Long Run Risk ModelEdit
The Long Run Risk Model (LRRM) is a macro-finance framework that explains how asset prices incorporate persistent, fundamental risks to the economy’s growth path. Developed and refined most notably by Bansal and Yaron, the model extends traditional consumption-based asset pricing by allowing low-frequency, long-horizon components of consumption to carry risk premia. In doing so, it helps reconcile observed patterns in returns with plausible macroeconomic forces, rather than relying solely on short-term mispricing or highly behavioral explanations.
At its core, the LRRM attributes part of the time-varying premia on stocks and bonds to two persistent risks: (1) shifts in the expected growth rate of aggregate consumption, and (2) fluctuations in the volatility of consumption itself. Because these risk factors unfold slowly over time, even modest risk aversion can lead to sizable compensation demanded by investors for bearing them. The framework thus provides a link between macroeconomic fundamentals and asset prices, offering a parsimonious account of phenomena such as the equity premium puzzle and the sensitivity of bond yields to macro news. For more on the general theory of asset prices under risk, see Asset pricing and Stochastic discount factor.
Core concepts
Overview of the model: The LRRM assumes a forward-looking, representative agent whose intertemporal choices hinge on the evolution of consumption over time. The stochastic discount factor that prices assets responds to predictable components of consumption growth, particularly the long-run trend in expected consumption and its volatility. See Long-Run Risk Model for the formal structure.
Long-run risks: The model emphasizes two persistent drivers: a slowly evolving path for consumption growth and a persistent, time-varying component of its risk. These low-frequency factors generate a nontrivial risk premium for assets, especially when investors anticipate that future growth will be uncertain orVariable in the months and years ahead. See consumption growth and risk premium for related concepts.
Time-varying risk premia: Because the long-run factors evolve gradually, the premium investors require for holding risky assets should itself vary over time. This helps explain why returns on equities and long-term bonds show persistent periods of higher or lower risk-adjusted performance, even when instantaneous risk is not extreme. See risk premium and asset pricing.
Economic intuition: The LRRM argues that assets price not only current consumption relative to future consumption, but also exposure to the risk that long-run growth and its uncertainty will change. In a world where households derive utility from consumption today and in the future, the intertemporal trade-off places a premium on assets that are sensitive to these long-run risks. See consumption-based asset pricing.
Mathematical structure (high level): The stochastic discount factor (SDF) in the LRRM is linked to the growth rate of consumption and its volatility, with adjustment for risk aversion. While the precise equation involves CRRA-style utility and coupled state processes, the practical takeaway is that asset prices reflect the covariance between asset payoffs and the long-run consumption risk factors. See Stochastic discount factor and consumption for foundational ideas.
Implications for policy and markets: If long-run consumption risk is a meaningful driver of asset prices, then macro stabilization—through prudent fiscal and monetary policy—can indirectly affect risk premia and expected returns. Proponents argue this lends support to rules-based, credible stabilization frameworks, while critics/debaters point to the limits and distributional questions of policy interventions. See macroeconomics and fiscal policy for related topics.
Evidence and estimation
Empirical support: A large body of work finds that factors tied to long-run consumption risk help explain the pattern and magnitude of observed returns on equities and long-duration bonds. In particular, measures of expected consumption growth and its volatility correlate with time-varying risk premia, aligning with the LRRM’s central claims. See the primary literature on Long-Run Risk Model and the original work by Bansal and Yaron.
Estimation challenges: The LRRM relies on latent, slowly moving factors in macro data, which makes estimation sensitive to data vintages, measurement error, and model specification. Researchers use a mix of macro-finance data, forecast revisions, and stochastic setups to test the model’s predictions against actual returns. See econometrics and consumption data for methodological context.
Relationship to alternative theories: The LRRM sits among several explanations for asset prices, including Habit formation (economics)habits and extrapolative expectations, Rare disasters">rare disaster, and other macro-finance models. Proponents argue the LRRM complements these views by targeting persistent risk rather than just extreme events, while critics contend that no single model captures all facets of observed returns. See Cochrane and Campbell for related discussions of competing theories.
Controversies and debates
Strengths and explanatory power: From a market-oriented perspective, the LRRM provides a coherent story linking macro fundamentals to expected returns, and it helps explain why risk premia can remain substantial even when instantaneous risks appear muted. Supporters view it as a parsimonious bridge between macroeconomics and asset pricing.
Critiques and limits: Critics point out that the model’s success depends on the persistence and accurate measurement of long-run consumption risk, which can be hard to pin down empirically. Some studies show uneven robustness across countries, time periods, or asset classes, suggesting that additional factors or model variants may be needed. See discussions around habit formation and rare disaster models for alternative routes to similar empirical puzzles.
Competing theories and integration: The LRRM does not rule out other mechanisms for time-varying premia, such as changes in liquidity, investor sentiment, or risk aversion that can shift with the macro environment. Critics of any single-factor narrative argue for a more pluralistic approach that tests how much of asset pricing can be explained by long-run risk versus other channels. See asset pricing and macro-finance debates for broader context.
Policy and political economy dimension: A practical takeaway is that macro stability and credible policy regimes can reduce long-run risk premia, potentially lowering the cost of capital and improving resource allocation. Proponents emphasize market-based risk sharing and the efficiency of pricing, while critics caution against overreliance on any single macro narrative or the risk of misreading long-run dynamics during structural shifts. In debates around policy, the LRRM is often cited as supporting predictability and rules-based policy, rather than activist interventions.
Why some criticisms are discounted in practice: Supporters argue that the core insights of the LRRM—persistence in consumption growth, risk exposure to that persistence, and the resulting pricing of long-run risk—are robust to a range of specifications and economies. Critics who frame the model as overly optimistic about stability or as ignoring distributional impact sometimes misunderstand the model’s focus on risk pricing rather than policy prescriptions. See equity premium puzzle and Cochrane for contrasting views.