New Frontiers in Asset Pricing

We introduce a class of interpretable tree-based models (P-Tree) for analyzing (unbalanced) panel data, with iterative and global (instead of recursive and local) split criteria. We apply PTree to split the cross section of returns under the no-arbitrage condition, generating a stochastic discount factor model and diversified test portfolios for asset pricing. P-Tree visualizes nonlinear feature interactions, accommodates time-series splits, and allows interactions between macroeconomic states and firm characteristics. In an empirical study of U.S. equities, data-driven P-Tree reveals that long-term reversal, volume volatility, and industry-adjusted market equity interact to drive cross-sectional return variation, and that inflation constitutes the most critical regime switching when interacting with firm characteristics. P-Tree models consistently outperform observable and latent factor models at pricing individual asset and portfolio returns, while delivering profitable and transparent trading strategies utilizing characteristic interactions. The methodology is broadly applicable in building trees with vectorized outcomes and economic restrictions as split criteria to guard against overfitting and improve model performance.

We develop an endogenous growth model with heterogeneous firms, intermediate goods, and financial frictions, in which misallocation emerges explicitly as a crucial state variable. In equilibrium, misallocation endogenously generates longrun uncertainty about economic growth by distorting innovation decisions, leading to significant welfare losses and risk premia in capital markets. Macroeconomic shocks that affect misallocation are likely to have overly persistent effects on aggregate growth. Using an empirical misallocation measure motivated by the model, we find evidence showing that misallocation captures low-frequency variations in both aggregate growth and stock returns. Empirically, a two-factor model with market and misallocation factors prices size, book-to-market, momentum, and bond portfolios with an R-squared and a mean absolute pricing error close to the Fama-French three-factor model.

I construct a non-parametric pricing kernel with consumption prices and expenditure by decomposing consumer’s indirect utility function. This pricing kernel establishes the fundamental connection between the inter-temporal financial asset-holding and the intra-temporal consumption portfolio. I examine the pricing kernel in explaining variation of expected returns across diverse equity portfolios. This pricing kernel is more successful than traded-factor models and simple consumption-based models. Allowing the generalized non-homothetic preference, I find the price of good requires relatively greater risk compensation in the good-service
two-sector economy. Dissecting the risk premium of expenditure and the risk premium of relative good price, I show that shrinking expenditure share in the good sector helps explain the structural transformation of risk premium.

When the Initial Jobless Claims (IJC) are higher than expected, investors may expect a more generous Federal Government support and drive up the aggregate stock prices through the cash flow channel, leading to a novel "Main Street pain, Wall Street gain'' phenomenon. We provide both time series and cross section evidence. First, we find that, in the past decade, this phenomenon emerges when news articles on IJC announcements also mention fiscal policy keywords more. Second, our main cross-sectional identification exploits the Covid period (April 2020 to March 2021), which features an unprecedented fiscal spending in focus. We find that firms/industries that are expected to suffer more fundamentally, get mentioned more in actual stimulus bills, or have higher obligated funding amounts from the Federal Government show higher individual stock returns when bad IJC news arrives. Lastly, we solve a conceptual asset pricing framework featuring a simple fiscal rule to reconcile our empirical results (e.g., pricing channel, cross-sectional heterogeneity). Our results highlight the important role of fiscal policy expectation as a new mechanism in explaining stock return responses to macro surprises.

Using order flow imbalance to estimate price impact, we find that the price elasticity to demand is higher at more aggregate levels. That is, pure idiosyncratic demand (e.g. buying a stock and hedging out all common return components) commands a smaller price elasticity of approximately two, and the parameter increases monotonically to around five for less diversifiable size-book/market style level demand. The results are consistent with liquidity providers being more reluctant to trade against price dislocations at more aggregate levels, possibly due to risk aversion or portfolio constraints, and inconsistent with information-based mechanisms of price impact. Together with the fact that there are large order flow imbalances at more aggregate levels, our results suggest that investor demand could be more important for driving price fluctuations at more aggregate levels.

We use a fully endogenous asset-pricing model to theoretically explain the performance of “green” and “brown” stocks in the recent years. Our model shows that belief disagreement among investors can explain why the realized returns of green stocks were higher than those of brown stocks, even though brown stocks had higher expected returns ex ante. Our model helps to connect the theoretical asset-pricing literature with recent empirical findings. Our model can be calibrated to quantitatively match the observed green equity premium, the risk-free rate and the shares of green and brown investments made.

