Davide Pettenuzzo

Forecasting Stock Returns Under Economic Constraints

We propose a new approach to imposing economic constraints on time-series forecasts of the equity premium. Economic constraints are used to modify the posterior distribution of the parameters of the predictive return regression in a way that better allows the model to learn from the data. We consider two types of constraints: Non-negative equity premia and bounds on the conditional Sharpe ratio, the latter of which incorporates timevarying volatility in the predictive regression framework. Empirically, we find that economic constraints systematically reduce uncertainty about model parameters, reduce the risk of selecting a poor forecasting model, and improve both statistical and economic measures of out-of-sample forecast performance. The Sharpe ratio constraint, in particular, results in considerable economic gains.

Optimal Portfolio Choice under Decision-Based Model Combinations

We extend the density combination approach of Billio et al. (2013) to feature combination weights that depend on the past forecasting performance of the individual models entering the combination through a utility-based objective function. We apply our model combination scheme to forecast stock returns, both at the aggregate level and by industry, and investigate its forecasting performance relative to a host of existing combination methods. Overall, we find that our combination scheme produces markedly more accurate predictions than the existing alternatives, both in terms of statistical and economic measures of out-of-sample predictability. We also investigate the performance of our model combination scheme in the presence of model instabilities, by considering individual predictive regressions that feature time-varying regression coefficients and stochastic volatility. We find that the gains from using our combination scheme increase significantly when we allow for instabilities in the individual models entering the combination.Length: 61 pages

Bond Return Predictability: Economic Value and Links to the Macroeconomy

Studies of bond return predictability find a puzzling disparity between strong statistical evidence of return predictability and the failure to convert return forecasts into economic gains. We show that resolving this puzzle requires accounting for important features of bond return models such as time varying parameters, volatility dynamics, and unspanned macro factors. A three-factor model comprising the Fama and Bliss (1987) forward spread, the Cochrane and Piazzesi (2005) combination of forward rates and the Ludvigson and Ng (2009) macro factor generates notable gains in out-of-sample forecast accuracy compared with a model based on the expectations hypothesis. Such gains in predictive accuracy translate into higher risk-adjusted portfolio returns after accounting for estimation error and model uncertainty, as evidenced by the performance of forecast combinations. Consistent with models featuring unspanned macro factors, our forecasts of future bond excess returns are strongly negatively correlated with survey forecasts of short rates.

Bayesian Compressed Vector Autoregressions

Macroeconomists are increasingly working with large Vector Autoregressions (VARs) where the number of parameters vastly exceeds the number of observations. Existing approaches either involve prior shrinkage or the use of factor methods. In this paper, we develop an alternative based on ideas from the compressed regression literature. It involves randomly compressing the explanatory variables prior to analysis. A huge dimensional problem is thus turned into a much smaller, more computationally tractable one. Bayesian model averaging can be done over various compressions, attaching greater weight to compressions which forecast well. In a macroeconomic application involving up to 129 variables, we find compressed VAR methods to forecast better than either factor methods or large VAR methods involving prior shrinkage.

Forecasting Macroeconomic Variables Under Model Instability

We compare different approaches to accounting for parameter instability in the context of macroeconomic forecasting models that assume either small, frequent changes versus models whose parameters exhibit large, rare changes. An empirical out-of-sample forecasting exercise for U.S. gross domestic product (GDP) growth and inflation suggests that models that allow for parameter instability generate more accurate density forecasts than constant-parameter models although they fail to produce better point forecasts. Model combinations deliver similar gains in predictive performance although they fail to improve on the predictive accuracy of the single best model, which is a specification that allows for time-varying parameters and stochastic volatility. Supplementary materials for this article are available online.

A MIDAS Approach to Modeling First and Second Moment Dynamics

We propose a new approach to predictive density modeling that allows for MIDAS effects in both the first and second moments of the outcome. Specifically, our modeling approach allows for MIDAS stochastic volatility dynamics, generalizing a large literature focusing on MIDAS effects in the conditional mean, and allows the models to be estimated by means of standard Gibbs sampling methods. When applied to monthly time series on growth in industrial production and inflation, we find strong evidence that the introduction of MIDAS effects in the volatility equation leads to improved in-sample and out-of-sample density forecasts. Our results also suggest that model combination schemes assign high weight to MIDAS-in-volatility models and produce consistent gains in out-of-sample predictive performance.

Option-Implied Equity Premium Predictions via Entropic Tilting

We propose a new method to improve density forecasts of the equity premium us- ing information from options markets. We tilt the predictive densities from standard econometric models suggested in the stock return predictability literature towards the second moment of the risk-neutral distribution implied by options prices. In so do- ing, we use a simple regression-based approach to remove the variance risk premium. By combining the backward-looking information contained in the econometric models with the forward-looking information from the options prices, tilting yields sharper predictive densities. Using density forecasts of the U.S. equity premium in Rapach and Zhou (2012), we nd that tilting leads to more accurate predictions, both in terms of statistical and economic performance.

Forecasting Stock Returns: A Predictor-Constrained Approach

We develop a novel method to impose constraints on univariate predictive regressions of stock returns. Unlike the previous approaches in the literature, we implement our constraints directly on the predictor, setting it to zero whenever its value falls below the variables past 12-month high. Empirically, we find that relative to standard unconstrained predictive regressions, our approach leads to significantly larger forecasting gains, both in statistical and economic terms. We also show how a simple equal-weighted combination of the constrained forecasts leads to further improvements in forecast accuracy, with predictions that are more precise than those obtained either using the Campbell and Thompson (2008) or Pettenuzzo, Timmermann, and Valkanov (2014) methods. Subsample analysis and a large battery of robustness checks confirm that these findings are robust to the presence of model instabilities and structural breaks.

Adaptive Minnesota Prior for High-Dimensional Vector Autoregressions

This paper proposes a simulation-free estimation algorithm for vector autoregressions (VARs) that allows fast approximate calculation of marginal parameter posterior distributions. We apply the algorithm to derive analytical expressions for independent VAR priors that admit a hierarchical representation and which would typically require computationally intensive posterior simulation methods. The bene fits of the new algorithm are explored using three quantitative exercises. First, a Monte Carlo experiment illustrates the accuracy and computational gains of the proposed estimation algorithm and priors. Second, a forecasting exercise involving VARs estimated on macroeconomic data demonstrates the ability of hierarchical shrinkage priors to find useful parsimonious representations. We also show how our approach can be used for structural analysis and that it can successfully replicate important features of news-driven business cycles predicted by a large-scale theoretical model.