Return predictability with endogenous growth (with Lorenzo Bretscher and Andrea Tamoni) (paper)

Journal of Financial Economics, 2023, 150.

The component of the volatility of total factor productivity (TFP) that is orthogonal to the dividend price ratio is shown to have long-run predictive ability for market returns. This finding implies that TFP volatility should also predict real cash flows and/or real interest rates: it is found to mainly predict real cash flows through inflation. A model with endogenous growth, Epstein-Zin preferences and price rigidities reconciles both TFP volatility-driven long-run predictability and its real implications. Within the model, we justify the cross-sectional pricing of TFP volatility risk in alternative asset classes as well as the similar (to that of TFP volatility) predictive ability of a suitable low-frequency notion of market volatility.

Conditional spectral methods (with Yinan Su)  (SSRN draft)

Journal of Econometrics, forthcoming

We model predictive scale-specific cycles. By employing suitable matrix representations, we express the forecast errors of covariance-stationary multivariate time series in terms of conditionally orthonormal scale-specific basis. The representations yield conditionally orthogonal decompositions of these forecast errors. They also provide decompositions of their variances and betas in terms of scale-specific variances and betas capturing predictive variability and co-variability over cycles of alternative lengths without spillovers across cycles. Making use of the proposed representations within the classical family of time-varying conditional volatility models, we document the role of time-varying volatility forecasts in generating orthogonal predictive scale-specific cycles in returns. We conclude by providing suggestive evidence that the conditional variances of the predictive return cycles may (i) be priced over short-to-medium horizons and (ii) offer economically-relevant trading signals over these same horizons.

Spectral financial econometrics (with Andrea Tamoni)  (paper)

Econometric Theory, 2022, 38, 1175-1220

We survey the literature on spectral regression estimation. We present a cohesive framework designed to model dependence on frequency in the response of economic time series to changes in the explanatory variables. Our emphasis is on the statistical structure and on the economic interpretation of time-domain specifications needed to obtain horizon effects over frequencies, over scales, or upon aggregation. To this end, we articulate our discussion around the role played by lead-lag effects in the explanatory variables as drivers of differential information across horizons. We provide perspectives for future work throughout.

Spectral factor models (with Shomesh Chaudhuri, Andrew W. Lo and Andrea Tamoni) (paper)

Journal of Financial Economics, 2021, 142, 214-238.

We represent risk factors as sums of orthogonal components capturing fluctuations with cycles of different length. The representation leads to novel spectral factor models in which systematic risk is allowed—without being forced—to vary across frequencies. Frequency-specific systematic risk is captured by a notion of spectral beta. We show that traditional factor models restrict the spectral betas to be constant across frequencies. The restriction can hide horizon-specific pricing effects that spectral factor models are designed to reveal. We illustrate how the methods may lead to economically meaningful dimensionality reduction in the factor space.

Business-cycle consumption risk and asset prices (with Andrea Tamoni) (paper)

Journal of Econometrics, 237, 2023.

Aggregation is routinely employed in asset pricing to capture frequency-specific effects. We formalize the theoretical mapping between aggregates of time series and their frequency-specific components as well as the mapping between factor loadings obtained upon aggregation of returns and factors and frequency-specific factor loadings. We show that business-cycle consumption, a component of the consumption growth process with cycles between 4 and 8 years, provides valuable pricing signal. In agreement with the implications of theory, we document that consumption growth aggregated over a 4-year horizon (4-year consumption) has analogous pricing ability, cross-sectionally and in the time series, to business-cycle consumption.

The scale of predictability (with Benoit Perron, Andrea Tamoni, and Claudio Tebaldi)  (paper)

Journal of Econometrics, 208, 120-140.

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.

Long-run risk-return trade-offs (with Benoit Perron) (paper)

Journal of Econometrics, 2008, 143, 349-374

Excess market returns are correlated with past market variance. This dependence is statistically mild at short horizons (thereby leading to a hard-to-detect risk-return trade-off, as in the existing literature) but increases with the horizon and is strong in the long run (i.e., between 6 and 10 years). From an econometric standpoint, we find that the long-run predictive power of past market variance is robust to the statistical properties of long-horizon stock-return predictive regressions. From an economic standpoint, we show that, when conditioning on past market variance, conditional versions of the traditional CAPM and consumption-CAPM yield considerably smaller cross-sectional pricing errors than their unconditional counterparts.

Long memory and the relation between implied and realized volatility (with Benoit Perron) (paper)

Journal of Financial Econometrics, 2006, 4, 636-670

We argue that the predictive regression between implied volatility (regressor) and realized volatility over the remaining life of a European option (regressand) is likely to be a fractional cointegrating relation. Since cointegration is associated with long-run co-movements, this classical regression cannot be used to test for option market efficiency and short-term unbiasedness of implied volatility as a predictor of realized volatility. Using narrow band spectral methods, we provide consistent estimates of the long-run relation between implied and realized volatility even when implied volatility is measured with error and/or volatility is priced but the volatility risk premium is unobservable. While little can be said about short-term unbiasedness, our results largely support a notion of long-run unbiasedness of implied volatility as a predictor of realized volatility.