Search Results
Working Paper
Robust inference in linear asset pricing models
We derive new results on the asymptotic behavior of the estimated parameters of a linear asset pricing model and their associated t-statistics in the presence of a factor that is independent of the returns. The inclusion of this "useless" factor in the model leads to a violation of the full rank (identification) condition and renders the inference nonstandard. We show that the estimated parameter associated with the useless factor diverges with the sample size but the misspecification-robust t-statistic is still well-behaved and has a standard normal limiting distribution. The asymptotic ...
Working Paper
Specification tests of asset pricing models using excess returns
We discuss the impact of different formulations of asset pricing models on the outcome of specification tests that are performed using excess returns. It is generally believed that when only excess returns are used for testing asset pricing models, the mean of the stochastic discount factor (SDF) does not matter. We show that the mean of the candidate SDF is only irrelevant when the model is correct. When the model is misspecified, the mean of the SDF can be a very important determinant of the specification test statistic, and it also heavily influences the relative rankings of competing ...
Working Paper
Pricing model performance and the two-pass cross-sectional regression methodology
Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, that is, expected returns are exactly linear in asset betas. This assumption can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general ...
Working Paper
Asymptotic variance approximations for invariant estimators in uncertain asset-pricing models
This paper derives explicit expressions for the asymptotic variances of the maximum likelihood and continuously updated GMM estimators under potentially misspecified models. The proposed misspecification-robust variance estimators allow the researcher to conduct valid inference on the model parameters even when the model is rejected by the data. Although the results for the maximum likelihood estimator are only applicable to linear asset-pricing models, the asymptotic distribution of the continuously updated GMM estimator is derived for general, possibly nonlinear, models. The large ...
Working Paper
Misspecification-robust inference in linear asset pricing models with irrelevant risk factors
We show that in misspecified models with useless factors (for example, factors that are independent of the returns on the test assets), the standard inference procedures tend to erroneously conclude, with high probability, that these irrelevant factors are priced and the restrictions of the model hold. Our proposed model selection procedure, which is robust to useless factors and potential model misspecification, restores the standard inference and proves to be effective in eliminating factors that do not improve the model's pricing ability. The practical relevance of our analysis is ...
Working Paper
Spurious Inference in Unidentified Asset-Pricing Models
This paper studies some seemingly anomalous results that arise in possibly misspecified and unidentified linear asset-pricing models estimated by maximum likelihood and one-step generalized method of moments (GMM). Strikingly, when useless factors (that is, factors that are independent of the returns on the test assets) are present, the models exhibit perfect fit, as measured by the squared correlation between the model's fitted expected returns and the average realized returns, and the tests for correct model specification have asymptotic power that is equal to the nominal size. In other ...
Working Paper
Chi-squared tests for evaluation and comparison of asset pricing models
Using data for the Philippines, I develop and estimate a heterogeneous agent model to analyze the role of monetary policy in a small open economy subject to sizable remittance fluctuations. I include rule-of-thumb households with no access to financial markets and test whether remittances are countercyclical and serve as an insurance mechanism against macroeconomic shocks. When evaluating the welfare implications of alternative monetary rules, I consider both an anticipated large secular increase in the trend growth of remittances and random cyclical fluctuations around this trend. In a ...
Working Paper
A note on the estimation of asset pricing models using simple regression betas
Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular tool for estimating and testing beta asset pricing models. In this paper, we focus on the case in which simple regression betas are used as regressors in the second-pass CSR. Under general distributional assumptions, we derive asymptotic standard errors of the risk premia estimates that are robust to model misspecification. When testing whether the beta risk of a given factor is priced, our misspecification robust standard error and the ...
Working Paper
The exact distribution of the Hansen-Jagannathan bound
Under the assumption of multivariate normality of asset returns, this paper presents a geometrical interpretation and the finite-sample distributions of the sample Hansen-Jagannathan (1991) bounds on the variance of admissible stochastic discount factors, with and without the nonnegativity constraint on the stochastic discount factors. In addition, since the sample Hansen-Jagannathan bounds can be very volatile, we propose a simple method to construct confidence intervals for the population Hansen-Jagannathan bounds. Finally, we show that the analytical results in the paper are robust to ...
Working Paper
Too Good to Be True? Fallacies in Evaluating Risk Factor Models
This paper is concerned with statistical inference and model evaluation in possibly misspecified and unidentified linear asset-pricing models estimated by maximum likelihood and one-step generalized method of moments. Strikingly, when spurious factors (that is, factors that are uncorrelated with the returns on the test assets) are present, the models exhibit perfect fit, as measured by the squared correlation between the model's fitted expected returns and the average realized returns. Furthermore, factors that are spurious are selected with high probability, while factors that are useful are ...