Surplus Consumption Ratio Research Articles

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.

Evaluating the Conditional CAPM using Consumption-based State Variables: Evidence from the Korean Stock Market

In this study, we evaluate the empirical performance of conditional asset pricing models using consumption-based measures as state variables. We incorporate three consumption variables known to forecast the equity risk premium as conditioning variables to capture time variations in the risk premium. These three variables are the consumption-aggregate wealth ratio, the surplus consumption ratio, and the labor income to consumption ratio. The asset pricing models evaluated in this study are the CAPM, the CAPM with human capital, the consumption CAPM, and the Fama-French three-factor model. We compare the unconditional and conditional specifications of these four asset pricing models using the two-pass cross-sectional regression methodology, using the size, book-to-market, turnover, and idiosyncratic risk sorted portfolios and sector portfolios as test assets. We demonstrate that the conditional CAPM with human capital performs far better than the unconditional specifications and about as well as the Fama and French three-factor model in explaining the crosssection of average stock returns in Korea.

Option-Implied Price of Risk

I use index prices and options to estimate the pricing kernel's elasticity, which equals the market price of risk. I show that my estimate predicts future market returns, is priced in a cross-sectional analysis, and that it is highly correlated to business cycle variables. Building on the external habits model of Campbell and Cochrane (1999), I rationalize my results by assuming a time-varying relationship between consumption growth and market returns, and therefore introduce a new way of estimating the latent surplus consumption ratio without using problematic consumption data. My results provide novel empirical support for consumption-based asset pricing models.

The predictability implied by consumption-based asset-pricing models: a review of the theory and empirical evidence

This paper examines whether two well-known models, Campbell and Cochrane’s habit model (1999) and Bansal and Yaron’s long-run risks model (2004), can produce significant return predictability. We find that a state variable, the surplus consumption ratio in the habit model, explains the countercyclical time-varying risk premium. In the long-run risks model, the main sources of volatility in the price–dividend ratio are a persistent and predictable consumption growth rate and economic uncertainty. Following Kirby’s work in 1998, we test whether the two models can explain the observed risk, ie, return volatility. Both models fail to generate any significant predictive power. However, the habit model exhibits relatively strong volatility, which implies that variation in the expected excess returns is largely attributable to the time-varying risk aversion.

Macroeconomic determinants of stock market betas

Abstract This paper proposes the mixed frequency conditional beta. We employ the MIDAS framework to estimate market betas as a weighted average of a high and low frequency components. Then, we analyze the macroeconomic determinants of stock market betas and the counter- or pro-cyclicality of betas across well-known portfolio sorts. The surplus consumption ratio with time-varying risk aversion and the default premium are the aggregate variables with the higher statistical impact on stock market betas across alternative portfolios. We show the implications of the mixed frequency betas for the term structure of holding-period expected excess returns, and for alternative investment strategies.

Macroeconomic Determinants of Stock Market Betas

This paper proposes the mixed frequency conditional beta. We employ the MIDAS framework to decompose market betas into high and low frequency components. The total mixed frequency beta is the weighted average of these two components. Then, we analyze the macroeconomic determinants of stock market betas, and the counter or pro-cyclicality of betas across well-known portfolio sorts. The surplus consumption ratio with time-varying risk aversion and the default premium are the aggregate variables with the higher statistical impact on stock market betas across alternative portfolios.

ELUCIDATING EQUITY PREMIUM USING CORPORATE DIVIDENDS AND HABIT FORMATION

This paper extends Longstaff and Piazzesi (2004, Journal of Financial Economics, 74, 401–421.) to a habit formation model. By combining corporate fraction ratio, and surplus consumption ratio, we derive closed-form solutions for stock values when dividends, habit ratio and consumption follow exponential affine jump-diffusion processes. We can prove that Longstaff and Piazzesi (2004) is only a special case of our model. In addition, calibrated results show that the corporate fraction and habit ratio to shocks significantly increases the equity premium and decreases the risk-free rate. The model determines realistic values for the equity premium and the risk-free rate.

Parametric Portfolio Policies in the Surplus Consumption Ratio

AbstractThe surplus consumption ratio plays a central role as a state variable in successful attempts to explain the time series properties of stock and bond prices with consumption‐based asset pricing models. In this paper, optimal portfolio policies for a strategic investor who maximizes the conditionally expected utility of terminal wealth are parameterized as a polynomial in the surplus consumption ratio. Optimal portfolio policies are estimated using a method of moments estimator based on Euler equations. Unconditional portfolio policies are rejected in favor of conditional policies. Lower order polynomials are rejected in favor of higher order polynomials. Optimal stock and bond allocations are clearly countercyclical.

