The Equity Premium Puzzle: Evidence from Chinese Data

1
The Equity Premium PuzzleEvidence from Chinese
Data

• Presenter Ming GuDepartment of
  EconomicsRutgers University

2
Abstract

• In this paper I have used 199503-200606 Chinese
  quarterly data to evaluate the existence of an
  equity premium puzzle.
• I have concluded that the model used by Mehra and
  Prescott (1985) is not able to satisfactorily
  rationalize the equity premium observed in the
  Chinese data
• Such a conclusion was obtained both under
  assumptions of lognormality or under simulations
  based on a discrete state approximation of the
  Markov process implied by the data.

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The Previous Literature

• Mehra and Prescott (1985)
• Weil(1989)
• Mehra (2003)

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Basic Model(1)

• We consider a frictionless economy that has a
  single representative 'stand-in' household.
• 
  (1)

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Basic Model(2)

• The utility function is further restricted to be
  of the constant relative risk aversion (CRRA)
  class
• (2)
• where the parameter a measures the curvature of
  the utility function. When a 1, the utility
  function is defined to be logarithmic, which is
  the limit of Equation 2 asa approaches 1.

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Basic Model(3)

• Assume one productive unit that produces in
  period t output Yt , which is the period
  dividend.
• There is one equity share with price Pt
  (denominated in consumption units) that is
  competitively traded.
• We can easily find the fundamental pricing
  relationship (Lucas 1978)
• 
  (3)

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Basic Model(4)

• Equation 3 is used to price both stocks and
  riskless one-period bonds.
• For equity, (4)
• For riskless one-period bond
  (5)
• the expected gross return on equity
• 
  (6)

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Methodology(1)

• Lognormality Test
• These assumptions are as follows

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Methodology(1) cont

• Since the growth rates of consumption and
  dividends are assumed to be lognormally
  distributed
• 
  (7)
• 
  (8)
• Where

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Methodology(2)

• I stick to basic model , assuming that the growth
  rate of the endowment follows a Markov process.
  The method is given by Mehra and Prescott (1985).
• The approach is to generate an approximation of
  the initial problem using two states for Xt (real
  per capita consumption growth rate) and a
  transition matrix T of the approximating
  discrete-state Markov chain.

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Methodology(2) cont

• This particular parameterization was selected
  because it permitted us to independently vary the
  average growth rate of output by changing µ, the
  variability of consumption by altering d, and the
  serial correlation of growth rates by adjusting f

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Empirical study(1)

• The Chinese data used in this work has a
  quarterly frequency and ranges from 199503 to
  200606.The data tested below are quarterly
  observations of closing prices on the Shanghai
  Stock Exchange
• The series are individually described below
• (1) Series P Quarterly average SSE Composite
  Stock Price Index divided by the Consumption
  Deflator.
• (2) Series D Real quarterly dividends rate for
  the SSEs series.
• (3) Series PC Consumption deflator series
• (4) Series RF Nominal three-month deposit rate

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Empirical study(2)

• The quarterly return for time t
• the real return on a relatively riskless security
• the Risk Premium is calculated as the difference
  between the Real Return on SSE and the Real
  Return on a Riskless security as defined above.

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Empirical study(3)
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Empirical study(4)
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Empirical study(5)

• We can thus raise the question If we set
  risk-aversion coefficient a to be 10 and ß to be
  0.99, what are the expected rates of return and
  the risk premium using the parameterization
• just described?
• which implies an equity risk premium of 0.47
  percentage points far lower than the 1.43
  percentage points historically observed.

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Empirical study(6)

• Note that in this calculation, I was very liberal
  in choosing the values for a and ß .Most studies
  indicate a value for a that is close to 2. If I
  were to pick a lower value for ß , the risk-free
  rate would be even higher and the premium lower.
• So, the 0.47 pp value represents the maximum
  equity risk premium that can be obtained, given
  the constraints on a and ß. This result
  demonstrates the existence of the equity premium
  puzzle under the assumption of lognormality.

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Empirical study(7)
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Empirical study(8)

• Given the estimated process on consumption,
  figure 4 shows the set of values of the average
  risk-free rate and equity risk premium which are
  both consistent with the model and result in
  average real risk-free rates between zero and
  three percent.
• These are values that can be obtained by varying
  preference parameters a between zero and ten and
  ß between zero and one. The observed real return
  of 0.97 percent and equity premium of 1.43
  percent is clearly inconsistent with the
  predictions of the model. The largest premium
  obtainable with the model is 0.49 percent, which
  is not close to the observed value.
• This result demonstrates the equity premium
  puzzle in the China market again.

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Conclusion and extension

• I have concluded that premium puzzle does exist
  in the Chinese data both under assumptions of
  lognormality and under simulations based on a
  discrete state approximation of the Markov
  process implied by the data.
• Future work alternative model are used to
  reinvestigated the existence of equity premium
  puzzle.