Long-run Risk Research Articles

Long-run risk in stationary vector autoregressive models

This paper introduces a local-to-unity/small sigma model for stationary processes with long-range persistence and non-negligible long-run prediction and estimation risks. The model represents a process containing unobserved short and long-run components measured on different time scales. The short-run component is defined in calendar time, while the long-run component evolves in rescaled time with ultra-long units. We develop estimation and long-run prediction methods for time series with multivariate Vector Autoregressive (VAR) short-run components and reveal the impossibility of estimating consistently some of the long-run parameters, which causes significant estimation and prediction risks in the long run. A simulation study and an application to macroeconomic data illustrate the approach.

The endogenous growth and asset prices nexus revisited with closed-form solution

Endogenous growth models exhibit long-run risks, which are considered a potential explanation of the equity premium puzzle. Unlike previous literature, we use a closed-form solution of a simplified model to make the following contributions. First, we derive a set of conditions for a positive and large equity premium. Second, we match a key driver of endogenous growth, the R&D spending-to-GDP ratio. Third, we include a novel discussion on the role of patent obsolescence. Given that the literature concerns the accuracy of loglinear-lognormal solutions, we solve our model numerically with third-order perturbation. We find additional risk correction due to higher-order terms.

Commercial Real Estate in the Face of Climate Risk: Insights from REITs

While climate risk is recognized as a substantial concern in finance and residential real estate, research examining its effects on commercial real estate markets remains limited. In this study, we contribute to this body of knowledge by constructing a firm-level climate risk measure. Our data, collected from the National Oceanic and Atmospheric Administration’s county-level temperature database and a detailed property-level dataset of U.S. equity REITs from 1995 to 2020, enable us to investigate the effects of climate risk on commercial real estate at the firm level. Our findings suggest that REITs with greater exposure to climate risk - characterized by a higher percentage of properties located in counties experiencing abnormally elevated temperature changes - exhibit lower cash flows and firm values, as well as inferior stock returns. These adverse impacts from climate risk persist across various model specifications and control variables. Our study thus illuminates the economic implications of rising temperatures on commercial real estate from a portfolio perspective and provides empirical support for the temperature-based long-run risk model.

The return on everything and the business cycle in production economies

Motivated by recent empirical evidence on returns on equity, bonds, and housing, we study interactions among an economy’s total net worth, consisting of housing and equity, the business cycle, and three specific types of productivity risk: standard, long-run, and disaster. Preferences include habits or follow a generalized recursive form. Procyclical housing adjustments reduce consumption risk as residential investment determines the next-period amount of housing as a fraction of the composite consumption good. The existence of an asset that is safe in real terms and has a positive supply prevents versions with habits or long-run risk from simultaneously replicating risk premia, investment volatility, and housing demand. The disaster risk version replicates these targets. In all versions, a perfectly negative correlation between equity returns and the marginal utility of consumption places the equity Sharpe ratios in the upper bound of any Sharpe ratios (the Hansen–Jagannathan bound). Consequently, replicating Sharpe ratios of housing larger than equity is impossible.

Do macroprudential policies reduce risk spillovers between energy markets?: Evidence from time-frequency domain and mixed-frequency methods

Preventing volatility spillovers between energy markets is essential for maintaining financial stability. Macroprudential policies play an invaluable tool in financial risk monitoring and help to reduce the incidence of systemic risk. However, the effectiveness of macroprudential policies on risk spreads in the energy system is still unclear. This article applies the TVP-VAR (time-varying parameter vector autoregression) spillover methods to capture the risk connectedness between energy markets in the time and frequency domains, and constructs an asymmetric GARCH-MIDAS-MPP model to investigate the influence of macroprudential policies on volatility overflows of the energy system. The results suggest that there are strong risk links between global energy markets and long-term risk resonances play a dominant role. Time-varying risk overflows occur throughout the energy sector, and market turbulence amplifies these risk communications. Whether on a time or frequency horizon, the oil market represents the largest emitter of fluctuation transmissions, while the fuel oil market stands out as the biggest recipient of risk diffusion. We do not observe that macroprudential policies can significantly reduce the average and long-run risk premiums of the energy system. Conversely, our results reveal that macroprudential policies intensify short- and medium-term risk spreads between global energy markets. This paper provides some insight into energy market risk contagion, which is conducive to the improvement of macroprudential policies for energy market risk management.

