Equilibrium Asset Pricing Model Research Articles

Downside Risks and the Cross-Section of Asset Returns

In an intertemporal equilibrium asset pricing model featuring disappointment aversion and changing macroeconomic uncertainty, we show that besides the market return and market volatility, three disappointment-related factors are also priced: a downstate factor, a market downside factor, and a volatility downside factor. We find that expected returns on various asset classes reflect premiums for bearing undesirable exposures to these factors. The signs of estimated risk premiums are consistent with the theoretical predictions. Our most general, five-factor model is very successful in jointly pricing stock, option, and currency portfolios, and provides considerable improvement over nested specifications previously discussed in the literature.

Will TLAC regulations fix the G-SIB too-big-to-fail problem?

The efficacy of the Financial Stability Board's proposed requirement for minimum “total loss absorbing capacity” (TLAC) at global systemically important banks (G-SIBs) is assessed using a stylized model of a bank holding company and an equilibrium asset pricing model to value financial claims. I identify a number of G-SIB strategies that satisfy minimum TLAC requirements but fail to reduce implicit safety net subsidies that accrue to G-SIB shareholders or increase the resources available to recapitalize a failing G-SIB subsidiary. To meet the FSB's stated goals, TLAC requirements must impose minimum TLAC at all subsidiaries and restrict how TLAC funds can be invested. An equivalent, but much simpler solution is to significantly increase regulatory capital requirements on systemically important bank subsidiaries.

Equilibrium asset pricing under the Lévy process with stochastic volatility and moment risk premiums

In this paper, we extend Zhang, Zhao and Chang's (2012) production-based equilibrium asset pricing model from a jump diffusion setting to a Lévy process with stochastic volatility. This paper is a further extension of Fu and Yang (2012), which is under a Lévy process with a constant volatility. Using newly developed closed-form formulas of equity premium and pricing kernel, we are able to price Schouten's (2005) moment swaps analytically. Numerical results show that our pricing formula performs very well. Our model explains Zhao, Zhang and Chang's (2013) empirical observations on moment risk premiums.

The Equilibrium Term Structure of Equity and Interest Rates

We develop an equilibrium asset pricing model with Epstein-Zin recursive preferences that accounts for major stylized facts of the term structure of bond and equity risk premia. While the term structure of bond risk premia tends to be upward-sloping on average, the term structure of equity risk premia is known to be downward-sloping. {{p}} The equilibrium asset pricing model with long-run consumption risks has difficulty matching these stylized facts simultaneously. The standard calibration of these models follows Bansal and Yaron (2004), in which agents prefer the early resolution of uncertainty and have the inter-temporal elasticity of substitution greater than one; this calibration implies an upward-sloping term structure of equity risk premia and a downward-sloping term structure of real bond risk premia. Although the standard model can match a downward-sloping term structure of equity risk premia by amplifying the short-run risk of dividend growth, it does not fully reconcile with empirical evidence implying an upward-sloping average yield curve and a downward-sloping term structure of Sharpe ratios of dividend strips. We extend a standard model in two dimensions. First, we incorporate time-varying market prices of risks by allowing marginal utility of consumption to be nonlinearly dependent on risk factors. Second, we endogenously determine expected cash flows and expected inflation as potentially nonlinear functions of risk factors. With these extensions, our model can match the average slope of both bond and equity risk premia together with the term structure of Sharpe ratios of dividend strips. At the same time, the model generates the behavior of the aggregate stock market return in line with the data.

Risk neutrality regions

An Expected Utility maximizer can be risk neutral over a set of nondegenerate multivariate distributions even though her NM (von Neumann Morgenstern) index is not linear. We provide necessary and sufficient conditions for an individual with a concave NM utility to exhibit risk neutral behavior and characterize the regions of the choice space over which risk neutrality is exhibited. The least concave decomposition of the NM index introduced by Debreu (1976) plays an important role in our analysis as do the notions of minimum concavity points and minimum concavity directions. For the special case where one choice variable is certain, the analysis of risk neutrality requires modification of the Debreu decomposition. The existence of risk neutrality regions is shown to have important implications for the classic consumption–savings and representative agent equilibrium asset pricing models.

