Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies

We consider various MIDAS (Mixed Data Sampling) regression models to predict volatility. The models differ in the specification of regressors (squared returns, absolute returns, realized volatility, realized power, and return ranges), in the use of daily or intra-daily (5-minute) data, and in the length of the past history included in the forecasts. The MIDAS framework allows us to compare models across all these dimensions in a very tightly parameterized fashion. Using equity return data, we find that daily realized power (involving 5-minute absolute returns) is the best predictor of future volatility (measured by increments in quadratic variation) and outperforms model based on realized volatility (i.e. past increments in quadratic variation). Surprisingly, the direct use of high-frequency (5-minute) data does not improve volatility predictions. Finally, daily lags of one to two months are sucient to capture the persistence in volatility. These findings hold both in- and out-of-sample.

The MIDAS Touch: Mixed Data Sampling Regression Models

We introduce Mixed Data Sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Technically speaking MIDAS models specify conditional expectations as a distributed lag of regressors recorded at some higher sampling frequencies. We examine the asymptotic properties of MIDAS regression estimation and compare it with traditional distributed lag models. MIDAS regressions have wide applicability in macroeconomics and finance. Nous introduisons des modèles de régression MIDAS (Mixed Data Sampling). Ce sont des modèles de régression avec des séries temporelles échantillonées à différentes fréquences. Nous analysons les liens avec les modèles à retards échelonnés.distributed log models, aliasing, discretization bias, retards échelonnés, aliasing, biais de discrétisation

Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies

We consider various MIDAS (Mixed Data Sampling) regression models to predict volatility. The models differ in the specification of regressors (squared returns, absolute returns, realized volatility, realized power, and return ranges), in the use of daily or intra-daily (5-minute) data, and in the length of the past history included in the forecasts. The MIDAS framework allows us to compare models across all these dimensions in a very tightly parameterized fashion. Using equity return data, we find that daily realized power (involving 5-minute absolute returns) is the best predictor of future volatility (measured by increments in quadratic variation) and outperforms model based on realized volatility (i.e. past increments in quadratic variation). Surprisingly, the direct use of high-frequency (5-minute) data does not improve volatility predictions. Finally, daily lags of one to two months are sufficient to capture the persistence in volatility. These findings hold both in- and out-of-sample. Nous utilisons les régressions MIDAS (Mixed Data Sampling) dans le contexte de prévision de volatilité mesurée par incréments de la variation quadratique. Nous trouvons que la 'realized power' (Barndorff-Nielsen and Shephard) est le meilleur régresseur pour prévoir la variation quadratique future.realized variance, power variation, MIDAS regression, variance réalisée, 'power variation', régression MIDAS

There is a Risk-Return Tradeoff After All

This paper studies the ICAPM intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns - the Mixed Data Sampling (or MIDAS) approach. Using MIDAS, we find that there is a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process, and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the ICAPM based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance. Dans ce papier, nous estimons le modèle ICAPM intertemporal avec une nouvelle classe d'estimateurs, intitulée MIDAS. Cette procédure d'estimation combine des données échantillonnées à différentes fréquences. Utilisant le nouvel estimateur, nous constatons une relation positive et significative entre le rendement et la volatilité.ICAPM, GARCH, volatility risk, ICAPM, GARCH, risque de volatilité

There is a Risk-Return Tradeoff After All

This paper studies the ICAPM intertemporal relation between conditional mean and conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns - the Mixed Data Sampling (or MIDAS) approach. Using MIDAS, we find that there is a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process, and to controlling for variables associated with the business cycle. We compare the MIDAS results with other tests of the ICAPM based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance. Nous étudions le modèle ICAPM à l'aide d'un nouvel estimateur MIDAS, basé sur un mélange de données temporelles échantillonnées à différentes fréquences. Nous trouvons une relation positive et significative avec cet estimateur. Nous analysons également des modèles avec asymétries.mixed data sampling, risk-return trade-off, stimation avec mélange de fréquence de séries temporelles, relation risque-rendement

Parametric Portfolio Policies: Exploiting Characteristics in the Cross Section of Equity Returns

We propose a novel approach to optimizing portfolios with large numbers of assets. We model directly the portfolio weight in each asset as a function of the asset's characteristics. The coefficients of this function are found by optimizing the investor's average utility of the portfolio's return over the sample period. Our approach is computationally simple, easily modified and extended, produces sensible portfolio weights, and offers robust performance in and out of sample. In contrast, the traditional approach of first modeling the joint distribution of returns and then solving for the corresponding optimal portfolio weights is not only difficult to implement for a large number of assets but also yields notoriously noisy and unstable results. Our approach also provides a new test of the portfolio choice implications of equilibrium asset pricing models. We present an empirical implementation for the universe of all stocks in the CRSP-Compustat dataset, exploiting the size, value, and momentum anomalies.

