Time-varying Risk Premia Research Articles

The Effectiveness of Asset Pricing Models Under Special Conditions: Evidence from the COVID-19 Pandemic, Emerging Markets, and Financial Crises

Asset pricing models are important tools in finance. However, special market conditions can make them highly ineffective. This paper evaluates the performance of classical asset pricing models (that is, CAPM and Fama-French models) under three specific scenarios: the COVID-19 pandemic, emerging markets, and financial crises. Recent research and market data are reviewed to conclude that these models have very low efficiency in times of extreme occurrences for capturing proper asset valuations. Our findings reveal that standard models lose a substantial part of their explanatory power in periods of crises while new context-specific risk factors come into existence in other exceptional conditions. This work argues for the inclusion of liquidity and tail risk considerations, especially during market stress, as we also observe a greater need for more dynamic and adaptive modeling approaches that capture time-varying risk premia and factor loadings. The findings drive home the point that standard asset pricing models cannot be applied across the board in all market conditions and stress the need for developing more flexible and situation-specific valuation tools. Therefore, this research lies in its dual contribution, both in academic terms and practical finance, by providing an understanding of the behavior of asset pricing models in extreme markets and giving indications for future model development.

Experiences, demand for risky investments, and implications for price dynamics

Personal experiences can impact investors’ risk taking, and this can explain market phenomena such as time-varying risk premia, asset price bubbles or wage–price spirals. Establishing the link from individual experiences to market outcomes is challenging, as together with experiences, several decision-relevant factors simultaneously change. The present work investigates the impact of prior experiences on subsequent investments in a laboratory experiment without confounds, which allows for the control of various factors that usually are correlated with experience. The results show that high (low) previously experienced outcomes lead to more (less) investment in a risky asset, even in a condition where experiences do not provide new information and should be ignored. A reinforcement learning model captures the observed individual behavior and allows us to explain market price dynamics. The experience effect on risk taking informs behavioral theories of markets and provides a cognitive explanation for trend-following and self-enforcing market dynamics.

Empirical Asset Pricing with Score-Driven Conditional Betas

Abstract We develop a novel empirical asset pricing framework to estimate time-varying risk premia, building upon score-driven conditional betas models. First, we extend the theory by establishing the asymptotic distribution of standard test statistics, allowing us to assess the significance of a given factor in the regression. Additionally, we introduce a bootstrap procedure and establish its validity. Second, we propose a two-step estimation procedure to recover time-varying risk premia. We illustrate the performance of our tests and risk premia estimation through simulations. Third, we estimate a time-varying premium associated with a carbon risk factor in the cross-section of U.S. industry portfolios.

Robust asset-liability management games for n players under multivariate stochastic covariance models

This paper investigates a non-zero-sum stochastic differential game among n competitive CARA asset-liability managers, who are concerned about the potential model ambiguity and aim to seek the robust investment strategies. The ambiguity-averse managers are subject to uncontrollable and idiosyncratic random liabilities driven by generalized drifted Brownian motions and have access to an incomplete financial market consisting of a risk-free asset, a market index and a stock under a multivariate stochastic covariance model. The market dynamics permit not only stochastic correlation between the risky assets but also path-dependent and time-varying risk premium and volatility, depending on two affine-diffusion factor processes. The objective of each manager is to maximize the expected exponential utility of his terminal surplus relative to the average among his competitors under the worst-case scenario of the alternative measures. We manage to solve this robust non-Markovian stochastic differential game by using a backward stochastic differential equation approach. Explicit expressions for the robust Nash equilibrium investment policies, the density generator processes under the well-defined worst-case probability measures and the corresponding value functions are derived. Conditions for the admissibility of the robust equilibrium strategies are provided. Finally, we perform some numerical examples to illustrate the influence of model parameters on the equilibrium investment strategies and draw some economic interpretations from these results.

Debt-stabilizing properties of GDP-linked securities: A macro-finance perspective

We study the debt-stabilizing properties of indexing debt to GDP using a consumption-based macro-finance model. To this end, we derive quasi-analytical pricing formulas for any type of bond/equity by exploiting the discretization of the state-space, making large-scale simulations tractable. We find that GDP-linked security prices would embed time-varying risk premiums of about 40 basis points. For a fixed budget surplus, issuing GDP-linked securities does not imply more beneficial debt-to-GDP ratios in the long-run, while the debt-stabilizing budget surplus is more predictable at the expense of being higher. Our findings call into question the view that such securities tame debt.

