Testing for a unit root in the volatility of asset returns

It is now well established that the volatility of asset returns is time varying and highly persistent. One leading model that is used to represent these features of the data is the stochastic volatility model. The researcher may test for non-stationarity of the volatility process by testing for a unit root in the log-squared time series. This strategy for inference has many advantages, but is not followed in practice because these unit root tests are known to have very poor size properties. In this paper I show that new tests that are robust to negative MA roots allow a reliable test for a unit root in the volatility process to be conducted. In applying these tests to exchange rate and stock returns, strong rejections of non-stationarity in volatility are obtained. Copyright © 1999 John Wiley & Sons, Ltd.     

Estimating stochastic volatility: the rough side to equity returns

Decisions in Economics and Finance - This paper evaluates the forecasting performance of a Brownian semi-stationary (BSS) process in modelling the volatility of 21 equity indices. We implement a...     

Forecasting the volatility of asset returns: The informational gains from option prices

A new class of forecasting models is proposed that extends the realized GARCH class of models through the inclusion of option prices to forecast the variance of asset returns. The VIX is used to approximate option prices, resulting in a set of cross-equation restrictions on the model’s parameters. The full model is characterized by a nonlinear system of three equations containing asset returns, the realized variance, and the VIX, with estimation of the parameters based on maximum likelihood methods. The forecasting properties of the new class of forecasting models, as well as a number of special cases, are investigated and applied to forecasting the daily S&P500 index realized variance using intra-day and daily data from September 2001 to November 2017. The forecasting results provide strong support for including the realized variance and the VIX to improve variance forecasts, with linear conditional variance models performing well for short-term one-day-ahead forecasts, whereas log-linear conditional variance models tend to perform better for intermediate five-day-ahead forecasts.     

Cross-sectional implications of dynamic asset pricing with stochastic volatility and ambiguity aversion

Building on recent research that highlights the importance of macroeconomic volatility and ambiguity aversion in explaining the dynamics of stock returns, in this paper we propose a dynamic asset pricing model that simultaneously accounts for stochastic macroeconomic volatility and ambiguity, assuming that investors deal with uncertainty about the mechanics of macroeconomic fluctuations using first-release consumption and revisions to aggregate consumption on vintage data. Our results show that the proposed model captures a large fraction of the cross-sectional variation of excess returns for a wide range of market anomaly portfolios. Furthermore, while the price of risk for ambiguity is positive and significant for the vast majority of assets under study, macroeconomic volatility yields ambiguous outcomes, although it significantly increases the explanatory power of the model for specific assets. Our results suggest that macroeconomic volatility and ambiguity complement each other in explaining the cross-sectional behavior of stock returns.     

Estimating the output gap in real time: A factor model approach

By using a dynamic factor model, we can substantially improve the reliability of real-time output gap estimates for the U.S. economy. First, we use a factor model to extract a series for the common component in GDP from a large panel of monthly real-time macroeconomic variables. This series is immune to revisions to the extent that revisions are due to unbiased measurement errors or idiosyncratic news. Second, our model is able to handle the unbalanced arrival of the data. This yields favorable nowcasting properties and thus starting conditions for the filtering of data into a trend and deviations from a trend. Combined with the method of augmenting data with forecasts prior to filtering, this greatly reduces the end-of-sample imprecision in the gap estimate. The increased precision has economic importance for real-time policy decisions and improves real-time inflation forecasts.     

Excess volatility and the cross-section of stock returns

We document a reliable positive relation between excess volatility and the cross-section of stock returns over the sample period of 1963 to 2010. Significantly positive differentials have been found between the two decile portfolios with the largest and the least excess volatility, under all the situations we have examined. Size, value, and momentum effects cannot explain our empirical results. Likewise they cannot be explained by liquidity, bid-ask bounce, and risk-aversion-related inventory effects.     

