Andrea Tamoni

Demographic Trends, the Dividend/Price Ratio and the Predictability of Long-Run Stock Market Returns ∗

This paper documents the existence of a slowly evolving trend in the dividend-price ratio, dpt, determined by a demographic variable, MY: the middle-aged to young ratio. Deviations of dpt from this long-run component explain transitory but persistent fluctuations in stock market returns. The relation between MY and dpt is a prediction of an overlapping generation model. The joint significance of MY and dpt in long-horizon forecasting regressions for market returns explain the mixed evidence on the ability of dpt to predict stock returns and provide a model-based interpretation of statistical corrections for breaks in the mean of this financial ratio.

The Scale of Predictability

We introduce a new stylized fact: the hump-shaped behavior of slopes and coefficients of determination as a function of the aggregation horizon when running (forward/backward) predictive regressions of future excess market returns onto past economic uncertainty (as proxied by market variance, consumption variance, or economic policy uncertainty). To justify this finding formally, we propose a novel modeling framework in which predictability is specified as a property of low-frequency components of both excess market returns and economic uncertainty. We dub this property scale-specific predictability. We show that classical predictive systems imply restricted forms of scale-specific predictability. We conclude that for certain predictors, like economic uncertainty, the restrictions imposed by classical predictive systems may be excessively strong.

The Multi-Horizon Dynamics of Risk and Returns

I study the effects of changes in risk on asset prices across different time horizons (or time-scales) and provide a new insight into the dynamics of equity premia. I find that, contrary to the implication of standard models such as the Consumption-CAPM, risk premia are weakly related to consumption volatility at short horizons whereas long-run past volatility strongly determines the long-run dynamics of expected stock returns. More importantly I show that a model specified at a fixed time-scale may not necessarily lead to obtain a significant long-term risk-returns relation upon aggregation of the one-period dynamics of volatility and returns. I thus develop a consumption-based model that simultaneously characterizes both the short- and long-term behaviors of risk and returns and successfully replicates the pattern observed in the data. Whereas previous empirical literature has mainly focused on stock market volatility, when I estimate the model I am able to relate movements of equity premia at specific frequency intervals to sources of macroeconomic risk, as measured by conditional volatility of consumption. The empirical results emphasize the importance of simultaneously modeling consumption at multiple time-scales and point to changing consumption volatility as an important long-run priced factor.

The Horizon of Systematic Risk: A New Beta Representation

We show that a business-cycle consumption factor can explain the differences in risk premia across alternative portfolios, including recently-proposed anomalies portfolios. We argue that explicit allowance for a separation between consumption fluctuations with heterogeneous durations is important for interpreting cross-sectional pricing as well as the time-series dynamics of consumption and returns across horizons (i.e., the hump-shaped pricing ability of the covariance between ultimate consumption and returns, the hump-shaped structure of long-run risk premia, the decaying pattern in consumption growth predictability). Using a novel modeling approach relying on a frequency-based decomposition, we formalize the important role that aggregation can play in asset pricing.While contemporaneous consumption growth is known not to price the cross section of stock returns, we nd that suitable sub-components (or details) of consumption growth with periodicities corresponding to the business cycle do. Specically, we disaggregate consumption growth into details with dierent levels of persistence and show that those corresponding to businesscycle scales can explain the dierences in risk premia across book-to-market and size-sorted portfolios. We argue that accounting for persistence heterogeneity in consumption is important for interpreting risk compensations in nancial markets but also for capturing the joint dynamics of consumption and returns across horizons (for instance, the hump-shaped pricing ability of the covariance between ultimate consumption and returns, the hump-shaped structure of long-run risk premia as well as the decaying pattern in consumption growth predictability). Using our proposed scale-based data generating process for consumption growth, we discuss implications for the cross-sectional pricing literature relying on aggregation.

Implications of Return Predictability across Horizons for Asset Pricing Models

Two broad classes of consumption dynamics - long-run risks and rare disasters - have proven successful in explaining the equity premium puzzle when used in conjunction with recursive preference. We show that bounds a-la Gallant, Hansen and Tauchen (1990) that restrict the volatility of the Stochastic Discount Factor by conditioning on a set of return predictors constitute a useful tool to discriminate between these alternative dynamics. In particular we document that models that rely on rare disasters meet comfortably the bounds independently of the forecasting horizon and the asset classes used to construct the bounds. However, the specific nature of disasters is a relevant characteristic at the 1-year horizon: disasters that unfold over multiple years are more successful in meeting the predictors-based bounds than one-period disasters. Instead, over a longer, 5-year horizon, the sole presence of disasters - even if one-period and permanent - is sufficient for the model to satisfy the bounds. Finally, the bounds point to multiple volatility components in consumption as a promising dimension for long-run risks models.

