Long-run Risk Research Articles

Government Control, Regulatory Enforcement Actions, and the Cost of Equity

Using a comprehensive manually collected dataset of regulatory enforcement actions against fraud in the Chinese capital market and a difference-in-differences (DID) research design, we examine the impact of such actions on the implied cost of equity and the role of the government as the controlling shareholder in moderating this relationship. We find that regulatory enforcement actions increase firms’ cost of equity, and that government controlling shareholders can mitigate the effect of these actions. Our results are robust to various sensitivity tests, including alternative measures of the cost of equity, alternative samples, additional control variables, and an alternative DID design. Additional analysis provides supporting evidence that the effect of enforcement actions on the cost of equity arises from investors’ perception of higher long-run information risk in the case of fraud firms. Further, government controlling shareholders can mitigate the impact of such actions on the cost of equity by lowering investors’ perceived information risk.

Ambiguity, long-run risks, and asset prices in continuous time

This paper extends the long-run risks (LRR) models coined by Bansal and Yaron (2004) and Bansal, Kiku, and Yaron (2012) with Epstein and Zin’s (1989) recursive preferences into the LRR models with Chen and Epstein’s (2002) recursive multiple-priors utility, which captures the investor’s ambiguity on uncertainties. Our empirical analysis shows that considering ambiguity on uncertainties, in particular, large ambiguity on the long-run risks, in the LRR models can significantly improve the fitting performance of the equity premium and the risk-free rate when using a low relative risk aversion coefficient.

COVID-19 and Conflict: Major Risks and Policy Responses.

The COVID-19 pandemic entails a medium- and long-run risk of heightened political conflict. In this short essay we distinguish four major consequences of COVID-19 that may fuel social tensions and political violence, namely i) spiking poverty, ii) education under stress, iii) potential for repression, and iv) reduced inter-dependence. After discussing them in turn, we will formulate policy recommendations on how to attenuate these risks.

Rare events and long-run risks

Rare events (RE) and long-run risks (LRR) are complementary approaches for characterizing macroeconomic variables and understanding asset pricing. We estimate a model with RE and LRR using long-term consumption data for 42 economies, identify these two types of risks simultaneously from the data, and reveal their distinctions. RE typically associates with major historical episodes, such as world wars and depressions and analogous country-specific events. LRR reflects gradual processes that influence long-run growth rates and volatility. A match between the model and observed average rates of return on equity and short-term bonds requires a coefficient of relative risk aversion, γ, around 6. Most of the explanation for the equity premium derives from RE, although LRR makes a moderate contribution. However, LRR helps in fitting the Sharpe ratio. Generating good matches to the equity premium and Sharpe ratio simultaneously is still challenging.

A Consumption-Based Identification of Global Economic Uncertainty

This paper identifies a global uncertainty factor by estimating an international asset pricing model featuring macroeconomic uncertainty with long-run risk factors. The global factor captures the time-varying fluctuations of common stochastic volatilities of consumption and dividend growths for countries, and reflects uncertainty in that it generates the highest volatility of volatility in transition period. The model quantitatively explains key asset pricing moments, and the estimated factor sharply increases during major international adverse events. Shocks to our global economic uncertainty factor significantly account for the likelihood of key economic and financial events, and outperforms existing measures of economic and financial uncertainties.

Geopolitical risk and renewable energy stock markets: An insight from multiscale dynamic risk spillover

This paper investigates the risk spillovers from geopolitical risk to five renewable energy stock markets by measuring four types of (normalized) delta conditional Value-at-Risk incorporating the variational mode decomposition and time-varying copula approaches, and further tests the possible asymmetries of risk spillovers. The empirical results manifest that, there are significant risk spillovers from geopolitical risk to renewable energy stock markets and the risk spillovers do not exhibit as clear positive or negative pattern. Next, the asymmetries of risk spillovers widely exist on the following three facets. First, the risk spillovers from stock and oil market uncertainties are obviously higher than that from geopolitical risk in most cases, whereas geopolitical risk manifests similar short-run effects on China’s renewable energy stock market as the other two uncertainties. Second, the downside risks of renewable energy stock markets are more sensitive to the variations of stock and oil market uncertainties, while the risk spillovers from geopolitical risk are more symmetric during bull and bear market periods. Finally, there are significantly greater long-run risk spillovers to China’s renewable energy stock market. Conversely, the other four markets are more heavily shocked in the short-run.

Does learning by observing matter for M&As? International evidence from the insurance industry

ABSTRACT This paper examines the role of learning by observing in insurance mergers and acquisitions (M&As) by employing an international sample across 18 countries spanning the years 1990 to 2014. The empirical results support a view of semi-strong market efficiency: the long-run improvements in financial performance and risk profiles are significantly related to past M&As in the insurance industry. Moreover, we find evidence of more accurate stock market predictions of long-run financial performance and risk profiles if there are more recent insurance merger activities. This paper provides a new explanation for the controversy observed in the failure of insurance M&As to create value.