Unexpected monetary tightening predicts a contraction in aggregate corporate bonds but an expansion in bank loans. Using micro-data, I demonstrate that large and high rated firms with high collateral value and low default risk rebalance towards bank loans and away from corporate bonds, as the relative spread of bond over loan increases. This demand-side “credit substitution channel” and firm heterogeneity together explain the aggregate evidence. I develop a heterogeneous-agent New Keynesian model where bank loans are senior and safer (collateralized) than defaultable bonds but issued at a greater intermediation cost. My model can quantitatively explain the response of corporate bonds and bank loans with respect to monetary policy surprises. An interest rate hike raises default risk and thus the relative cost of bond financing. In response, large and unconstrained firms substitute bank loans for corporate bond, while constrained firms tend to issue more equity. The redistribution effect of this credit substitution channel amplifies the negative effects of interest rate hike on consumption and investment by 8% and 14%, respectively.

We solve a general equilibrium model of an incomplete market with heterogeneous preferences, identifying first-order and second-order effects. Several long-lived agents with different absolute risk-aversion and discount rates make consumption and investment decisions, borrowing from and lending to each other, and trading a stock that pays a dividend whose growth rate has random fluctuations over time. For small fluctuations, the first-order equilibrium implies no trading in stocks, the existence of a representative agent, predictability of returns, multi-factor asset pricing, and that agents use a few public signals for consumption, borrowing, and lending. At the second-order, agents dynamically trade stocks and no representative agent exist. Instead, both the interest rate and asset prices depend on the dispersion of agents’ preferences and their shares of wealth. Dynamic trading arises from agents’ intertemporal hedging motive, even in the absence of personal labor income.

How do climate risks and heterogeneous climate beliefs impact financial mar-kets? We present novel theoretical predictions and empirical evidence from the mortgage market for properties at risk from sea level rise (SLR). We first develop a competitive search model of defaultable debt contracts with heterogeneous beliefs over future SLR, where property price, loan amount, repayment, and maturity are endogenous. Unlike existing two-period heterogeneous beliefs models, our infinite-horizon model allows for heterogeneity in maturity choices. In equilibrium, climate pessimists are more likely to leverage and to use longer maturity debt relative to optimists, trading their climate risk exposure to banks via long-term defaultable debt contracts. An expansionary monetary policy can induce more leverage by pessimists and make the mortgage market more vulnerable to climate change. We test several of the model implications using a comprehensive propriety dataset of single-family home sales and associated mortgage contracts along the U.S.Atlantic Coast from 2001 to 2016. In line with our theory, we find that purchases of houses more exposed to SLR risk are more likely to be leveraged and tend to use mortgage contracts with longer maturity, despite lower property prices (relative to similar but less exposed homes). These results are driven by buyers from counties with more pessimistic climate beliefs, who are more likely aware of future climate risks. Our results highlight the importance of heterogeneous climate beliefs in understanding the effects of climate change on the financial system

Portfolio allocation decisions increasingly incorporate social values. We develop a tractable framework to study how competition between investors mediates the creation of social impact. Relative to the most common social-investing strategies, we identify alternative strategies that result in higher welfare and higher financial returns. From the firm perspective, increasing profitability can have a greater social impact than directly increasing social value creation. Whether investors and firms exhibit positive or negative assortative matching depends on the nature of social preferences. We present empirical evidence that socially-guided mutual funds allocate their capital inefficiently from the perspective of generating impact and financial returns.

Social discounting is a critical and contentious issue in evaluating the costs and benefits of climate policy, infrastructure projects, and other long-term public policies. In this paper, we look at the asymptotic statistical properties of the Weitzman (2001) gamma discounting in a dynamic stochastic continuous-time framework where individual discount rates are heterogeneous. We use the Fokker-Planck equation approach to compute the time-dependent distribution density of individual discount rates and the associated certainty-equivalent social discount factor and rate. We show that the certainty-equivalent social discount rate includes the Weitzman’s gamma discounting rate as a special case, in addition to terms capturing changes in the shape of the heterogeneity distributions of discount rates over time. It is shown that for short time horizons, the path of the social discount rate computed from the dynamic stochastic framework is in near perfect agreement with the Weitzman approach. However, for larger time horizons, the asymptotic statistical behavior of the certainty-equivalent social discount rate differs from the Weitzman’s discounting path because the statistical property of discount rates for the dynamic case is no longer stationary over large time horizons. Numerical simulations illustrate how changes in the initial distribution of discount rates and uncertainty shocks would lead to deviations from the Weitzman’s gamma discounting. Using several examples, we show that greater spread of the initial heterogeneity distribution of discount rates causes the certainty-equivalent social discount rate to decline more rapidly. In addition, the effects of truncating the initial distribution as well as the effects of the stochastic fluctuations on the certainty-equivalent discounting path and its degree of representativity for heterogeneous discounting agents are discussed.

