The Conditional Equity Premium, Cross-Sectional Returns and Stochastic Volatility

Ka Wai Terence Fung, Chi Keung Marco Lau, Kwok Ho Chan

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Bansal and Yaron (2004) demonstrate, by calibration, that the Consumption-based Capital Asset Pricing Model (CCAPM) can be rescued by assuming that consumption growth rate follows a stochastic volatility model. They show that the conditional equity premium is a linear function of conditional consumption and market return volatilities, which can be estimated handily by various Generalized Autoregressive Conditonal Heteroskedasticity (GARCH) and Stochastic Volatility (SV) models. We find that conditional consumption and market volatilities are capable of explaining cross-sectional return differences. The Exponential GARCH (EGARCH) volatility can explain up to 55% variation of return and the EGARCH model augmented with cay^ — a cointegrating factor of consumption, labor income and asset wealth growth — greatly enhances model performance. We proceed to test another hypothesis: if Bansal and Yaron estimator is an unbiased estimator of true conditional equity premium, then the instrumental variables for estimating conditional equity premium should no longer be significant. We demonstrate that once the theoretical conditional risk premium is added to the model, it renders all instrumental variables redundant. Also, the model prediction is consistent with observed declining equity premium.
LanguageEnglish
Pages316-327
Number of pages12
JournalEconomic Modelling
Volume38
DOIs
Publication statusPublished - Feb 2014
Externally publishedYes

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Equity premium
Return volatility
Stochastic volatility
Heteroskedasticity
Instrumental variables
Stochastic volatility model
Estimator
Market volatility
Assets
Labor income
GARCH model
Market returns
Risk premium
Capital asset pricing model
Wealth
Factors
Calibration
Consumption growth
Hypothesis test
Prediction model

Cite this

@article{75fbf09434594efbad46615e06260418,
title = "The Conditional Equity Premium, Cross-Sectional Returns and Stochastic Volatility",
abstract = "Bansal and Yaron (2004) demonstrate, by calibration, that the Consumption-based Capital Asset Pricing Model (CCAPM) can be rescued by assuming that consumption growth rate follows a stochastic volatility model. They show that the conditional equity premium is a linear function of conditional consumption and market return volatilities, which can be estimated handily by various Generalized Autoregressive Conditonal Heteroskedasticity (GARCH) and Stochastic Volatility (SV) models. We find that conditional consumption and market volatilities are capable of explaining cross-sectional return differences. The Exponential GARCH (EGARCH) volatility can explain up to 55{\%} variation of return and the EGARCH model augmented with cay^ — a cointegrating factor of consumption, labor income and asset wealth growth — greatly enhances model performance. We proceed to test another hypothesis: if Bansal and Yaron estimator is an unbiased estimator of true conditional equity premium, then the instrumental variables for estimating conditional equity premium should no longer be significant. We demonstrate that once the theoretical conditional risk premium is added to the model, it renders all instrumental variables redundant. Also, the model prediction is consistent with observed declining equity premium.",
keywords = "Financial economics, Macroeconomics and monetary economics, Equity premium puzzle, Fama-French model",
author = "Fung, {Ka Wai Terence} and Lau, {Chi Keung Marco} and Chan, {Kwok Ho}",
year = "2014",
month = "2",
doi = "10.1016/j.econmod.2014.01.009",
language = "English",
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The Conditional Equity Premium, Cross-Sectional Returns and Stochastic Volatility. / Fung, Ka Wai Terence; Lau, Chi Keung Marco; Chan, Kwok Ho.

In: Economic Modelling, Vol. 38, 02.2014, p. 316-327.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The Conditional Equity Premium, Cross-Sectional Returns and Stochastic Volatility

AU - Fung, Ka Wai Terence

AU - Lau, Chi Keung Marco

AU - Chan, Kwok Ho

PY - 2014/2

Y1 - 2014/2

N2 - Bansal and Yaron (2004) demonstrate, by calibration, that the Consumption-based Capital Asset Pricing Model (CCAPM) can be rescued by assuming that consumption growth rate follows a stochastic volatility model. They show that the conditional equity premium is a linear function of conditional consumption and market return volatilities, which can be estimated handily by various Generalized Autoregressive Conditonal Heteroskedasticity (GARCH) and Stochastic Volatility (SV) models. We find that conditional consumption and market volatilities are capable of explaining cross-sectional return differences. The Exponential GARCH (EGARCH) volatility can explain up to 55% variation of return and the EGARCH model augmented with cay^ — a cointegrating factor of consumption, labor income and asset wealth growth — greatly enhances model performance. We proceed to test another hypothesis: if Bansal and Yaron estimator is an unbiased estimator of true conditional equity premium, then the instrumental variables for estimating conditional equity premium should no longer be significant. We demonstrate that once the theoretical conditional risk premium is added to the model, it renders all instrumental variables redundant. Also, the model prediction is consistent with observed declining equity premium.

AB - Bansal and Yaron (2004) demonstrate, by calibration, that the Consumption-based Capital Asset Pricing Model (CCAPM) can be rescued by assuming that consumption growth rate follows a stochastic volatility model. They show that the conditional equity premium is a linear function of conditional consumption and market return volatilities, which can be estimated handily by various Generalized Autoregressive Conditonal Heteroskedasticity (GARCH) and Stochastic Volatility (SV) models. We find that conditional consumption and market volatilities are capable of explaining cross-sectional return differences. The Exponential GARCH (EGARCH) volatility can explain up to 55% variation of return and the EGARCH model augmented with cay^ — a cointegrating factor of consumption, labor income and asset wealth growth — greatly enhances model performance. We proceed to test another hypothesis: if Bansal and Yaron estimator is an unbiased estimator of true conditional equity premium, then the instrumental variables for estimating conditional equity premium should no longer be significant. We demonstrate that once the theoretical conditional risk premium is added to the model, it renders all instrumental variables redundant. Also, the model prediction is consistent with observed declining equity premium.

KW - Financial economics

KW - Macroeconomics and monetary economics

KW - Equity premium puzzle

KW - Fama-French model

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SN - 0264-9993

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