Jump and Volatility Risk and Risk Premia: A New Model and Lessons from S&P 500 Options

We use a novel pricing model to filter times series of diffusive volatility and jump intensity from S&P 500 index options. These two measures capture the ex-ante risk assessed by investors. We find that both components of risk vary substantially over time, are quite persistent, and correlate with each other and with the stock index. Using a simple general equilibrium model with a representative investor, we translate the filtered measures of ex-ante risk into an ex-ante risk premium. We find that the average premium that compensates the investor for the risks implicit in option prices, 10.1 percent, is about twice the premium required to compensate the same investor for the realized volatility, 5.8 percent. Moreover, the ex-ante equity premium that we uncover is highly volatile, with values between 2 and 32 percent. The component of the premium that corresponds to the jump risk varies between 0 and 12 percent.

Flexible multivariate GARCH modeling with an application to international stock markets

This paper offers a new approach to estimating time-varying covariance matrices in the framework of the diagonal-vech version of the multivariate GARCH(1,1) model. Our method is numerically feasible for large-scale problems, produces positive semidefinite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the nev^ estimator with a number of existing ones

Dynamic Portfolio Selection by Augmenting the Asset Space

We present a novel approach to dynamic portfolio selection that is no more difficult to implement than the static Markowitz model. The idea is to expand the asset space to include simple (mechanically) managed portfolios and compute the optimal static portfolio in this extended asset space. The intuition is that a static choice among managed portfolios is equivalent to a dynamic strategy. We consider managed portfolios of two types: "conditional" and "timing" portfolios. Conditional portfolios are constructed along the lines of Hansen and Richard (1987). For each variable that affects the distribution of returns and for each basis asset, we include a portfolio that invests in the basis asset an amount proportional to the level of the conditioning variable. Timing portfolios invest in each basis asset for a single period and therefore mimic strategies that buy and sell the asset through time. We apply our method to a problem of dynamic asset allocation across stocks, bonds, and cash using the predictive ability of four conditioning variables.

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.

Flexible multivariate GARCH modeling with an application to international stock markets

The goal of this paper is to estimate time-varying covariance matrices. Since the covariance matrix of financial returns is known to change through time and is an essential ingredient in risk measurement, portfolio selection, and tests of asset pricing models, this is a very important problem in practice. Our model of choice is the Diagonal-Vech version of the Multivariate GARCH(1,1) model. The problem is that the estimation of the general Diagonal-Vech model model is numerically infeasible in dimensions higher than 5. The common approach is to estimate more restrictive models which are tractable but may not conform to the data. Our contribution is to propose an alternative estimation method that is numerically feasible, produces positive semi-definite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the new estimator to a number of existing ones.Diagonal-Vech model multivariate GARCH, unrestricted estimation

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.