Date of Award

5-14-2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Economics

Advisor(s)

Chihwa Kao

Second Advisor

Yoonseok Lee

Keywords

High dimensional factor model, Long-term risk, Misspecification, Number of factors, Recovery theorem

Subject Categories

Social and Behavioral Sciences

Abstract

This dissertation examines misspecification issues in two contexts: (i) signal (or equivalently factor) detection in high-dimensional factor models and (ii) the identification of the physical probability distribution of stock returns in the asset pricing literature.

The first essay revisits the panel information criteria (IC) proposed by Bai and Ng (2002), which is a popular estimator for the number of factors in high-dimensional factor models, and studies its over-detection risk in finite samples. First, we analyze the finite sample performance of IC by computing the over-detection probability bound. In particular, we specify the asymptotic over-detection condition of IC in terms of eigenvalues coming from pure noise and then derive the computable formula for a non-asymptotic upper bound on the overestimation probability by adopting random matrix theory. We show that unless the sample size is sufficiently large, the overestimation probability is not negligible even for the case in which factors have strong explanatory power. Second, we show that for small sample sizes the over-detection risk of IC is significantly reduced by the degrees of freedom adjustment in the penalty of the original criteria. Finally, we propose modified information criteria (MIC) as a practical guide to improving the finite sample performance of IC. Simulations show that our MIC outperforms IC for the case with weakly serially or cross-sectionally correlated errors as well as i.i.d. errors.

The second essay examines the misdetection risk of the panel information criteria (IC) proposed by Bai and Ng (2002) for detecting the number of factors in high-dimensional factor models and examines the optimal penalty to minimize an upper bound on the misdetection probability of the IC estimator in finite samples. This study extends the first chapter, which analyzed the finite sample performance of the IC estimator regarding its over-detection risk, to the comprehensive misdetection risk considering under-detection risk as well. We derive the computable formula for a non-asymptotic upper bound on the misdetection probability by employing recent results from random matrix theory. Using the formula, we analyze the misdetection risk of the IC estimator and achieve the minimum upper bound of the misdetection probability by finding the optimal weight for the penalty function. Our numerical examples suggest that modified criteria with the optimized penalization improve the finite sample performance of the original IC estimator.

In my third essay, we revisit the Recovery theorem on the identification of the physical probability distribution of stock returns, proposed by Ross (2015). First, its applicability in fixed-income markets is considered. We suggest a new procedure for applying the Recovery theorem to the Gaussian affine term structure. As a result, we can recover a particular probability distribution and decompose forward rates into the investors' short-rate expectations and term premia under this recovered probability measure. Next, the reliability of the Recovery theorem is examined. In particular, we study its misspecification issue in line with the claim of misspecified recovery by Borovička, Hansen, and Scheinkman (2015). Our empirical result verifies that what Ross really recovers is not the physical probability but the long-term risk-neutral probability which absorbs compensation for exposure to permanent shocks. In consequence, we can decompose forward term premia into nearly constant short-term risk premia associated with transitory shocks and highly volatile long-term risk premia corresponding to permanent shocks. Finally, we find that a secular decline in forward rates is mostly attributed to investors' short-rate expectations under the long-term risk-neutral probability measure, and all important variations in term premia can be captured by long-term risk premia. Concisely, long-term risk matters for asset pricing.

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