Cash Flow and Risk Premium Dynamics in an Equilibrium Asset Pricing Model with Recursive Preferences

Under linear approximations for asset prices and the assumption of independence between expected consumption growth and time-varying volatility, long-run risks models imply constant market prices of risks and often generate counterfactual results about asset return and cash ow predictability. We develop and estimate a nonlinear equilibrium asset pricing model with recursive preferences and a exible econometric specication

Generalized asset pricing: Expected Downside Risk-based equilibrium modeling

We introduce an equilibrium asset pricing model, which we build on the relationship between a novel risk measure, the Expected Downside Risk (EDR), and the expected return. On the one hand, our proposed risk measure uses a nonparametric approach that allows us to get rid of any assumption on the distribution of returns. On the other hand, our asset pricing model is based on loss-averse investors of Prospect Theory, through which we implement the risk-seeking behavior of investors in a dynamic setting. By including EDR in our proposed model, unrealistic assumptions of commonly used equilibrium models – such as the exclusion of risk-seeking or price-maker investors and the assumption of unlimited leverage opportunity for a unique interest rate – can be omitted. Therefore, we argue that based on more realistic assumptions, our model is able to describe equilibrium expected returns with higher accuracy, which we support by empirical evidence as well.

Learning to smile: Can rational learning explain predictable dynamics in the implied volatility surface?

We develop a general equilibrium asset pricing model under incomplete information and rational learning in order to understand the unexplained predictability of option prices. In our model, the fundamental dividend growth rate is unknown and subject to breaks. Immediately after a break, there is insufficient information to price option contracts accurately. However, as new information arrives, a representative Bayesian agent recursively learns about the parameters of the process followed by fundamentals. We show that learning makes beliefs time-varying and generates predictability patterns across option contracts with different strike prices and maturities; as a result, the implied movements in the implied volatility surface resemble those observed empirically.

Hybrid Perturbation-Projection Method for Solving DSGE Asset Pricing Models

This paper conduct a quantitative experiment to assess the effectiveness of a hybrid perturbation-projection (HPP) method to solve dynamic stochastic general equilibrium (DSGE) asset pricing models. We employ a macro-based asset pricing model to compare HPP method and value function iteration (VFI) method based on the same reasonable calibrations. This DSGE asset pricing model in the paper incorporates nonlinearities in both household preferences and firm production technologies. Additionally, the market for debt introduces its own type of nonlinearity; leverage can force a nonlinear wedge between asset rates. In the paper, we first show how to apply the HPP method and then assess its accuracy and speed compared with the old VFI method. Accuracy of solutions is demonstrated by comparing standard deviations of the logged values of first order conditions errors of important financial assets. Speed of the solution methods is shown by comparing the computational time. By comparing the results from applying the same DSGE asset pricing model to the competing methods, we find that the HPP method is not only feasible but also robust to the extreme nonlinearities in the asset pricing model.

W-MPS risk aversion and the shadow CAPM: theory and empirical evidence

This paper presents the shadow capital asset pricing model (CAPM) of Ma [2011a. Advanced Asset Pricing Theory. London: Imperial College Press] as an intertemporal equilibrium asset pricing model, and tests it empirically. In contrast to the classical CAPM – a single-factor model based on a strong behavioral or distributional assumption – the shadow CAPM can be represented as a two-factor model, and only requires a modest behavioral assumption of weak form mean-preserving spread risk aversion. The empirical tests provide support in favor of the shadow CAPM over the classical CAPM, the consumption CAPM, or the Epstein and Zin [1991. “Substitution, Risk Aversion and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis”. Journal of Political Economy 99, 263–286] model. Moreover, the shadow CAPM provides a consistent explanation for the cross-sectional variations of expected returns on the stocks and for the time-varying equity premium.

