# Research

## Serhiy Kozak

Assistant Professor of Finance

Research Interests: empirical and theoretical asset pricing, financial economics, machine learning.

## Published and forthcoming

Journal of Finance, June 2018, 73(3), 1183-1223 (with Stefan Nagel and Shri Santosh).

JF version | Data | BibTeX

Abstract: We argue that tests of reduced-form factor models and horse races between "characteristics" and "covariances" cannot discriminate between alternative models of investor beliefs. Since asset returns have substantial commonality, absence of near-arbitrage opportunities implies that the SDF can be represented as a function of a few dominant sources of return variation. As long as some arbitrageurs are present, this conclusion applies even in an economy in which all cross-sectional variation in expected returns is caused by sentiment. Sentiment investor demand results in substantial mispricing only if arbitrageurs are exposed to factor risk when taking the other side of these trades.

Journal of Financial Economics, February 2020, 135(2), 271-292, Lead Article (with Stefan Nagel and Shrihari Santosh).

Fama-DFA Prize for the Best Paper Published in the Journal of Financial Economics in the Areas of Capital Markets and Asset Pricing, 2020 (First place)

JFE version | Data | Code | Internet Appendix | BibTeX | Slides (TeX)

Abstract: We construct a robust stochastic discount factor (SDF) that summarizes the joint explanatory power of a large number of cross-sectional stock return predictors. Our method achieves robust out-of-sample performance in this high-dimensional setting by imposing an economically motivated prior on SDF coefficients that shrinks the contributions of low-variance principal components of the candidate factors. While empirical asset pricing research has focused on SDFs with a small number of characteristics-based factors—e.g., the four- or five-factor models discussed in the recent literature—we find that such a characteristics-sparse SDF cannot adequately summarize the cross-section of expected stock returns. However, a relatively small number of principal components of the universe of potential characteristics-based factors can approximate the SDF quite well.

Journal of Financial Economics, September 2020, 137(3), 740-751(with Shri Santosh).

JFE version | Data | Internet Appendix | BibTeX

Abstract: Controlling for changes in wealth, the price of "discount-rate" risk reveals whether increases in equity risk premia represent "good" or "bad" news to rational investors. We employ a new empirical methodology and find that the price is negative. This finding suggests that discount rates are high during times of high marginal utility of wealth. Our approach relies on using future realized market returns to consistently estimate covariances of asset returns with the market risk premium. Covariances drive observed patterns in a broad cross-section of stock and bond expected returns.

Review of Financial Studies, May 2020, 33(5), 1980-2018 (with Valentin Haddad and Shri Santosh).

2018 Q-Group Jack Treynor Prize

RFS version | Data | Internet Appendix | BibTeX

Abstract: The optimal factor timing portfolio is equivalent to the stochastic discount factor. We propose and implement a method to characterize both empirically. Our approach imposes restrictions on the dynamics of expected returns which lead to an economically plausible SDF. Market-neutral equity factors are strongly and robustly predictable. Exploiting this predictability leads to substantial improvement in portfolio performance relative to static factor investing. The variance of the corresponding SDF is larger, more variable over time, and exhibits different cyclical behavior than estimates ignoring this fact. These results pose new challenges for theories that aim to match the cross-section of stock returns.

Journal of Monetary Economics, March 2022, 126, 188-209.

JME version | Data | Internet Appendix | BibTeX

Abstract: A production-based equilibrium model jointly prices bond and stock returns and produces time-varying correlation between stock and real treasury returns that changes in both magnitude and sign. The term premium is time-varying and changes sign. The model incorporates time-varying risk aversion and two physical technologies with different cash-flow risks. Bonds hedge risk-aversion shocks and command negative term premium through this channel. Cash-flow shocks produce co-movement of bond and stock returns and positive term premium. Relative strength of these two mechanisms varies over time. The correlation is a powerful predictor of relative bond-stock and long-short equity returns in the data.

(with Stefano Giglio and Bryan Kelly)

Journal of Finance, Forthcoming.

Slides | Data | BibTeX

Abstract: We use a large cross-section of equity returns to estimate a rich affine model of equity prices, dividends, returns and their dynamics. Using the model, we price dividend strips of the aggregate market index, as well as any other well-diversified equity portfolio. We do not use any dividend strips data in the estimation of the model; however, model-implied equity yields generated by the model match closely the equity yields from the traded dividend forwards reported in the literature. Our model can be used to extend the data on the term structure of aggregate (market) discount rates over time (back to the 1970s) and across maturities, since we are not limited by the maturities of actually traded dividend claims. Most importantly, the model generates term structures for any portfolio of stocks (e.g., small and value portfolios, high and low investment portfolios, etc). The novel cross-section of term structure data estimated by our model, covering a span of 45 years that includes several recessions, represents a rich set of new empirical moments that can be used to guide and evaluate asset pricing models, beyond the aggregate term structure of dividend strips that has been studied in the literature.

## Working Papers

(with Stefan Nagel)

Data | BibTeX

Abstract: When expected returns are linear in asset characteristics, the stochastic discount factor (SDF) that prices individual stocks can be represented as a factor model with GLS cross-sectional regression slope factors. Factors constructed heuristically by aggregating individual stocks into characteristics-based factor portfolios using sorting, characteristics-weighting, or OLS cross-sectional regression slopes do not span this SDF unless the covariance matrix of stock returns has a specific structure. These conditions are more likely satisfied when researchers use large numbers of characteristics simultaneously. Methods to hedge unpriced components of heuristic factor returns allow partial relaxation of these conditions. We also show the conditions that must hold for dimension reduction to a number of factors smaller than the number of characteristics to be possible without having to invert a large covariance matrix. Under these conditions, instrumented and projected principal components analysis methods can be implemented as simple PCA on certain portfolio sorts.

Slides | Data | BibTeX

Abstract: Characteristics-based asset pricing implicitly assumes that factor betas or risk prices are linear functions of pre-specified characteristics. Present value identities, such as Campbell-Shiller or clean-surplus accounting, however, clearly predict that expected returns are highly non-linear functions of all characteristics. While basic non-linearities can be easily accommodated by adding non-linear functions to the set of characteristics, the problem quickly becomes infeasible once interactions of characteristics are considered. I propose a method to construct a stochastic discount factor (SDF) when the set of characteristics is extended to an arbitrary---potentially infinitely-dimensional---set of non-linear functions of original characteristics. The method borrows ideas from a machine learning technique known as the "kernel trick" to circumvent the curse of dimensionality. I find that allowing for interactions and non-linearities of characteristics leads to substantially more efficient SDFs; out-of-sample Sharpe ratios for the implied MVE portfolio double.

(with Denis Sosyura)

BibTeX

Abstract: We exploit staggered removals of interstate banking restrictions to identify the causal effect of access to credit on households’ stock market participation and asset allocation. Using micro data on retail brokerage accounts and proprietary data on personal credit histories from TransUnion, we document two effects of the loosening of credit constraints on households’ financial decisions. First, households enter the stock market by opening new brokerage accounts. Second, households increase their asset allocation to risky assets and reduce their allocation to cash, consistent with a lower need for precautionary savings. The effects are stronger for younger and more credit constrained investors. Overall, we establish one of the first direct links between access to credit and households’ investment decisions.