A consumption-based term structure model of bonds and equity

In this study, I propose a consumption-based asset pricing model to capture the dynamic properties of term structures of bonds and equity. I extend the long-run risks model by introducing a mean-reversion of dividend growth and the external habit formation of a representative agent. The mean-reverting dividend growth generates a negative equity term premium, while the habit formation augments the equity premium and renders an upward-sloping bond yield curve, on average. In addition, fluctuations in the surplus consumption ratio and the conditional variance of consumption growth allow the model to reproduce pro-cyclical variations in bond and equity yield spreads and counter-cyclical variations in bond and equity term premiums, as observed in the U.S. data.

Fiery trails: tourism's forest fire dance

ABSTRACT Tourism drives global economic growth and cultural exchange, but also raises climate vulnerability and forest fire concerns. This study explores the relationship between tourism and forest fires in emerging and advanced economies, aligned with UN's SDGs. Using ARDL model, findings show that a 1% increase in tourism development leads to 1% & 0.575% surge in forest fires in advanced and emerging economies respectively. In the short run, tourism leads to a decrease in forest fires in emerging economies, while in long-run risks increases for both panels of economies. This emphasises the need for eco-friendly practices for sustainable tourism. Governments should prioritise eco-tourism, green infrastructure, and SDG-13, SDG-9, SDG-11 for climate action, tech and sustainable transport.

Risk and causality Co-movement of Malaysia's stock market with its emerging and OECD trading partners. Evidence from the wavelet approach.

The growing trend of interdependence between the international stock markets indicated the amalgamation of risk across borders that plays a significant role in portfolio diversification by selecting different assets from the financial markets and is also helpful for making extensive economic policy for the economies. By applying different methodologies, this study undertakes the volatility analysis of the emerging and OECD economies and analyzes the co-movement pattern between them. Moreover, with that motive, using the wavelet approach, we provide strong evidence of the short and long-run risk transfer over different time domains from Malaysia to its trading partners. Our findings show that during the Asian financial crisis (1997-98), Malaysia had short- and long-term relationships with China, Germany, Japan, Singapore, the UK, and Indonesia due to both high and low-frequency domains. Meanwhile, after the Global financial crisis (2008-09), it is being observed that Malaysia has long-term and short-term synchronization with emerging (China, India, Indonesia), OECD (Germany, France, USA, UK, Japan, Singapore) stock markets but Pakistan has the low level of co-movement with Malaysian stock market during the global financial crisis (2008-09). Moreover, it is being seen that Malaysia has short-term at both high and low-frequency co-movement with all the emerging and OECD economies except Japan, Singapore, and Indonesia during the COVID-19 period (2020-21). Japan, Singapore, and Indonesia have long-term synchronization relationships with the Malaysian stock market at high and low frequencies during COVID-19. While in a leading-lagging relationship, Malaysia's stock market risk has both leading and lagging behavior with its trading partners' stock market risk in the selected period; this behavior changes based on the different trade and investment flow factors. Moreover, DCC-GARCH findings shows that Malaysian market has both short term and long-term synchronization with trading partners except USA. Conspicuously, the integration pattern seems that the cooperation development between stock markets matters rather than the regional proximity in driving the cointegration. The study findings have significant implications for investors, governments, and policymakers around the globe.

Investing in a leveraged world

PurposeThroughout the 21st century, US households have experienced unprecedented levels of leverage. This dynamic has been exacerbated by income shortfalls during the COVID-19 crisis. Leveraging and deleveraging decisions affect household consumption. This study investigates the effect of the dynamics of household leverage and consumption on the stock market.Design/methodology/approachThe authors explore the relation between household leverage and consumption in the context of the consumption capital asset pricing model (CCAPM). The authors test the model's implication that leverage has a negative risk premium by transforming the asset pricing restriction into an unconditional linear factor model and estimate the model using the general method of moments procedure. The authors run time-series regressions to estimate individual stocks' exposures to leverage, and cross-sectional regressions to investigate the leverage risk premium.FindingsThe authors show that shocks to household debt have strong and lasting effects on consumption growth. The authors extend the CCAPM to accommodate this effect and find, using various test assets, a negative risk premium associated with household deleveraging. Looking at individual stocks the authors show that the deleveraging risk premium is not explained by well-known risk factors.Originality/valueThis paper contributes to the literature on the role of leverage in economics and finance by establishing a relation between household leverage and spending decisions. The authors provide novel evidence that households' leveraging and deleveraging decisions can be a fundamental and influential force in determining asset prices. Further, this paper argues that household leverage might explain the small, persistent, and predictable component in consumption growth hypothesised in the long-run risk asset pricing literature.