Asset Market Equilibrium with Liquidity Risk

This paper derives an equilibrium asset pricing model with liquidity risk. Liquidity risk is modeled as a stochastic quantity impact on the price from trading, where the size of the impact depends on trade size. Under a mild set of assumptions, we prove that an equilibrium price process exists for our economy and we characterize the market’s state price density, which enables the derivation of the risk-return relation for the stock’s expected return including liquidity risk. In contrast to the traditional models without liquidity risk, there is an additional systematic liquidity risk factor which is related to the stock return’s covariation with the market’s stochastic liquidity cost. Traditional transaction costs are a special case of our formulation.

Will TLAC Regulations Fix the G-SIB Too-Big-To-Fail Problem?

The efficacy of the Financial Stability Board’s proposed requirement for minimum “total loss absorbing capacity” (TLAC) at global systemically important banks (G-SIBs) is assessed using a stylized model of a bank holding company and an equilibrium asset pricing model to value financial claims. I identify a number of G-SIB strategies that satisfy minimum TLAC requirements but fail to reduce implicit safety net subsidies that accrue to G-SIB shareholders or increase the resources available to recapitalize a failing G-SIB subsidiary. To meet the FSB’s stated goals, TLAC requirements must impose minimum TLAC at all subsidiaries and restrict how TLAC funds can be invested. An equivalent, but much simpler solution is to significantly increase regulatory capital requirements on systemically important bank subsidiaries.

Long Run Expectations, Learning and the U.S. Housing Market

This paper examines key facts about the U.S. housing market. The price to rent ratio is highly volatile and significantly autocorrelated. Returns on housing are positively autocorrelated. The price to rent ratio is negatively correlated with future returns on housing and future rent growth. Finally, housing returns exhibit significant time varying volatility. I show that a benchmark rational expectations general equilibrium asset pricing model is inconsistent with these facts. I modify the model in two ways to improve its fit with the data. First, I allow for pricing frictions so prices adjust slowly to their fundamental value. Second, I assume the agent does not know if housing fundamentals, captured by rental flows, are stationary or non-stationary and has changing beliefs depending on how well each model fits the current data. I find that these modifications allow the model to increase the volatility of the price to rent ratio and to match the autocorrelation of housing returns. The price to rent ratio then negatively forecasts returns and rent growth. Finally the model generates time varying volatility consistent with the data.

Market Excess Returns, Variance and the Third Cumulant

In this paper, we develop an equilibrium asset pricing model for the market excess return, variance and the third cumulant by using a jump-diffusion process with stochastic variance and jump intensity in Cox, Ingersoll and Ross' (1985) production economy. Empirical evidence with S&P 500 index and options from January 1996 to December 2005 strongly supports our model prediction that lower the third cumulant, higher the market excess returns. Consistent with existing literature, the theoretical mean-variance relation is supported only by regressions on risk-neutral variance. We further demonstrate empirically that the third cumulant explains significantly the variance risk premium.

W-MPS Risk Aversion and the Shadow CAPM: Theory and Empirical Evidence

This paper presents the shadow Capital Asset Pricing Model (CAPM) of Ma (2011a) as an intertemporal equilibrium asset pricing model, and tests it empirically. In contrast to the classical CAPM - a single factor model based on a strong behavioral or distributional assumption, the shadow CAPM can be represented as a two factor model, and only requires a modest behavioral assumption of weak form mean-preserving spread (w-MPS) risk aversion. The empirical tests provide support in favor of the shadow CAPM over the classical CAPM, the Consumption CAPM, or the Epstein and Zin (1991) model. Moreover, the shadow CAPM provides a consistent explanation for the cross-sectional variations of expected returns on the stocks and for the time-varying equity premium.

The Vulture Spread Premium: Distressed Investorss Impact on Recovery Rates and Bond Prices

Debt pricing models typically ignore the bankruptcy process by specifying recovery rates as an exogenous function of the state space. I develop a parsimonious model in which corporate default induces a transfer of bond ownership away from traditional diversified holders toward risk-averse activist investors (vultures). Vulture funds improve emergence recovery values but demand a premium which increases with the amount of risk they take. The ratio of activist wealth to defaulted debt emerges as the key state variable that drives prices and returns for defaulted debt and expected recovery rates for pre-default bondholders. In empirical tests, this ratio is a significant determinant of risk-adjusted returns and explains 82% of the time series variation in aggregate post-default trading prices. Exactly as the model predicts, the relationship between the activists wealth ratio and returns is strongest firms with assets that are difficult to monetize and for fulcrum classes where the creditors are likely to emerge from bankruptcy holding the newly issued equity. Through its determination of recovery rates, my renegotiation framework can be easily incorporated into a partial equilibrium asset pricing model where it helps to reduce pricing errors relative to models with exogenously-specified recovery rates. The improvement spans the rating spectrum and for 10 year debt in particular, is able to simultaneously match AAA-BBB and AAA-B spreads.