Return Predictability under Equilibrium Constraints on the Equity Premium

This paper proposes a new approach for incorporating theoretical constraints on return forecasting models such as non-negativity of the conditional equity premium and sign restrictions on the coefficients linking state variables to the equity premium. Our approach makes use of Bayesian methods that update the estimated parameters at each point in time in a way that optimally exploits information in these constraints. Using a variety of predictor variables from the literature on predictability of stock returns, we find that theoretical constraints have an important effect on the coefficient estimates and can significantly reduce biases and estimation errors in these. In out-of-sample forecasting experiments we find that models that exploit the theoretical restrictions produce better forecasts than unconstrained models.Return Predictability, Constraints, Out-of-Sample Forecasts

Valuation in US Commercial Real Estate

We consider a log-linearized version of a discounted rents model to price commercial real estate as an alternative to traditional hedonic models. First, we verify a key implication of the model, namely, that cap rates forecast commercial real estate returns. We do this using two different methodologies: time series regressions of 21 US metropolitan areas and mixed data sampling (MIDAS) regressions with aggregate REITs returns. Both approaches confirm that the cap rate is related to fluctuations in future returns. We also investigate the provenance of the predictability. Based on the model, we decompose fluctuations in the cap rate into three parts: (i) local state variables (demographic and local economic variables); (ii) growth in rents; and (iii) an orthogonal part. About 30% of the fluctuation in the cap rate is explained by the local state variables and the growth in rents. We use the cap rate decomposition into our predictive regression and find a positive relation between fluctuations in economic conditions and future returns. However, a larger and significant part of the cap rate predictability is due the orthogonal part, which is unrelated to fundamentals. This implies that economic conditions, which are also used in hedonic pricing of real estate, cannot fully account for future movements in returns. We conclude that commercial real estate prices, at least at an aggregate level, are better modeled as financial assets and that the discounted rent model might be more suitable than traditional hedonic models, at least at an aggregate level

The neglected effect of fiscal policy on stock and bond returns

We analyze the effect of taxes and government spending on quarterly market returns of stocks, government bonds, and corporate bonds. In US data from 1960 to 2000, a one standard deviation increase in the share of tax receipts in GDP has a statistically and economically significant effect on returns, lowering annualized expected returns by 4% and 9% at quarterly and yearly horizons, respectively. Istrestingly, the impact of taxes is quantitatively similar for stock and bond returns. These results can partly be explained by the high persistence of the tax series so that increases today imply permanently higher tax levels in the future. An increase in government spending has a positive impact on expected returns, but the effect is statistically significant only for bonds, at short horizons. Our findings represent a novel test of Ricardian Equivalence, using market returns. Fiscal Policy shocks account for 3-4% of the variation in unexpected excess stock returns and 8-10% of the variation in unexpected excess bond returns. When fiscal and monetary policy changes are jointly identified, our results remain qualitatively unchanged and the quantitative results are only reinforced. More importantly, we find that fiscal policy is at least as important a source of return variability as is the policy of the Federal Reserve. The findings are surprisingly robust to various system specifications, such as cointegration assumptions and variable choice. Our results strongly suggest that fiscal policy shocks should be given more serious consideration in asset pricing.

Expected returns and expected erowth in rents of commercial real estate

Commercial real estate expected returns and expected rent growth rates are time-varying. Relying on transactions data from a cross-section of U.S. metropolitan areas, we find that up to 30% of the variability of realized returns to commercial real estate can be accounted for by expected return variability, while expected rent growth rate variability explains up to 45% of the variability of realized rent growth rates. The cap rate - that is, the rent-price ratio in commercial real estate - captures fluctuations in expected returns for apartments, retail properties, as well as industrial properties. For offices, by contrast, cap rates do not forecast (in-sample) returns even though expected returns on o±ces are also time-varying. As implied by the present value relation, cap rates marginally forecast o±ce rent growth but not rent growth of apartments, retail properties, and industrial properties. We link these differences in in-sample predictability to differences in the stochastic properties of the underlying commercial real estate data- generating processes. Also, rent growth predictability is observed mostly in locations characterized by higher population density and stringent land use restrictions. The opposite is true for return predictability. The dynamic portfolio implications of time-varying commercial real estate returns are also explored in the context of a portfolio manager investing in the aggregate stock market, Treasury bills, as well as commercial real estate