Mispricing in linear asset pricing models

ABSTRACT In the framework of a reduced-form asset pricing model featuring linear-in-instrument betas and time-varying risk premiums and allowing for missing factors, I propose a measure of mispricing that is largely free from the bias due to missing factors or missing instruments. Applying the model to U.S. equity data, I find evidence of mispricing in stock returns. A mispricing-based zero-dollar investment strategy intersecting momentum and contrarian horizons is highly profitable when applied to both firm- and portfolio-level returns, even after controlling for Fama-French factors, momentum and liquidity effects. Focusing on momentum, I find that the phenomenon is partially caused by the mispricing that does not vary with macro variables. Time-varying betas reduce the mispricing by 40% or better.

Moment Conditions and Time-Varying Risk Premia

Moment Conditions and Time-Varying Risk Premia

Risky Gravity

Abstract We consider the canonical trade model with heterogeneous firms, love for variety and trade costs, and integrate it in the consumption CAPM model. This yields a structural gravity equation that includes an additional factor related to risk premia. Empirical evidence based on firm-level data confirms the importance of cross-sectional heterogeneity in risk and time-varying risk premia to shape bilateral trade flows. The structural gravity model augmented to account for fluctuations in risk premia offers a compelling explanation for trade collapses during abrupt economic downturns.

Robust optimal asset-liability management with mispricing and stochastic factor market dynamics

This paper investigates a robust optimal asset-liability management problem under an expected utility maximization criterion. More specifically, the manager is concerned about the potential model uncertainty and aims to seek the robust optimal investment strategies. We incorporate an uncontrollable random liability described by a generalized drifted Brownian motion. Also, the manager has access to an incomplete financial market consisting of a risk-free asset, a market index with potentially path-dependent, time-varying risk premium and volatility, and a pair of mispriced stocks. The market dynamics are assumed to rely on an affine-form, square-root factor process and the price error is modeled by a co-integrated system. We adopt a backward stochastic differential equation approach hinging on the martingale optimality principle to solve this non-Markovian robust control problem. Closed-form expressions for the robust optimal investment strategies, the probability perturbation process under the well-defined worst-case scenario and the corresponding value function are derived. The admissibility of the robust optimal controls is verified under some technical conditions. Finally, we perform some numerical examples to illustrate the effects of model parameters on the robust investment strategies and draw some economic interpretations from these results.

When do investors go green? Evidence from a time-varying asset-pricing model

This study employs individual stock returns to examine the evolution of the greenium, which is the risk premium linked to firms’ carbon emissions and environmental transparency. We estimate an asset-pricing model with time-varying risk premia, in which the greenium is associated with a priced ‘greenness and transparency’ factor. We show that investors in the European equity market tend to accept lower returns, ceteris paribus, and hold greener and more transparent assets when economic shifts toward low carbon become more credible. This occurred after the Paris Agreement, the first global climate strike, and the announcement of the EU Green Deal. Opposite signals, such as increases in the prices of oil or critical minerals for the low-carbon transition, are associated with increases in the greenium; that is, more polluting firms are perceived as less risky.

High Discounts and Low Fundamental Surplus: An Equivalence Result for Unemployment Fluctuations

We establish an observational equivalence between unemployment fluctuations of the Diamond-Mortensen-Pissarides search economy augmented with time varying risk premia and an otherwise identical economy without risk premia but with a time varying value of leisure. This equivalence holds for general risk premia processes and allows us to view the effects of different models of risk premia as operating through a single channel—one that alters the value of leisure. We derive simple expressions for semielasticities of labor market tightness with respect to productivity and risk premium shocks. We show wages can be used to detect misspecification in the discount rate process used in hiring decisions. This paper was accepted by Lukas Schmid, finance. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.03712 .

Momentum turning points

We use slow and fast time-series momentum to characterize four stock market cycles—Bull, Correction, Bear, and Rebound. The steep market declines of Bears concentrate in high-risk states, yet predict negative expected returns, which is difficult to rationalize by most models of time-varying risk premia. Using a model to analyze slow and fast momentum strategies, we estimate both relatively high mean persistence and realization noise in U.S. stock market returns. Intermediate-speed momentum portfolios, formed by blending slow and fast momentum strategies, translate predictive information in market cycles into positive unconditional alpha, for which we propose a novel decomposition.

Score-driven asset pricing: Predicting time-varying risk premia based on cross-sectional model performance

This paper proposes a new parametric approach for estimating linear factor pricing models with dynamic risk premia. Time-varying risk prices and exposures follow an observation-driven updating scheme that reduces the one-step-ahead prediction error from a cross-sectional factor model at the current observation. This agnostic approach is particularly useful in situations where predictors are unknown or of uncertain quality. Updating schemes for elliptically distributed returns are derived and propose cross-sectional regression errors as driving sequence for the parameter dynamics. Estimation and inference are performed by likelihood maximization. A simulation study confirms that the novel method is capable of filtering and predicting substantial risk price movements. The empirical performance of the method is illustrated by an application to a panel of equity portfolios.