Detecting identification failure in moment condition models

This paper develops an approach to detect identification failure in moment condition models. This is achieved by introducing a quasi-Jacobian matrix computed as the slope of a linear approximation of the moments on an estimate of the identified set. It is asymptotically singular when local and/or global identification fails, and equivalent to the usual Jacobian matrix which has full rank when the model is globally and locally identified. Building on this property, a simple test with chi-squared critical values is introduced to conduct subvector inferences allowing for strong, semi-strong, and weak identification without a priori knowledge about the underlying identification structure. Monte-Carlo simulations and an empirical application to the Long-Run Risks model illustrate the results.

Toward an economic reformulation of public pension funding

Abstract We propose an economic reformulation of contribution policy integrating: (1) formalization of sustainability as the steady-state contribution rate, incorporating both the expected return on risky assets and a low-risk discount rate for liabilities; (2) derivation of contribution adjustment policies required for convergence toward the target funded ratio and contribution rate; and (3) a stylized optimization framework for simultaneous determination of the target portfolio return and funded ratio. This analysis provides new theoretical insights into the basis for pre-funding vs. pay-as-you-go, resting on the convexity of the long-run risk–return relationship, and also potentially practical guidelines for contribution policy.

The long-run risk premium in the intertemporal CAPM: International evidence

This study investigates whether long-run conditional covariance risk is linked to expected returns in the Intertemporal CAPM framework. We observe that the long-run value risk is positively associated with the expected returns on the global portfolios excluding the US. We also find that the long-run momentum risk is negatively related to the expected returns. In contrast, the long-run market risk is not associated with them, due to the low covariance variation across portfolios. Finally, we uncover that the long-run value premiums were strong for the global and European portfolios before the COVID-19 pandemic.

How far can the long-run risk model with durable goods explain the variation of the yield curve?

A consumption-based, long-run risk equilibrium model with nondurable and durable goods is estimated using US nominal interest rate data. The model generates upward-sloping nominal yield curves and nearly flat real yield curves, implying that the term structure of inflation risk premia is upward-sloping. Though both nondurable and durable consumption have statistically significant explanatory power for the movement of the short-term nominal rate, the overall explanatory power of the model is small. The estimated relation between the durable consumption growth and stochastic discount factor is opposite to that in previous studies that estimate similar models with equity data.

Asset pricing with costly and delayed firm entry

AbstractSurvey evidence tells us that stock prices reflect the risks investors associate with long-run technological change. However, there is a shortage of models that can rationalize long-run risks. Unlike the previous literature assuming a fixed number of products, our model allows for new product varieties that appear in the form of new firms which face entry costs and delay in the entry process. The fixed variety model has a significant limitation in translating macroeconomic volatility into asset return volatility. Our model with growing varieties induces endogenous low-frequency fluctuations in productivity driving large, persistent variations in consumption growth and asset prices. It also changes the valuation of assets through the increase in the volatility of the pricing kernel (with a positive long-run component) and leads to higher excess returns. Our model is motivated by a simple recursively identified VAR model containing quarterly US data 1992Q3-2018Q4 with the following list of variables: total factor productivity, output, a measure of firm entry, and the excess return on stocks.

Fast-Moving Habit: Implications for Equity Returns

AbstractWe find that the Campbell–Cochrane external-habit model can generate a value premium if the persistence of the consumption surplus is sufficiently low. Such low persistence is supported by micro evidence on consumption. If the mean and conditional volatility of consumption growth are highly persistent, as in the Bansal–Yaron long-run risk model, then fast-moving habit can also generate, without eroding the value premium: i) empirically sensible long horizon return predictability; and ii) a price–dividend ratio for market equity that exhibits the high autocorrelation found in the data. Fast-moving habit also delivers several empirical properties of market-dividend strips.