Leisure and long-run risks: An empirical evaluation on value premium puzzle

I study the ability of a long-run risk model, with nonseparable leisure and consumption, to price the cross-section of U.S. equity returns over the 1948–2015 period. The stochastic discount factor features innovations to future leisure and consumption growth as factors. The model performs well, in terms of a variety of criteria, relative to competing models in explaining the cross-section of the spread in size and value portfolios.

Price Dividend Ratio and Long-Run Stock Returns: A Score-Driven State Space Model

–In this article, we develop a general framework to analyze state space models with time-varying system matrices, where time variation is driven by the score of the conditional likelihood. We derive a new filter that allows for the simultaneous estimation of the state vector and of the time-varying matrices. We use this method to study the time-varying relationship between the price dividend ratio, expected stock returns and expected dividend growth in the United States since 1880. We find a significant increase in the long-run equilibrium value of the price dividend ratio over time, associated with a fall in the long-run expected rate of return on stocks. The latter can be attributed mainly to a decrease in the natural rate of interest, as the long-run risk premium has only slightly fallen.

Macro-Finance Decoupling: Robust Evaluations of Macro Asset Pricing Models

This paper shows that robust inference under weak identification is important to the evaluation of many influential macro asset pricing models, including long-run risk models and (time-varying) rare-disaster risk models. Building on recent developments in the conditional inference literature, we provide a novel conditional specification test by simulating the critical value conditional on a sufficient statistic. This sufficient statistic can be intuitively interpreted as a measure capturing the macroeconomic information decoupled from the underlying content of asset pricing theories. Macro-finance decoupling is an effective way to improve the power of the specification test when asset pricing theories are difficult to refute because of a severe imbalance in the information content about the key model parameters between macroeconomic moment restrictions and asset pricing cross-equation restrictions. For empirical application, we apply the proposed conditional specification test to evaluate a time-varying rare-disaster risk model and construct data-driven robust model uncertainty sets. The supplemental appendix can be found at: https://ssrn.com/abstract=3609598. The additional materials can be found at: https://ssrn.com/abstract=3787125.

Bayesian Estimation of Long-Run Risk Models Using Sequential Monte Carlo

We propose a likelihood-based Bayesian method that exploits up-to-date sequential Monte Carlo methods to efficiently estimate long-run risk models in which the conditional variance of consumption growth follows either an autoregressive (AR) process or an autoregressive gamma (ARG) process. We use the U.S. quarterly consumption and asset returns data from the postwar period to implement estimation. Our findings are: (1) informative priors on the preference parameters can help to improve model performance; (2) expected consumption growth has a very persistent component, whereas consumption volatility is less persistent; (3) while the ARG-based model performs better than the AR-based one statistically, the latter could fit asset returns better; and (4) the solution method matters more for estimation in the AR-based model than in the ARG-based model.

Fundamental Sources of the Time Variation in Equity Risk Levels

I propose an asset-pricing model with preference shocks and contemporaneous cash-flow risk that can explain key asset-pricing patterns related to business cycle. In this consumption-based model with preference shocks, contemporaneous cash-flow risk of equities drives the cross section of risk premia in bad times, i.e. during periods with a high recession probability, relatively more than in good times. This model makes new predictions about the conditional relevance of cash flow risk for asset prices that are confirmed in data. Unlike in models with external habits or long-run risks, a model with preference shocks correlated with business-cycle shocks further implies that reasonable quantities of contemporaneous cash-flow risk have a significant effect on conditional risk premia of assets and return volatility.

An energy-based measure for long-run horizon risk quantification

Capital requirements for financial institutions are based on the accurate quantification of the inherent risk. To this end, time is the important parameter for all the well-established risk measures, whereas risk managers make no explicit distinction between the information captured by patterns of different frequency content. Accordingly, the original full-time-resolution series of returns is considered, regardless of the selected trading horizon. To address this issue, we propose a novel risk quantification method exploiting the time-evolving energy distribution of returns, which is expressed by the sum of squared magnitudes of a set of transform coefficients. Specifically, a wavelet-based time-scale decomposition is applied first on the returns series to extract the energy contribution of the wavelet coefficients at multiple frequencies. Then, the statistics of an optimal subset of frequencies are linearly combined to estimate the overall risk at a given trading horizon. Most importantly, our proposed energy-based method can be coupled with the commonly used quantile-based risk measures to enhance their performance. The experimental results reveal an increased robustness of our method at efficiently controlling under- or over-estimated risk values, especially for long-run horizons.

Insurance against Long-Run Volatility Risk: Demand, Supply, and Pricing

Despite its importance implied in asset pricing and macroeconomic models, insurance against long-run volatility risk has received little empirical documentation regarding its demand, supply, or pricing. This paper bridges the gap. First, I show that households have directly purchased large quantities of insurance against long- run volatility risk through the minimum return guarantees available in variable annuities, a form of retail retirement and savings product offered by life insurance companies. Total net assets with such insurance grew from zero when the guarantees were first introduced in the early 2000s to close to $1 trillion in 2015. To supply the guarantees to households, life insurance companies hedged themselves with large quantities of long-maturity (> 5Y) options and variance swaps, which led to a sharp increase in the prices of these long-term volatility assets: the ten- year implied volatility increased from 20.0% before 2000 to 27.3% afterwards while the short-term counterpart (VIX) has remained unchanged (from 19.2% to 19.7%). Insurers’ hedging activities therefore explain the significant steepening of volatility term structure in the early 2000s. Relative to the price they paid on hedging, how- ever, the price that life insurance companies charged on the guarantees was much lower, at 15.2% implied volatility prior to the Great Recession. I show evidence of extensive product-cross subsidization – under-pricing of guarantees was used to induce sales and lock in customers that would be subject to over-priced base fees and mutual fund expenses.

