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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 ...
Working Paper
On the Hansen-Jagannathan distance with a no-arbitrage constraint
We provide an in-depth analysis of the theoretical and statistical properties of the Hansen-Jagannathan (HJ) distance that incorporates a no-arbitrage constraint. We show that for stochastic discount factors (SDF) that are spanned by the returns on the test assets, testing the equality of HJ distances with no-arbitrage constraints is the same as testing the equality of HJ distances without no-arbitrage constraints. A discrepancy can exist only when at least one SDF is a function of factors that are poorly mimicked by the returns on the test assets. Under a joint normality assumption on the ...
Working Paper
Further results on the limiting distribution of GMM sample moment conditions
In this paper, we extend the results in Hansen (1982) regarding the asymptotic distribution of generalized method of moments (GMM) sample moment conditions. In particular, we show that the part of the scaled sample moment conditions that gives rise to degeneracy in the asymptotic normal distribution is T-consistent and has a nonstandard limiting distribution. We derive the asymptotic distribution for a given linear combination of the sample moment conditions and show how to conduct statistical inference. We demonstrate the finite-sample properties of the proposed asymptotic approximation ...
Working Paper
Mimicking portfolios, economic risk premia, and tests of multi-beta models
This paper considers two alternative formulations of the linear factor model (LFM) with nontraded factors. The first formulation is the traditional LFM, where the estimation of risk premia and alphas is performed by means of a cross-sectional regression of average returns on betas. The second formulation (LFM*) replaces the factors with their projections on the span of excess returns. This formulation requires only time-series regressions for the estimation of risk premia and alphas. We compare the theoretical properties of the two approaches and study the small-sample properties of estimates ...
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 ...
Journal Article
Asset returns and economic risk
The capital asset pricing model (CAPM), favored by financial researchers and practitioners fifteen years ago, holds that the extra return on a risky asset comes from bearing market risk only. But newer evidence supports the intertemporal CAPM (I-CAPM) theory (Merton 1973), which suggests that the premium on any risky asset is related not only to market risk but also to additional economic variables. ; This article reviews and interprets recent advances in the asset pricing literature. The study seeks to shed light on the sources of economic risk that investors should track and hedge against ...
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
Dynamic strategies, asset pricing models, and the out-of-sample performance of the tangency portfolio
In this paper, I study the behavior of an investor with unit risk aversion who maximizes a utility function defined over the mean and the variance of a portfolio's return. Conditioning information is accessible without cost and an unconditionally riskless asset is available in the market. ; The proposed approach makes it possible to compare the performance of a benchmark tangency portfolio (formed from the set of unrestricted estimates of portfolio weights) to the performance of a restricted tangency portfolio which uses single-index and multi-index asset pricing models to constrain the first ...
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 ...