Pricing Kernels and Risk Premia implied in Bitcoin Options

Bitcoin Pricing Kernels (PKs) are estimated using a novel data set from Deribit, the leading Bitcoin options exchange. The PKs, as the ratio between risk-neutral and physical density, dynamically reflect the change in investor preferences. Thus, the PKs improve the understanding of investor expectations and risk premiums in a new asset class. Bootstrap-based confidence bands are estimated in order to validate the results. Investors are heterogeneous in their risk profiles and preferences with respect to volatility and investment horizon. The empirical PKs turn out to be U-shaped for short-dated instruments and W-shaped for long-dated instruments. We find that investors are willing to pay a substantial risk premium to insure themselves against short-term price movements. The risk premium is smaller for longer-dated instruments and their traders are risk averse. The shape of the empirical PKs reveals the existence of a time-varying risk premium. The similarity between the shape of empirical PKs for Bitcoin and other markets that represent aggregate wealth shows that Bitcoin is becoming an established asset class.

Business Cycles, Regime Shifts, and Return Predictability

AbstractConsistent with the empirical properties of the consumption data, I develop a model in which consumption and dividend growth follow regime-switching dynamics. I show that regime-shift risk is priced in the model. Regime-shift risk exhibits dominant influence on asset prices: It generates a high equity premium and also induces time-varying risk premiums. The model explains major business cycle-dependent asset market phenomena and, in particular, the stronger predictability of stock returns during recessions.

A penalized two-pass regression to predict stock returns with time-varying risk premia

We develop a penalized two-pass regression with time-varying factor loadings. The penalization in the first pass enforces sparsity for the time-variation drivers while also maintaining compatibility with the no-arbitrage restrictions by regularizing appropriate groups of coefficients. The second pass delivers risk premia estimates to predict equity excess returns. Our Monte Carlo results and our empirical results on a large cross-sectional data set of US individual stocks show that penalization without grouping can yield to nearly all estimated time-varying models violating the no-arbitrage restrictions. Moreover, our results demonstrate that the proposed method reduces the prediction errors compared to a penalized approach without appropriate grouping or a time-invariant factor model.

A conditional higher-moment CAPM

This paper investigates whether dynamic and moment extensions to the traditional CAPM can improve its empirical performance and offer some alternative explanation to the cross-section of average returns on portfolios of stocks double sorted on book-to-market ratios and size. We consider three extensions. First, we introduce time-varying factor loadings obtained from a multivariate GARCH and dynamic conditional correlations. Second, we extend the model to a four-moment CAPM, which incorporates coskewness and cokurtosis. Finally, we allow for time-varying risk premia, based on a Markov-switching process. Our results confirm that the higher-moment CAPM does not perform well in its unconditional version, but its performance is significantly improved when we introduce a conditional version that accounts for both time-varying factor loadings and time-varying risk premia. The four-moment CAPM tests lead to a positive total risk premium estimate of 0.67% per month over the period 1926–2021, with all risk premia (beta, coskewness, and cokurtosis) exhibiting the expected theoretical signs.

Time-Varying Risk Premia, Labor Market Dynamics, and Income Risk

Time-Varying Risk Premia, Labor Market Dynamics, and Income Risk

Asymmetric Covariance, Volatility, and Time-Varying Risk Premium: Evidence from the Finnish Stock Market

Asymmetric Covariance, Volatility, and Time-Varying Risk Premium: Evidence from the Finnish Stock Market

Determinants of time-varying equity risk premia in an emerging market

PurposeThis study aims to document the time varying risk premia for market, size, value and momentum factors for an emerging market using a sophisticated conditional asset pricing model. The focus of this study is Turkish stock market denominated in local currency with its peculiar risk premia.Design/methodology/approachThe authors employ Gagliardini et al.'s (2016) econometric method that uses cross-sectional and time series information simultaneously to infer the path of risk premia from individual stocks.FindingsUsing this methodology, the authors assess several conditioning information and conclude that local dividend yield, inflation and exchange rates have the most explanatory power. The authors document the time varying risk premia in Turkey over three decades.Originality/valueExisting studies on dynamic estimation of risk premia lack a consensus as to which state variables should be included and to what extent they impact the magnitude of the premium. The authors extend the conditioning information set beyond the ones existing in the literature to determine variables that are specifically important for an emerging market.