The idea of component models for volatility is extended to dynamic correlations. We propose a model of dynamic correlations with a short- and long-run component specification. We call it the class of models DCC-MIDAS as the key ingredients are a combination of the Engle (2002) DCC model, the Engle and Lee (1999) component GARCH model to replace the original DCC dynamics with a component specification and the Engle, Ghysels, and Sohn (2006) GARCH-MIDAS component specification that allows us to extract a long-run correlation component via mixed data sampling. We provide a comprehensive econometric analysis of the new class of models, including conditions for positive semi-definiteness, and provide extensive empirical evidence that supports the model specification. (with Robert Engle and Eric Ghysels)

Brandt, Cochrane, and Santa-Clara (2004) point out that the implicit stochastic discount factors computed using prices on the one hand and consumption growth on the other hand have very different implications for their cross country correlation. They leave this as an unresolved puzzle. We explain it by combining Epstein and Zin (1989) preferences with a model of predictable returns and by positing a very correlated long run component. We also assume that the intertemporal elasticity of substitution is larger than one. This setup brings the stochastic discount factors computed using prices and quantities close together, by keeping the volatility of the depreciation rate in the order of 14% and the cross country correlation of consumption growth around 30%. (with Max Croce)

Cole and Obstfeld (1991) pointed out that the welfare benefits of international portfolio diversification might be negligible. They obtain this result in the context of a model in which agents have time-additive constant relative risk aversion preferences. We revisit their conclusion by showing that a preference for the timing of the resolution of uncertainty combined with endowments containing a slowly moving trend can result in extremely high welfare gains. (With Max Croce)

We study how a concern for robustness modifies a policy maker's incentive to experiment. A policy maker has a prior over two submodels of inflation-unemployment dynamics. One submodel implies an exploitable trade-off, the other does not. Bayes' law gives the policy maker an incentive to experiment. The policy maker fears that both submodels and prior probability distribution over them are misspecified. We compute decision rules that are robust to misspecifications of the dynamics posited by each submodel as well as the prior distribution over submodels. We compare robust rules to ones that Cogley, Colacito, and Sargent (2007) computed assuming that the models and the prior distribution are correctly specified. We explain why the policy maker's desires to protect against misspecifications of the submodels, on the one hand, and misspecifications of the prior over them, on the other, have different effects on the decision rule. (With Tim W. Cogley, Lars Peter Hansen and Tom J. Sargent)

In this paper we document the presence of a time structure of risk and we propose how to measure it using alternative models to forecast volatility and the VaR at different horizons. We then quantify the benefits of an investor that is aware of the existence of a term structure of risk in the context of an asset allocation exercise. (With Robert Engle)

A policy maker knows two models of inflation-unemployment dynamics. One implies an exploitable trade-off. The other does not. The policy maker's prior probability over the two models is part of his state vector. Bayes law converts the prior into a posterior at each date and gives the policy maker an incentive to experiment. For a model calibrated to U.S. data through the early 1960s, we isolate the component of government policy that is due to experimentation by comparing the outcomes from two Bellman equations, the first of which embodies a `experiment and learn' setup, the second of which embodies a `don't experiment, do learn' view. We interpret the second as an example of an `anticipated utility' model and study how well its outcomes approximate those from the `experiment and learn' Bellman equation. (With Tim Cogley and Tom Sargent)

We evaluate alternative models of variances and correlations with an economic loss function. We construct portfolios to minimize predicted variance subject to a required return. It is shown that the realized volatility is smallest for the correctly specified covariance matrix for any vector of expected returns. A test of relative performance of two covariance matrices is based on Diebold and Mariano (1995). The method is applied to stocks and bonds and then to highly correlated assets. On average dynamically correct correlations are worth around 60 basis points in annualized terms but on some days they may be worth hundreds. (With Robert F. Engle)