Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets

This paper examines the optimal consumption and portfolio-choiceproblem of long-horizon investors who have access to a risklessasset with constant return and a risky asset ("stocks") withconstant expected return and time-varying precision—thereciprocal of volatility. Markets are incomplete, and investorshave recursive preferences defined over intermediate consumption.The paper obtains a solution to this problem which is exactfor investors with unit elasticity of intertemporal substitutionof consumption and approximate otherwise. The optimal portfoliodemand for stocks includes an intertemporal hedging componentthat is negative when investors have coefficients of relativerisk aversion larger than one, and the instantaneous correlationbetween volatility and stock returns is negative, as typicallyestimated from stock return data. Our estimates of the jointprocess for stock returns and precision (or volatility) usingU.S. data confirm this finding. But we also find that stockreturn volatility does not appear to be variable and persistentenough to generate large intertemporal hedging demands.     

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

We model consumption and dividend growth rates as containing (1) a small long‐run predictable component, and (2) fluctuating economic uncertainty (consumption volatility). These dynamics, for which we provide empirical support, in conjunction with Epstein and Zin's (1989) preferences, can explain key asset markets phenomena. In our economy, financial markets dislike economic uncertainty and better long‐run growth prospects raise equity prices. The model can justify the equity premium, the risk‐free rate, and the volatility of the market return, risk‐free rate, and the price–dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time‐varying.     

Generalized Disappointment Aversion and Asset Prices

We characterize generalized disappointment aversion (GDA) risk preferences that can overweight lower‐tail outcomes relative to expected utility. We show in an endowment economy that recursive utility with GDA risk preferences generates effective risk aversion that is countercyclical. This feature comes from endogenous variation in the probability of disappointment in the representative agent's intertemporal consumption‐saving problem that underlies the asset pricing model. The variation in effective risk aversion produces a large equity premium and a risk‐free rate that is procyclical and has low volatility in an economy with a simple autoregressive endowment‐growth process.     

Growth uncertainty,generalized disappointment aversion and production-based asset pricing

We study a production economy with regime switching in the conditional mean and volatility of productivity growth. The representative agent has generalized disappointment aversion (GDA) preferences. We show that volatility risk in productivity growth carries a positive and sizable risk premium in levered equity. Our model can endogenously generate long-run risks in the volatility of consumption growth observed in the data. We show that introducing leverage with a procyclical dividend process consistent with the data is critical for the GDA preferences to have a large impact on equity returns.     

Accurate minimum capital risk requirements: A comparison of several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of short and long memory stochastic volatility and GARCH-type models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns’ series. The results suggest that accurate modelling of extreme observations obtained for long and short trading investment positions is possible with an autoregressive stochastic volatility model. Moreover, modelling futures returns with a long memory stochastic volatility model produces, in general, excessive volatility persistence, and consequently, leads to large minimum capital risk requirement estimates. Finally, the models’ predictive ability is assessed with the help of out-of-sample conditional tests.     

The Cross-Section of Volatility and Expected Returns

We examine the pricing of aggregate volatility risk in the cross‐section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book‐to‐market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.     

Fair wages,labor relations and asset returns

The paper investigates the nexus between labor and financial markets, focusing on how labor union’s attitude in the wage-setting process and the firm’s investment strategy affect asset returns. We assume that the labor union’s relative preferences between wage and employment depend on selected measures of firm’s financial performance. The paper shows that if the labor union ties its preference for wage to the firm’s dividends (or to any other quantity measuring available liquidity), then the volatility of the firm’s returns increases. Consequently, equities have to grant high expected returns in order to remunerate the increased volatility. This mechanism offers an explanation for the “equity premium” (that is the difference between the equity return rate and the risk free rate). It is a welcome result that the simulated excess return is about the empirical estimate and that it is obtained with a plausibly low parameterization of the shareholders’ risk aversion.     

