By Jin-Chuan Duan and Weiqi Zhang

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By Jin-Chuan Duan and Weiqi Zhang
Forward-Looking Market Risk Premium

• Discussant Yao-Wen Hsu
• Department of International Business
• College of Management
• National Taiwan University

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• This paper firstly derives a formula for
  estimating the market risk premium on a
  forward-looking basis. The derivation is achieved
  mainly by two steps
• (1) Express the equilibrium risk-free
  interest rate in terms of risk-neutral return
  moments.
• (2) Express the risk-neutral return
  moments in terms of investors risk aversion and
  physical return moments.

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Implicit Assumptions

• Assumptions underlying the derivation of the
  formula includes
• (1) Rational asset prices.
• (2) The distribution of market return
  exists and remains fixed within some investment
  horizon. However, this distribution changes
  across different periods. No long-run, stationary
  distribution is assumed.

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Econometric Implementation

• To estimate the market risk premium
• (1) The risk aversion parameter is
  estimated by the GMM method.
• (2) Physical return moments are obtained
  by using a GARCH(1,1) model.

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Advantages of the Forward-Looking Approach

• In comparison with historical-data based
  approach, the forward-looking approach has the
  following advantages
• (1) The estimated market risk premium is
  never negative.
• (2) The estimated market risk premium is
  much higher during stock market crises.
• (3) The forward-looking approach is
  consistent with the Net Present Value method.
• (4) The time-varying skewness and kurtosis
  of market return helps explain the illiquidity
  risk premium.

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A Brief Conclusion

• This is an exciting paper. The framework proposed
  by this study is innovative, elegant, and
  flexible.
• The forward-looking approach is sensible and very
  promising. At the same time, it is a challenging
  task to estimate a quantity that is highly
  theoretical and time-varying.

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Question 1

• The monthly forward-looking market risk
  premium reflects the economic condition closely
  the estimated market risk premium goes up during
  a recession or a crisis period.
• Can this result be attributed to the nice
  short-term forecasting ability of the chosen
  GARCH(1,1) model? Does this result still hold
  when the horizon is lengthened to, say, more than
  two years?

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Question 2

• The forward-looking market risk premium
  tends to be much higher than its backward-looking
  counterparts.
• Under the forward-looking approach, is the
  equity premium puzzle even more puzzling?

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Question 3

• How can we apply the forward-looking
  method to estimate the risk premium of individual
  stock?
• If the distribution of individual stock
  return is also time-varying, do CAPM and its
  variations (eg. Fama-French 3-factor model)
  sustain?
• If the risk premium of individual stock
  varies period-by-period, how can we calculate the
  discounted value of a distant-in-the-future cash
  flow when using the Net Present Value method?

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Question 4

• Is the momentum phenomenon still an
  anomaly under the forward-looking approach?
• Again, we need to find the normal return
  of individual stocks/portfolios first. To be
  consistent, the normal return should also be
  estimated by a forward-looking method.

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Thanks for your attention.