End-of-the-year economic growth and time-varying expected returns

We show that macroeconomic growth at the end of the year (fourth quarter or December) strongly influences expected returns on risky financial assets, whereas economic growth during the rest of the year does not. We find this pattern for many different asset classes, across different time periods, and for US and international data. We also show that movements in the surplus consumption ratio of Campbell and Cochrane (1999), a theoretically well-founded measure of time-varying risk aversion linked to macroeconomic growth, influence expected returns stronger during the fourth quarter than the other quarters of the year. Our findings suggest that expected returns, risk aversion, and economic growth are particularly related at the end of the year, when we also expect consumers׳ portfolio adjustments to be concentrated.

What drives stochastic risk aversion?

This paper examines determinants of stochastic relative risk aversion in conditional asset pricing models. Novel time-series specification tests are proposed as direct extensions of Guo, Wang, and Yang (2013, JMCB)'s model using nonlinear state-space models with heteroskedasticity. I then establish the following facts. First, the surplus consumption ratio implied by the external habit formation model is the most important determinant of relative risk aversion. Second, the CAY of Lettau and Ludvigson (2001a) without a look-ahead bias and the short term interest rate explain part of relative risk aversion. Third, the estimated risk aversion from 1957Q2 to 2010Q3 is countercyclical and positive. Finally, the selected models explain part of the momentum and the financial distress premiums.

Surplus Consumption Ratio and Expected Stock Returns

Based on Campbell and Cochrane [1999] Consumption-Based Asset Pricing Model (C)CAPM with habit formation, this paper provides empirical evidence in favor of the importance of habit persistence in asset pricing. Using U.S data, we show that the surplus consumption ratio is a strong predictor of excess returns at long-horizons and that it captures a component of expected returns, not explained by the consumption-wealth ratio. Moreover, this paper shows that the (C)CAPM with habit formation performs far better than the standard (C)CAPM in accounting for the cross-sectional variations in average excess returns on the 25 FA MA-FRENCH portfolios sorted by size and book-to-market value.

Habit Formation, Equity Premium and the Evidence of Chinese Market

This paper expands CCAPM by introducing habit Formation. It is introduced in utility function, and combines with real consumption to produce surplus consumption ratio. Surplus consumption ratio is used to describe economic boom or depression. Simulated data is also offered in the process when we look surplus consumption ratio as state variable, and then simulated data is produced. The result proves that the model can describe historic trend of financial data. It is necessary to support Chinese finical development that all Chinese’s habit formation has steadily improved.

The Predictability Implied by Consumption-Based Asset Pricing Models: A Review of the Theory and Empirical Evidence

The consumption-based models have a lack of predictive power for explaining variability of stock returns. This paper examines two well-known models, Campbell and Cochrane (1999)’s habit model and Bansal and Yaron (2004)’s long-run risks model, to see whether they produce a significant power of return predictability. For the habit model, empirical tests reveal that the state variable, the surplus consumption ratio, explains counter-cyclical time-varying expected returns. The long-run risks model also proves to explain that main sources of volatility in price-dividend ratio are a persistent and predictable consumption growth rate and fluctuating economic uncertainty. The models are also tested by following the work of Kirby (1998) whether they can explain the observed return predictability. Both models fail to generate any significant predictive power. The habit model is relatively strong in volatility, which implies that variation in expected excess return is largely attributable to the time-varying risk aversion.

Stock returns and consumption factors in the Australian market: Cross-sectional tests

We test conditional consumption capital asset pricing models (CCAPMs) in the Australian equity market. The conditional variables used are Lettau and Ludvigson’s (2001a , b ) consumption–wealth ratio, Campbell and Cochrane’s (1999) surplus consumption ratio and Santos and Veronesi’s (2006) labour income to consumption ratio. We examine the cross-sectional implications of these variables using the Fama–French 25 size and book-to-market portfolios and Australian industry portfolios. The Fama–MacBeth (1973) cross-sectional regressions on the 25 size/book-to-market portfolios show that the conditional models perform better than the unconditional models. However, these conditional models cannot outperform the Fama–French three-factor model. The conditional CCAPM, with the labour income to consumption ratio as a scaling factor, can match more closely the performance of the Fama–French three-factor model. We also find that consumption growth is non-contemporaneously related to portfolio returns.

An External Habit Model Subject to Long Run Risk in Continuous Time: A Multi-Dimensional Asset Pricing Model

This work develops an external habit model of the equity premium subject to long run risk in continuous time. The solution to this model is an analytic price-dividend function of the surplus consumption ratio and the long run risk variable. As a result, the equity premium can be accurately approximated by a two variable higher order Taylor polynomial within the region of convergence for the price-dividend function. Numerical evidence shows that this region of convergence is large enough to cover 99.37% of the observations in a Monte Carlo simulation. In this simulation, the equity premium and its standard deviation match the historic observations in the U.S. In addition, the auto-correlations and variance ratios support long term mean reversion in the equity premium.