Forecasting daily exchange rate volatility using intraday returns

This study investigates whether intraday returns contain important information for forecasting daily volatility. Whereas in the existing literature volatility models for daily returns are improved by including intraday information such as the daily high and low, volume, the number of trades, and intraday returns, here the volatility of intraday returns is explicitly modelled. Daily volatility forecasts are constructed from multiple volatility forecasts for intraday intervals. It is shown for the DEM/USD and the YEN/USD exchange rates that this results in superior forecasts for daily volatility.     

The frequency of regime switching in financial market volatility

The mechanism of risk responses to market shocks is considered as stagnant in recent financial literature, whether during normal or stress periods. Since the returns are heteroskedastic, a little consideration was given to volatility structural breaks and diverse states. In this study, we conduct extensive simulations to prove that the switching regime GARCH model, under the highly flexible skewed generalized t (SGT) distribution, is remarkably efficient in detecting different volatility states. Next, we examine the switching regime in the S&P 500 volatility for weekly, daily, 10-minute and 1-minute returns. Results show that the volatility switches regimes frequently, and differences between the distributions of the high and low volatility states become more accentuated as the frequency increases. Moreover, the SGT is highly preferable to the usually employed skewed t distribution.     

Predictability in Consumption Growth and Equity Returns: A Bayesian Investigation

We use a Bayesian method to estimate a consumption-based asset pricing model featuring long-run risks. Although the model is generally consistent with consumption and dividend growth moments in annual data, the conditional mean of consumption growth (a latent process) is not persistent enough to satisfy the restriction that the price-dividend ratio be an affine function of the latent process. The model also requires relatively high intertemporal elasticity of substitution to match the low volatility of the risk-free return. These two restrictions lead to the equity volatility puzzle. The model accounts for only 50% of the total variation in asset returns.     

Stock Market Volatility and Learning

We show that consumption‐based asset pricing models with time‐separable preferences generate realistic amounts of stock price volatility if one allows for small deviations from rational expectations. Rational investors with subjective beliefs about price behavior optimally learn from past price observations. This imparts momentum and mean reversion into stock prices. The model quantitatively accounts for the volatility of returns, the volatility and persistence of the price‐dividend ratio, and the predictability of long‐horizon returns. It passes a formal statistical test for the overall fit of a set of moments provided one excludes the equity premium.     

Equilibrium moment restrictions on asset returns: normal and crisis periods

Empirically, the covariance between stock returns varies with their volatility. We seek a robust theoretical explanation of this. With minimal assumptions, we model stochastic properties of equilibrium returns which result from the interaction between inter-temporal traders and noisy, price-sensitive short-term traders. The inter-temporal traders can have arbitrary investment rules, preferences and information. In all cases we find a set of restrictions between second moments of equilibrium returns. With two assets there is also a bound on the correlation between asset returns. Estimation with second moments of global stock returns supports our theoretical framework. Higher volatility in at least one market can increase comovement among markets. With globalization, covariances between two stock markets can also affect covariances between two other stock markets. We also find that the changes in trader behavior between normal and crisis periods lead to changes in the moment restrictions between asset returns.     

Expected Returns and Habit Persistence

Using a consumption-based asset pricing model with infinite-horizonnonlinear habit formation, Campbell and Cochrane (1999) showthat low consumption in surplus of habit should forecast highexpected returns. This article argues that the finite-horizonlinear habit model also implies an inverse relation betweenexpected returns and surplus consumption. This article alsopresents empirical evidence, which indicates that expected returnson stocks and bonds vary with surplus consumption implied bythe habit models. The volatility of returns and the reward tovolatility are also related to surplus consumption. However,less than 30% of the predictable variation of expected returns,using standard lagged information variables, is attributed tosurplus consumption.     

