## Abstract

A new semiparametric estimator for an empirical asset pricing model with general nonpara-

metric risk-return tradeoff and a GARCH process for the underlying volatility is introduced.

The estimator does not rely on any initial parametric estimator of the conditional mean func-

tion, and this feature facilitates the derivation of asymptotic theory under possible nonlinearity

of unspecified form of the risk-return tradeoff. Besides the nonlinear GARCH-in-mean effect,

our specification accommodates exogenous regressors that are typically used as conditioning

variables entering linearly in the mean equation, such as the dividend yield. Using the profile

likelihood approach, we show that our estimator under stated conditions is consistent, asymp-

totically normal, and efficient, i.e. it achieves the semiparametric lower bound. A sampling

experiment provides evidence on finite sample properties as well as comparisons with the fully

parametric approach and the iterative semiparametric approach using a parametric initial esti-

mate proposed by Conrad and Mammen (2008). An empirical application to the daily S&P 500

stock market returns suggests that the linear relation between conditional expected return and

conditional variance of returns from the literature is misspecified, and this could be the reason

for the disagreement on the sign of the relation.

metric risk-return tradeoff and a GARCH process for the underlying volatility is introduced.

The estimator does not rely on any initial parametric estimator of the conditional mean func-

tion, and this feature facilitates the derivation of asymptotic theory under possible nonlinearity

of unspecified form of the risk-return tradeoff. Besides the nonlinear GARCH-in-mean effect,

our specification accommodates exogenous regressors that are typically used as conditioning

variables entering linearly in the mean equation, such as the dividend yield. Using the profile

likelihood approach, we show that our estimator under stated conditions is consistent, asymp-

totically normal, and efficient, i.e. it achieves the semiparametric lower bound. A sampling

experiment provides evidence on finite sample properties as well as comparisons with the fully

parametric approach and the iterative semiparametric approach using a parametric initial esti-

mate proposed by Conrad and Mammen (2008). An empirical application to the daily S&P 500

stock market returns suggests that the linear relation between conditional expected return and

conditional variance of returns from the literature is misspecified, and this could be the reason

for the disagreement on the sign of the relation.

Original language | English |
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Place of publication | Aarhus |

Publisher | Institut for Økonomi, Aarhus Universitet |

Number of pages | 47 |

Publication status | Published - 2008 |

## Keywords

- Efficiency bound, GARCH-M model, Profile likelihood, Risk-return relation, Semiparametric inference