Risk Neutrality Regions

The notion of risk neutrality is a basic element in standard textbook treatments of the economics of risk. In the single variable case, it is well known that an Expected Utility maximizer will be risk neutral toward all distributions if and only if her NM (von Neumann Morgenstern) index is linear. In the multivariate case, an individual can be risk neutral over a set of non-degenerate distributions even if her NM index is not linear. We provide necessary and sufficient conditions for when an individual with a nonlinear NM index is risk neutral and characterize the regions of the choice space over which risk neutrality is exhibited. The least concave decomposition of the NM index introduced by Debreu [4] plays an important role in our analysis as do the notions of minimum concavity points and minimum concavity directions. For the special case where one choice variable is certain, the analysis of risk neutrality requires modification of the Debreu decomposition. The existence of risk neutrality regions are shown to have potentially important implications for classic consumption-savings, consumption-leisure and representative agent equilibrium asset pricing models.

Learning and Leverage Dynamics in General Equilibrium

This paper develops and empirically tests a general equilibrium model of asset pricing, financing and investment dynamics in a trade-off economy where heterogeneous firms face unobservable "disaster" risk exposure and engage in rational Bayesian updating. The model sheds light on recent leverage cycles. During periods absent disasters [e.g. "The Great Moderation"]: equity premia decrease; credit spreads decrease; expected loss given default increases; and leverage ratios increase, especially amongst firms with high bankruptcy costs. Time since prior disasters is the key model conditioning variable. In response to a disaster, risk premia increase while firms reduce labor, capital and leverage, with response size increasing in time since prior disasters. Disaster responses are more pronounced than in an otherwise equivalent economy featuring observed disaster risk. Further, business cycles are more pronounced than in an otherwise equivalent economy with frictionless financing. Empirical tests of novel model predictions are conducted. Consistent with simulated model regressions, in the real-world data leverage and investment are increasing in time-since-prior-recessions, with the effect more pronounced for firms with low recovery ratios.

Asset Pricing with Return Asymmetries: Theory and Tests

I derive an equilibrium asset pricing model incorporating both systematic and idiosyncratic return asymmetries, and show their respective impact on expected returns. With systematic return asymmetry, investors allocate their wealth between the risk-free security, the market portfolio, and a factor which overweights assets with high systematic asymmetry. Investors who prefer positive asymmetry remain underdiversified from a mean-variance perspective to preserve skewness in their portfolio, and idiosyncratic asymmetry therefore is priced in equilibrium. I find that a systematic asymmetry factor and a factor capturing idiosyncratic asymmetry help explain the cross-sectional variation of expected returns across U.S. equities, international equity markets, government bonds, currencies, and commodities. My results offer a risk-based explanation of expected returns that contributes to our understanding of asset pricing across multiple markets.

Learning How to Smile: Can Rational Learning Explain the Predictable Dynamics in the Implied Volatility Surface?

We develop a general equilibrium asset pricing model under incomplete information and rational learning to explain the yet unexplained predictability of option prices. In our model, the fundamental dividend growth rate is unknown and subject to breaks, with time periods between breaks that follow a memory-less stochastic process. Immediately after a break there is insufficient information to price option contracts accurately. However, as new information arrives a representative Bayesian agent recursively learns about the parameters of the process followed by fundamentals. We show that learning makes beliefs time-varying in ways that induce large and dynamic risk premia in option prices and their implied volatilities. In addition, we find that learning generates different effects across option contracts with different strike prices and maturities. This induces realistic movements in the volatility surface implicit in option prices.