Information Quality and Long‐Run Risk: Asset Pricing Implications

I study the asset pricing implications of the quality of public information about persistent productivity shocks in a general equilibrium model with Kreps–Porteus preferences. Low information quality is associated with a high equity premium, a low volatility of consumption growth, and a low volatility of the risk‐free interest rate. The relationship between information quality and the equity premium differs from that in endowment economies. My calibration improves substantially upon the Bansal–Yaron model in terms of the moments of the wealth–consumption ratio and the return on aggregate wealth.     

Equity Returns and Business Cycles in Small Open Economies

This is the first paper in the dynamic stochastic general equilibrium literature to match key business cycle moments and long‐run equity returns in a small open economy with production. These results are achieved by introducing four modifications to a standard real business cycle model: (i) borrowing and lending costs are imposed to increase the volatility of the marginal rate of substitution over time, (ii) capital adjustment costs are assumed to make equity returns more volatile, (iii) GHH preferences are employed to smooth consumption, and (iv) a working capital constraint to generate countercyclical trade balances. Our results are based on data from Argentina, Brazil, and Chile.     

Is stochastic volatility relevant for dynamic portfolio choice under ambiguity?

Literature on dynamic portfolio choice has been finding that volatility risk has low impact on portfolio choice. For example, using long-run US data, Chacko and Viceira [2005. “Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets.” The Review of Financial Studies 18 (4): 1369–1402] found that intertemporal hedging demand (required by investors for protection against adverse changes in volatility) is empirically small even for highly risk-averse investors. We want to assess if this continues to be true in the presence of ambiguity. Adopting robust control and perturbation theory techniques, we study the problem of a long-horizon investor with recursive preferences that faces ambiguity about the stochastic processes that generate the investment opportunity set. We find that ambiguity impacts portfolio choice, with the relevant channel being the return process. Ambiguity about the volatility process is only relevant if, through a specific correlation structure, it also induces ambiguity about the return process. Using the same long-run US data, we find that ambiguity about the return process may be empirically relevant, much more than ambiguity about the volatility process. Anyway, intertemporal hedging demand is still very low: investors are essentially focused on the short-term risk–return characteristics of the risky asset.     

Stock return volatility,operating performance and stock returns: International evidence on drivers of the ‘low volatility’ anomaly

This study highlights the link between stock return volatility, operating performance, and stock returns. Prior studies suggest that there is a ‘low volatility’ anomaly, where firms with a low stock return volatility out-perform firms with a high stock return volatility. This paper confirms that low volatility stocks earn higher returns than high volatility stocks in emerging markets and developed markets outside of North America. We also show that low volatility stocks have higher operating returns and this might explain why low volatility stocks earn higher stock returns. These results provide a partial explanation for the ‘low volatility effect’ that is independent from the existence of market anomalies or per se inefficiencies that might otherwise drive a low volatility effect. We emphasize the importance of controlling for stock return volatility when analyzing operating performance and stock performance.     

Can Time‐Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?

Why is the equity premium so high, and why are stocks so volatile? Why are stock returns in excess of government bill rates predictable? This paper proposes an answer to these questions based on a time‐varying probability of a consumption disaster. In the model, aggregate consumption follows a normal distribution with low volatility most of the time, but with some probability of a consumption realization far out in the left tail. The possibility of this poor outcome substantially increases the equity premium, while time‐variation in the probability of this outcome drives high stock market volatility and excess return predictability.     

tay's as good as cay

The empirical evidence that the consumption–wealth ratio, cay, has strong in-sample predictive power for future stock returns has been interpreted as evidence that consumers take account of future investment opportunities in planning their consumption expenditures. In this paper we show that the predictive power of cay arises mainly from a “look-ahead bias” introduced by estimating the parameters of the cointegrating regression between consumption, assets, and labor income in-sample. When a similar regression is run, replacing the log of consumption with an inanimate variable, calendar time, the resulting residual, which we label tay, is shown to be able to forecast stock returns as well as, or better than, cay. In addition, both cay and tay lose their out-of-sample forecasting power when they are re-estimated every period with only available data.