The Present-Value Model of the Exchange Rate with a Persistently Time-Varying Risk Premium: Evidence from the Dollar-Yen Rate

In this study, I formulate a present value model of the exchange rate with a risk premium and introduce exchange rate risk exposure as a factor of the persistently time-varying risk premium. The present value model incorporates expectations for the distant future, and therefore, indicates that spot exchange rate variations reflect changes in long-run future interest rate differential and exchange rate expectations, in addition to a risk premium for long-run risk exposure. I also conduct empirical analyses using mainly the USD/JPY rate and other exchange rates against the USD. The Japanese current account balance provides a better estimation of the change in USD/JPY rate market risk exposure as USD invoiced trades are prevalent in Japan. Then, I demonstrate the possibility that a persistently time-varying risk premium offsets the effect of the interest rate differential on exchange rate variations, which can be a solution to the uncovered interest rate parity puzzle.

Twisted probabilities, uncertainty, and prices

A decision maker constructs a convex set of nonnegative martingales to use as likelihood ratios that represent alternatives that are statistically close to a decision maker’s baseline model. The set is twisted to include some specific models of interest. Max–min expected utility over that set gives rise to equilibrium prices of model uncertainty expressed as worst-case distortions to drifts in a representative investor’s baseline model. Three quantitative illustrations start with baseline models having exogenous long-run risks in technology shocks. These put endogenous long-run risks into consumption dynamics that differ in details that depend on how shocks affect returns to capital stocks. We describe sets of alternatives to a baseline model that generate countercyclical prices of uncertainty.

Evaluating Private Equity Performance Using Stochastic Discount Factors

We examine the performance of 2,790 private equity (PE) funds incepted during 1979-2008 using Stochastic Discount Factors (SDFs) implied by the two leading consumption-based asset pricing models (CBAPMs) — external habit and long-run risks — as their assumptions appear consistent with investment objectives of avid PE investors. In contrast to CAPM-based inference, venture funds did not destroy value under these CBAPMs in post-2000 vintages and may even have outperformed buyouts and generalists in the full sample. We find that 2007-08 venture vintages provide a better hedge for post-crises consumption shocks than other types of PE, and that the temporal variation in PE excess returns is significantly smaller under CBAPMs. Our contribution is also methodological. We extend the realized risk premia matching insight of Korteweg and Nagel (2016) to a more general class of SDFs, namely portfolio-specific discount factors that reflect non-tradeable assets unspanned by standard benchmarks. To this end, we propose a more efficient estimation of SDF parameters in this context and develop a finite sample bias correction for NPV-based inference with long-duration assets.

Uncertainty, Long-Run, and Monetary Policy Risks in a Two-Country Macro Model

We study international currency risk in a two-country dynamic stochastic general equilibrium model under incomplete markets. The underlying sources of risk are direct shocks to productivity growth, shocks to a long-run risk component of productivity growth, shocks to a stochastic volatility component of productivity growth, and shocks to monetary policy. The long-run risk and stochastic volatility shocks have the interpretation of aggregate demand shocks. Cross-country heterogeneity in the model arises from three sources: differences in the long-run risk and stochastic volatility process parameters that we estimate using United States and Japanese total factor productivity data, differences in monetary policy parameters, and differences in export pricing. The driving force behind currency risk is heterogeneity in precautionary saving. Differences in monetary policy can generate moderate currency risk, but structural differences in productivity growth are more important. Export pricing conventions are not important sources of currency risk. Stochastic volatility shocks are key to generating volatility in the currency risk premium, but they do not help at all in explaining the forward premium bias/anomaly.

Long-Run Risk, the Timing of Its Resolution, and the Interpretation of the Long-Run Risk Model

Long-Run Risk, the Timing of Its Resolution, and the Interpretation of the Long-Run Risk Model

Price Dividend Ratio and Long-Run Stock Returns: A Score Driven State Space Model

In this paper we develop a general framework to analyze state space models with time-varying system matrices where time variation is driven by the score of the conditional likelihood. We derive a new filter that allows for the simultaneous estimation of the state vector and of the time-varying parameters. We use this method to study the time-varying relationship between the price dividend ratio, expected stock returns and expected dividend growth in the US since 1880. We find a significant increase in the long-run equilibrium value of the price dividend ratio over time, associated with a fall in the long-run expected rate of return on stocks. The latter can be attributed mainly to a decrease in the natural rate of interest, as the long-run risk premium has only slightly fallen. JEL Classification: C22, C32, C51, C53, E31