
  informativeness and ivol