Investigating ICAPM with Dynamic Conditional Correlations

1

• Investigating ICAPM with Dynamic Conditional
  Correlations
• Turan Bali and Robert Engle
• Oxford University
• VAST DATA CONFERENCE
• September 15, 2008

2
Introduction

• Merton (1973)s ICAPM predicts a positive
  relation between the expected excess return on a
  stock or stock portfolio and its conditional
  covariance with the market portfolio return.
• The literature generally focused on the relation
  between the expected excess return on the market
  portfolio and its conditional variance, thus
  confining the estimation to a single series of
  the market portfolio.

3
Introduction

• We exploit the cross-sectional consistency of the
  intertemporal risk-return relation and estimate
  the common relation across 30 stocks in the Dow
  Jones Industrial Average.
• Using daily returns from July 1986 to September
  2007, we estimate the conditional covariances
  between the excess returns on each stock and the
  market portfolio.

4
Introduction

• The mean-reverting DCC model of Engle (2002) is
  used to estimate a stocks conditional covariance
  with the market and test whether the conditional
  covariance predicts time-variation in the stocks
  expected return.
• We estimate a system of equations between the
  excess returns and their conditional covariances
  with the market, while constraining all equations
  to have the same slope coefficient.

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Introduction

• The positive risk-return tradeoff is robust after
  controlling for conditional covariation of
  individual stocks with
• macroeconomic variables (fed funds rate, default
  spread, and term spread)
• financial factors (size, book-to-market, and
  momentum)
• volatility measures (implied, GARCH, and range
  volatility).

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FINDINGS

• By pooling the time series and cross section
  together, the mean-reverting DCC-based
  conditional covariance estimates generate
  significant and reasonable risk premiums.
• The significantly positive, robust, and sensible
  estimates of risk aversion highlight the added
  benefits of using the conditional measures of
  covariance risk and maintaining the
  cross-sectional consistency in estimating the
  ICAPM.

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Literature Review

• Insignificant relation
• French, Schwert and Stambaugh (1987)
• Baillie and DeGennaro (1990)
• Chan, Karolyi, and Stulz (1992)
• Campbell and Hentschel (1992)
• Glosten, Jagannathan, and Runkle (1993)
• Harrison and Zhang (1999)
• Goyal and Santa-Clara (2003)
• Bali, Cakici, Yan, and Zhang (2005)
• Bollerslev and Zhou (2006)

8
Literature Review

• Negative relation
• Abel (1988), Backus and Gregory (1993), and
  Gennotte and Marsh (1993)
• Campbell (1987)
• Breen, Glosten, and Jagannathan (1989)
• Turner, Startz, and Nelson (1989)
• Nelson (1991)
• Glosten, Jagannathan, and Runkle (1993)
• Whitelaw (1994, 2000)
• Harvey (2001)
• Brandt and Kang (2004)

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Literature Review

• Positive relation
• Bollerslev, Engle, and Wooldridge (1988)
• Scruggs (1998)
• Gyhsels, Santa-Clara, and Valkanov (2005)
• Guo and Whitelaw (2006)
• Bali and Peng (2006)
• Lundblad (2007)
• Bali (2008)

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ICAPM Specification

• Mertons (1973) ICAPM implies
• Almost Everyone agrees with this theory. However
  implementations differ in many ways
• Assets Index, portfolios or individual returns
• Covariances constant betas, 5 year constant,
  conditional
• State Variables none, Fama-French, macro,
  interest rates, inflation, volatility
• Data Frequency Annual, monthly, daily
• Sample Period 100 years, 50 years, 10 years

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ICAPM Specification

• Traditional empirical studies focus on the
  risk-return tradeoff for the market portfolio
  with and without hedging demand
• Many studies sort portfolios based on previously
  estimated covariances or characteristics such as
  FF.

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Data

• Financial Factors
• SMB Size Factor of Fama-French (1993)
• HML Book-to-Market Factor of Fama-French (1993)
• MOM Momentum Factor of Fama-French (1993)
• Volatility Measures
• Implied Volatility (VXO VIX)
• GARCH Volatility
• Range Volatility
• Idiosyncratic Volatility

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THE SPECIFICATION

• i.e.
• And test

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THE METHOD

• Estimate GARCH for all series
• Estimate bivariate DCC for each series and the
  market
• Jointly estimate A and intercepts with
  covariances as regressors
• Use SUR to control for equation error covariances
• Test that intercepts are jointly zero
• Add other regressors
• Add DCC covariances with other state variables

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Data

• Daily excess returns on Dow 30 stocks from July
  10, 1986 to September 28, 2007 total of 5,354
  daily observations
• Five different stock market indices
• Value-weighted NYSE/AMEX/NASDAQ index
• New York Stock Exchange (NYSE) index
• SP 500 index
• SP 100 index
• Dow Jones Industrial Average (DJIA)

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Data

• Macroeconomics Variables
• Federal funds rate
• 3-month Treasury bill
• 10-year Treasury bond yields
• BAA-rated corporate bond yields
• AAA-rated corporate bond yields
• Dependent Variables
• Daily excess return on the market portfolio
• Daily excess return on Dow 30 stocks

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DCC CORRELATION ESTIMATES
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DCC CORRELATIONS CONT
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Risk Return Tradeoff
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SUB SAMPLES
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RESULTS MACRO VARIABLES

• Default spread
• Term spread
• Federal funds rate
• Differences of these variables
• NO SIGNIFICANT VARIABLES
• ESTIMATE IN COVARIANCES
• STILL NOTHING SIGNIFICANT

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FAMA FRENCH FACTORS
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INDIVIDUAL STOCK VOLATILITY
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MARKET VOLATILITY
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MARKET VOLATILITY COVARIANCE
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Future Research

• Bali and Engle (2008) Can DCC-based conditional
  measures of covariance risk explain the value
  premium?
• Monthly Decile Portfolios of BM July 1926 - Dec
  2007
• Daily returns of thousands of stocks. Are there
  more factors? Can this be done with composite
  likelihood methods?

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CONCLUSIONS

• RISK RETURN TRADE-OFF IS RELIABLY ESTIMATED AND
  SIGNIFICANTLY POSITIVE
• MARKET VOLATILITY IS A SIGNIFICANT STATE VARIABLE
  HOWEVER IT IS MEASURED
• OTHER FACTORS DO NOT APPEAR IMPORTANT