Climate change affects financial health of corporate pension plans. Using a representative sample of US corporate defined benefit pension plans, we show that firms affected by climate disasters are more likely to freeze their plans. Relatedly, the affected firms reduce employer contributions per participant, experience lower pension profitability, increase plan investments toward riskier assets in a failed effort to boost plan returns, and transfer assets from the pension. Using corporate defined contribution pension plans, we find that being hit by climate disaster, plan participants allocate more assets in equity, and they experience greater returns on its pension assets. Our evidence suggests that affected firms respond to the climate disaster shock by extracting internal cash flows from pension assets.

The extant literature predicts market returns with "simple" models that use only a few parameters. Contrary to conventional wisdom, we theoretically prove that simple models severely understate return predictability compared to "complex" models in which the number of parameters exceeds the number of observations. We empirically document the virtue of complexity in US equity market return prediction. Our findings establish the rationale for modeling expected returns through machine learning.

We develop a novel measure of firm-level inflation exposure by applying a deep learning approach to firms’ earnings conference call transcripts. Our methodology not only identifies sentences that discuss price changes, but also differentiates price increases from price decreases, and input prices from output prices. In the time series, our aggregate inflation exposure measure strongly correlates with official inflation measures. In the cross section, firms that have higher inflation exposure experience a strong negative stock price reaction to earnings calls. Firms’ market power attenuates the negative market reaction. Consistent with the market reaction, firms with higher inflation exposure have higher future costs of goods sold due to an increase in raw material costs and wages. We also observe a negative drift in the firm’s stock return after the earnings call, suggesting that it takes time for investors to fully incorporate firm-level inflation exposure into stock prices.

This paper builds a model of interactive belief hierarchies to derive the conditions under which judging an arbitrage opportunity requires Bayesian market participants to exercise their higher order beliefs. Methodologically, the approach of the paper is to take the standard asset pricing setup that gives rise to arbitrage and transform it into a Bayesian decision problem faced by a representative market agent. As a Bayesian, such an agent must carry a complete recursion of priors over the uncertainty about future asset payouts, the strategies employed by other market participants that are aggregated in the price, other market participants’ beliefs about the agent’s strategy, other market participants beliefs about what the agent believes their strategies to be, and so on ad infinitum. Defining this infinite recursion of priors — the belief hierarchy so to speak — along with how they update gives the Bayesian decision problem equivalent to the standard asset pricing formulation of the question. In this setting, any update to the belief hierarchy of an agent is one of two kinds: a change in belief about the asset payouts, or a change in belief about the strategies and beliefs employed by other market participants. The main results of the paper show that an arbitrage trade corresponds to special updates of the second kind. When an agent anticipates market participant responses will be generated using k levels of the belief hierarchy but finds that the actual asset prices are supported by k + 1 or higher levels, there is an arbitrage opportunity. It is shown that the presence of arbitrage depends on the degree of optimality of the belief hierarchies employed by market agents and responsiveness of the price aggregation mechanism, and is closely related to market tatonnement. The paper connects the foundations of finance to the foundations of game theory by identifying a bridge from market arbitrage to market participant belief hierarchies

I develop a hybrid methodology that incorporates an econometric identification strategy into artificial neural networks when studying conditional latent factor models. The time-varying betas are assumed to be unknown functions of numerous firm characteristics, and the statistical factors are population cross-sectional OLS estimators for given beta values. Hence, identifying betas and factors boils down to identifying only the function of betas, which is equivalent to solving a constrained optimization problem. For estimation, I construct neural networks customized to solve the constrained optimization problem, which gives a feasible non-parametric estimator for the function of betas. Empirically, I conduct my analysis on a large unbalanced panel of monthly data on US individual stocks with around 30, 000 firms, 516 months, and 94 characteristics. I find that 1) the hybrid method outperforms the benchmark econometric method and the neural networks method in terms of explaining out-of-sample return variation, 2) betas are highly non-linear in firm characteristics, 3) two conditional factors explain over 95% variation of the factor space, and 4) hybrid methods with literature-based characteristics (e.g., book-to-market ratio) outperform ones with COMPUSTAT raw features (e.g., book value and market value), emphasizing the value of academic knowledge from an angle of Man vs. Machine.

One implication of the Black-Scholes arbitrage theory of option pricing is that introducing options has no impact on anything including social welfare. One justification of options is that there are transaction costs including the bid-ask spread to buy or sell stocks for risk management hedging, and options reduce those costs. Moreover, investors often face constraints in shorting stocks or borrowing bonds in reality. We apply numerical dynamic programming methods to solve dynamic portfolio optimization problems with transaction costs and constraints for the case where only stocks and bonds are available, and compare that to investor behavior and welfare after options are introduced. Our results show that the options have some social value, but it is becoming small as transaction costs decline.