A Persistence-Based Wold-Type Decomposition for Stationary Time Series

If the aggregate response of the economy to an exogenous shock is a superposition of effects which develop over different time scales, then the statistical estimation of low frequency components is difficult. In fact highly persistent shocks have generally low instantaneous volatility and are hidden by those shocks with high instantaneous volatility and fast decay. We refer to this situation as heterogeneity of persistence levels phenomenon. This paper introduces a new spectral approach which is applicable to the analysis of time series in the presence of persistence heterogeneity. A new linear decomposition of a time series is introduced which generalizes the Wold decomposition for stationary time series and the Beveridge-Nelson permanent transitory decomposition for non stationary integrated ones. In order to prove the relevance of this new methodology for financial valuation, we apply it to clarify some open issues which arise in the empirical analysis of gdp and inflation forecasting. JEL Classification Codes: E32, E43, E44, G12.The Classical Wold Decomposition Theorem allows to split a weakly stationary time series x into a non-deterministic component, driven by uncorrelated innovations, and a deterministic term. This decomposition is a special case of the Abstract Wold Theorem, which deals with isometric operators defined on Hilbert spaces. As the lag operator is isometric on the Hilbert space H_t(x) spanned by the sequence {x_{t-k}_k}, the Classical Wold Decomposition for time series obtains. Moreover, the \emph{scaling operator} is isometric on the Hilbert space H_t(e), spanned by the classical Wold innovations of x, and it provides an Extended Wold Decomposition. Thus, the process x may be seen as a sum, across scales, of uncorrelated components that explain different layers of persistence, from temporary fluctuations to low-frequency shocks. Multiscale impulse response functions are, then, defined. Conversely, the sum of suitable uncorrelated components delivers a weakly stationary process. This decomposition fruitfully applies to ARMA and fractional ARIMA processes.

Long-Run Factors and Fluctuations in Dividend/Price

The dynamic dividend growth model linking the log dividend yield to future expected dividend growth and stock market returns has been extensively used in the literature for forecasting stock returns. The empirical evidence on the performance of the model is mixed as its strength varies with the sample choice. This model is derived on the assumption of stationary log dividend-price ratio. The empirical validity of such hypothesis has been challenged in the recent literature (Lettau&Van Nieuwerburgh, 2008) with strong evidence on a time varying mean, due to breaks, in this financial ratio. In this paper, we show that the slowly evolving mean toward which the dividend price ratio is reverting is driven by a demographic factor and a technological trend. We also show that an empirical model using information in long-run factors overperforms virtually all alternative models proposed in the literature within the framework of the dynamic dividend growth model. Finally, we exploit the exogeneity and predictability of the demographic factor to simulate the equity risk premium up to 2050.

Value Return Predictability Across Asset Classes and Commonalities in Risk Premia

Returns to value strategies in individual equities, commodities, currencies, global bonds and stock indexes are predictable by the value spread. Common and asset-class-specific components of the value spread contribute equally to this predictability. Return variation due to common value is closely associated with standard proxies for risk premia, such as dividend yield, intermediary leverage and illiquidity, but it is at odds with models that exclusively generate a value premium in equities. Return variation due to asset-classspecific value presents another challenge for asset pricing models. The outperformance of value timing and rotation strategies indicates that investors can benefit from the value spread in real-time.

Implementing Stochastic Volatility in DSGE Models: A Comment

We highlight a state variable misspecification with one accepted method to implement stochastic volatility (SV) in DSGE models when transforming the nonlinear state-innovation dynamics to its linear representation. Although the technique is more efficient numerically, we show that it is not exact but only serves as an approximation when the magnitude of SV is small. Not accounting for this approximation error may induce substantial spurious volatility in macroeconomic series, which could lead to incorrect inference about the performance of the model. We also show that, by simply lagging and expanding the state vector, one can obtain the correct state-space specification. Finally, we validate our augmented implementation approach against an established alternative through numerical simulation.

Risk Aversion and the Response of the Macroeconomy to Uncertainty Shocks

Uncertainty shocks are also risk premium shocks. With countercyclical risk aversion (RA), a positive shock to uncertainty increases risk and elevates RA as consumption growth falls. The combination of high RA and high uncertainty produces significant risk premia in bad times, which in turn exacerbate the decline of macroeconomic aggregates and equity prices. Moreover, uncertainty is a priced risk factor in the cross-section of equity returns only when the factor exposure is a time-varying function of RA. In a model with endogenously time-varying RA, uncertainty produces large falls in investment and equity prices that closely match state-dependent data responses.Uncertainty shocks are also risk premium shocks. With countercyclical risk aversion (RA), a positive shock to uncertainty not only increases risk, but it also elevates RA as consumption growth falls. The combination of high RA and high uncertainty produces significant risk premia in bad times, which in turn exacerbate the decline of macroeconomic aggregates and equity prices. Empirically, we document that local projection coefficients capturing the data response to the interaction of risk aversion and uncertainty are statistically significant and economically large. Indeed, heightened levels of RA during the 2008 crisis amplified the drop in output and investment by 41% and 28%, respectively, at the recession trough. Theoretically, we show that a New-Keynesian model with endogenously time-varying risk aversion via Campbell and Cochrane (1999) can produce large falls in output and investment close to matching their data counterparts following positive uncertainty shocks.