Surplus Consumption Ratio and Expected Stock Returns

This paper shows, from Consumption Asset Pricing Model with Habit Formation, that the surplus consumption ratio is a linear predictor of stock returns at long horizons. I also find that the surplus consumption ratio should explain the cross section of expected returns. Using annual U.S stock market returns, I find that the surplus consumption ratio is a strong predictor of excess returns at long horizons but has little capacity to forecast short horizons. Moreover, the (C)CAPM with habit formation performs far better than the standard (C)CAPM to explain for the average returns across the Fama-French(25) portfolios.

What Drives Stochastic Risk Aversion?

I examine determinants of stochastic relative risk aversion in conditional asset pricing models. I first develop time-series specification tests with non-linear state-space models with heteroskedasticity based on Merton (1973)'s ICAPM. I then established the following facts. First, the surplus consumption ratio implied by the external habit formation model is the most important determinant of relative risk aversion. Second, the CAY of Lettau and Ludvigson (2001a) without a look-ahead bias explains part of relative risk aversion, and the short term interest rate has some explanatory power for hedging components. Finally, I show the selected models from extensive time-series analysis are at least comparable to or better than the Fama-French three-factor model in explaining the value premium and the cross-section of industry portfolios.

Habit formation, surplus consumption and return predictability: International evidence

On an international post World War II dataset, we use an iterated GMM procedure to estimate and test the Campbell and Cochrane (1999, By force of habit: a consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251.) habit formation model with a time-varying risk-free rate. In addition, we analyze the predictive power of the surplus consumption ratio for future stock and bond returns. We find that, although there are important cross-country differences and economically significant pricing errors, for the majority of countries in our sample the model gets empirical support in a variety of different dimensions, including reasonable estimates of risk-free rates. Further, for the majority of countries the surplus consumption ratio captures time-variation in expected returns. Together with the price-dividend ratio, the surplus consumption ratio contains significant information about future stock returns, also during the 1990s. In addition, in most countries the surplus consumption ratio is also a powerful predictor of future bond returns. Thus, the surplus consumption ratio captures time-varying expected returns in both stock and bond markets.

The predictability of industry portfolio returns

This article studies the predictability of stock returns from industry portfolios. Consistent with the habit formation framework of Campbell and Cochrane (1999, 2000), we find that reasonably large portions of predictability of long-horizon industry portfolio returns are explained by the ratio of aggregate consumption in surplus of habit or its instrument, the consumption–wealth ratio. The time-varying βs and, more importantly, time-varying market risk premium associated with either the surplus consumption ratio or the consumption–wealth ratio help explain the predictable variation of long-horizon expected returns on over half of the industry portfolios. The conditional Capital Asset Pricing Model (CAPM) with βs varying with the proposed conditioning variable performs better than the static CAPM, but not as well as the Fama–French (1993, 1997) three-factor model in explaining the time-series variability of returns.

Why Surplus Consumption in the Habit Model May Be Less Persistent than You Think

In U.S. data, value stocks have higher expected excess returns and higher CAPM alphas than growth stocks. We find the external-habit model of Campbell and Cochrane (1999) can generate a value premium in both CAPM alpha and expected excess return so long as the persistence of the log surplus-consumption ratio is not too high. In contrast, Lettau and Wachter (2007) find that when the log surplus-consumption ratio is assumed to be highly persistent as in Campbell and Cochrane, the external-habit model generates a growth premium in expected excess return. However, the micro evidence favors a less persistent log surplus-consumption ratio. We choose a value for this persistence which is sufficiently low that the most recent 2 years of log consumption contribute over 98% of all past consumption to log habit, which is a much more reasonable number than the 25% contribution generated by the Lettau-Wachter value. In our model, expected consumption is slowly mean-reverting, as in the long-run risk model of Bansal and Yaron (2004), which is why our model is able to generate a price-dividend ratio for aggregate equity that exhibits the high autocorrelation found in the data, despite the very low persistence of the price-of-risk state variable. Our results suggest that an external habit model in the spirit of Campbell and Cochrane can deliver an empirically sensible value premium once the persistence of the surplus consumption ratio is calibrated to the micro evidence rather than set to a value close to one. When we allow the conditional volatility of consumption growth to also be slowly mean reverting as in the long-run risk model of Bansal and Yaron, our model is also able to generate empirically sensible predictability of long-horizon returns using the price-dividend ratio, without eroding the value premium. Our results also suggest that models with fast-moving habit can deliver several empirical properties of aggregate dividend strips that have been recently documented.