Exploration of industrial risk contagion characteristics and mechanism under geopolitical events: evidence from China

ABSTRACT Based on the TVP-VAR-DY and TVP-VAR-BK models, this article examines the characteristics and mechanisms of systemic risk contagion in the Chinese industries under geopolitical events by selecting data spans from 1 January 2010 to 31 August 2022. First, dynamic analysis of full-sample risk contagion shows that there is a significant climb in total risk during geopolitical events. Then the static analysis of risk contagion in the full sample specifically shows the correlation between risk contagion and industry chain between the financial and real sectors. Besides, the sub-sample analysis illustrates that during geopolitical events such as the Sino-US Trade War, the COVID-19 Pandemic and the Russia-Ukraine Conflict, Chinese industrial stock indexes show short-term risk spillovers from key industries related to geopolitical events, and gradually spread along the industrial chain in the long run compared to the Chinese ‘Stock Market Crash’. Through further mechanistic tests, we find that the irrational behaviour of investors in the market exacerbates short-term risk contagion, while the financial distress of real firms due to financing constraints exacerbates long-term risk contagion. In addition, geopolitical risk, economic uncertainty, and policy uncertainty as macro variables also have an impact on the short-run and long-run risk contagion.

Lifetime asset allocation with long run risk and time various risk aversion

We propose in this article an optimal lifetime asset allocation model in which we simultaneously consider two important stylized facts, long-run risk and time-varying risk aversion. Our model also accounts for the uncertainty and correlation of long-run returns and volatility. Based on American Consumer Expenditure Survey data and macroeconomic data, we have three main findings. First, individual’s risk attitude roughly rises with age, and it has a significant effect on the individual’s best asset allocation choice. Second, two pairs of correlations between the movement of returns and volatility impact an individual’s choice. In the long run, individuals may take the comovement of returns and volatility into account and adjust their optimal investment strategy. The effects of the adjustment term are determined by the direction and strength of the correlations. Third, the economy has a clear business cycle path, and the optimal fraction of risky assets in portfolio vary within a wide range when the risk premium is high during one’s lifetime. We further, based on our data and parameters, perform a simulation to identify the path of the optimal investment strategy. The result implies that individuals and households with lifetime investments such as pension funds should take risk preferences variation into account, and this is especially for older individuals.

Asset Management as Creator of Market Inefficiency

In this paper, we describe how agency frictions in asset management can generate prime violations of the Efficient Markets Hypothesis, such as momentum, value and an inverted risk-return relationship. Momentum in our theory is associated with procyclical fund flows and price over-reaction, and is more pronounced for overvalued assets. The investors who generate the momentum and who are losing from it are those requiring their asset managers to keep their portfolios close to benchmark indices. Our theory suggests a rethinking of asset management contracts. Contracts should employ measures of long-run risk and return, and benchmark indices that emphasize asset fundamentals. There should also be greater transparency on managers’ choice of strategies.

Estimating sentiment and risk in a consumption model: a factor analysis approach

Abstract This empirical paper deals with the impacts of sentiment about the future, short-run risk, and long-run risk in a dynamic economic model of optimal consumption decisions with Schroder and Skiadas [(1999) Journal of Economic Theory 89, 68–126.] continuous-time stochastic recursive preferences. The empirical strategy combines both a latent factor method and a democratic orthogonalization technique. The latent factor method is applied to a large database of macroeconomic indicators, and a democratic orthogonalization technique is used to separate the relative importance of sentiment about the future and long-run risk channels in shaping optimal consumption decisions. The empirical results suggest that consumers with recursive preferences are not indifferent to long-run uncertainty shocks to future consumption prospects. Endogenous consumption variations are driven by a multicomponent mechanism, where on average, the sentiment component accounts for 15.33%, the short-run risk accounts for 16.89%, and the long-run risk pertains to 34.51%.

Stock profiling using time–frequency-varying systematic risk measure

This study proposes a wavelets approach to estimating time–frequency-varying betas in the capital asset pricing model (CAPM) framework. The dynamic of systematic risk across time and frequency is analyzed to investigate stock risk-profile robustness. Furthermore, we emphasize the effect of an investor’s investment horizon on the robustness of portfolio characteristics. We use a daily panel of French stocks from 2012 to 2022. Results show that varying systematic risk varies in time and frequency, and that its short and long-run evolutions differ. We observe differences in short and long dynamics, indicating that a stock’s betas differently fluctuate to early announcements or signs of events. However, short-run and long-run betas exhibit similar dynamics during persistent shocks. Betas are more volatile during times of crisis, resulting in greater or lesser robustness of risk profiles. Significant differences exist in short-run and long-run risk profiles, implying a different asset allocation. We conclude that the standard CAPM assumes short-run investment. Then, investors should consider time–frequency CAPM to perform systematic risk analysis and portfolio allocation.