Estimating the returns to schooling: a likelihood approach based on normal mixtures

In this paper we develop likelihood‐based methods for statistical inference in a joint system of equations for the choice of length of schooling and earnings. The model for schooling choice is assumed to be an ordered probit model, whereas the earnings equation contains variables that are flexible transformations of schooling and experience, with corresponding coefficients that are allowed to be heterogeneous across individuals. Under the assumption that the distribution of the random terms of the model can be expressed as a finite mixture of multinormal distributions, we show that the joint probability distribution for schooling and earnings can be expressed on closed form. In an application of our method on Norwegian data, we find that the mixed Gaussian model offers a substantial improvement in fit to the (heavy‐tailed) empirical distribution of log‐earnings compared to a multinormal benchmark model. Copyright © 2010 John Wiley & Sons, Ltd.     

OPEC news and predictability of oil futures returns and volatility: Evidence from a nonparametric causality-in-quantiles approach

This paper provides a novel perspective to the predictive ability of OPEC meeting dates and production announcements for (Brent Crude and West Texas Intermediate) oil futures market returns and GARCH-based volatility using a nonparametric quantile-based methodology. We show a nonlinear relationship between oil futures returns and OPEC-based predictors; hence, linear Granger causality tests are misspecified and the linear model results of non-predictability are unreliable. When the quantile-causality test is implemented, we observe that the impact of OPEC variables is restricted to Brent Crude futures only (with no effect observed for the WTI market). Specifically, OPEC production announcements, and meeting dates predict only lower quantiles of the conditional distribution of Brent futures market returns. While, predictability of volatility covers the majority of the quantile distribution, barring extreme ends.     

International propagation of shocks: A dynamic factor model using survey forecasts

This paper studies the pathways for the propagation of shocks across the G7 and major Asia-Pacific countries using multi-horizon forecasts of real GDP growth from 1995 to 2017. We show that if the forecasts are efficient in the long run, the results obtained using these forecasts are comparable to those obtained from the actual outturns. We measure global business cycle connectedness and study the impacts of both country-specific shocks and common international shocks using a panel factor structural VAR model. Our results suggest that there is a strong convergence of business cycles within the group of industrialized countries, as well as within the group of developing economies during non-recessionary periods. In particular, we find an increased decoupling between the industrialized and developing economies after the 2008 recession. However, the direction of shock spillovers during recessions and other crisis periods varies, depending on the nature and origin of the episode.     

Estimating willingness to pay for medicare using a dynamic life-cycle model of demand for health insurance

Medicare is the largest health insurance program in the US. This paper uses a dynamic random utility model of demand for health insurance in a life-cycle human capital framework with endogenous production of health to calculate the individual willingness to pay (WTP) for Medicare. The model accounts for the feature that the demand for health insurance is derived through the demand for health, which is jointly determined with the production of health over the life-cycle. The WTP measure incorporates the effects of Medicare insurance on aggregate consumption through effects on medical expenditures and mortality, and consumption utility of health. The model is estimated using panel data from the Health and Retirement Study. The average WTP or change in lifetime expected utility resulting from delaying the age of eligibility to 67 is found to be $ 24,947 in 1991 dollars ($ 39,435 in 2008 dollars). However, there is considerable variation in the WTP, e.g., in 1991 dollars the WTP of individuals who have less than a high school education and are white is $ 28,347 ($ 44,810 in 2008 dollars), while the WTP of those with at least a college degree and who are neither white nor black is $ 15,584 ($ 24,635 in 2008 dollars). More generally, the less educated have a higher WTP to avoid a policy change that delays availability of Medicare benefits. Additional model simulations imply that the primary benefits of Medicare are insurance against medical expenditures with relatively smaller benefits in terms of improved health status and longevity. Medicare also leads to large increases in medical utilization due to deferring of medical care prior to eligibility.     

Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model

We extend the class of dynamic factor yield curve models in order to include macroeconomic factors. Our work benefits from recent developments in the dynamic factor literature related to the extraction of the common factors from a large panel of macroeconomic series and the estimation of the parameters in the model. We include these factors in a dynamic factor model for the yield curve, in which we model the salient structure of the yield curve by imposing smoothness restrictions on the yield factor loadings via cubic spline functions. We carry out a likelihood-based analysis in which we jointly consider a factor model for the yield curve, a factor model for the macroeconomic series, and their dynamic interactions with the latent dynamic factors. We illustrate the methodology by forecasting the U.S. term structure of interest rates. For this empirical study, we use a monthly time series panel of unsmoothed Fama–Bliss zero yields for treasuries of different maturities between 1970 and 2009, which we combine with a macro panel of 110 series over the same sample period. We show that the relationship between the macroeconomic factors and the yield curve data has an intuitive interpretation, and that there is interdependence between the yield and macroeconomic factors. Finally, we perform an extensive out-of-sample forecasting study. Our main conclusion is that macroeconomic variables can lead to more accurate yield curve forecasts.     

Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach

We develop new tests of the capital asset pricing model that take account of and are valid under the assumption that the distribution generating returns is elliptically symmetric; this assumption is necessary and sufficient for the validity of the CAPM. Our test is based on semiparametric efficient estimation procedures for a seemingly unrelated regression model where the multivariate error density is elliptically symmetric, but otherwise unrestricted. The elliptical symmetry assumption allows us to avoid the curse of dimensionality problem that typically arises in multivariate semiparametric estimation procedures, because the multivariate elliptically symmetric density function can be written as a function of a scalar transformation of the observed multivariate data. The elliptically symmetric family includes a number of thick‐tailed distributions and so is potentially relevant in financial applications. Our estimated betas are lower than the OLS estimates, and our parameter estimates are much less consistent with the CAPM restrictions than the corresponding OLS estimates. Copyright © 2002 John Wiley & Sons, Ltd.     

Expected market returns: SVIX,realized volatility,and the role of dividends

This note provides a replication of Martin's (Quarterly Journal of Economics, 2017, 132(1), 367–433) finding that the implied volatility measure SVIX predicts US stock market returns up to 12‐month horizons. I find that this result holds for both S&P 500 and CRSP market returns, regardless of whether returns include or exclude dividends. The predictability largely disappears after the SVIX index is replaced by an exponentially weighted moving average measure of realized volatility, suggesting that SVIX holds incremental forward‐looking information compared to realized volatility, despite the high correlation between the two volatility measures.     

Dynamic volatility modelling of Bitcoin using time-varying transition probability Markov-switching GARCH model

Bitcoin (BTC), as the dominant cryptocurrency, has attracted tremendous attention lately due to its excessive volatility. This paper proposes the time-varying transition probability Markov-switching GARCH (TV-MSGARCH) models incorporated with BTC daily trading volume and daily Google searches singly and jointly as exogenous variables to model the volatility dynamics of BTC return series. Extensive comparisons are carried out to evaluate the modelling performances of the proposed model with the benchmark models such as GARCH, GJRGARCH, threshold GARCH, constant transition probability MSGARCH and MSGJRGARCH. Results reveal that the TV-MSGARCH models with skewed and fat-tailed distribution predominate other models for the in-sample model fitting based on Akaike information criterion and other benchmark criteria. Furthermore, it is found that the TV-MSGARCH model with BTC daily trading volume and student-t error distribution offers the best out-of-sample forecast evaluated based on the mean square error loss function using Hansen’s model confidence set. Filardo’s weighted transition probabilities are also computed and the results show the existence of time-varying effect on transition probabilities. Lastly, different levels of long and short positions of value-at-risk and the expected shortfall forecasts based on MSGARCH, MSGJRGARCH and TV-MSGARCH models are also examined.     

Market efficiency,asset returns,and the size of the risk premium in global equity markets

An important economic insight is that observed equity prices must equal the present value of the cash flows associated with the equity claim. An implication of this insight is that present values of cash flows must also quantitatively justify the observed volatility and cross-correlations of asset returns. In this paper, we show that parametric economic models for present values can indeed account for the observed high ex post return volatility and cross-correlation observed across five major equity markets—the U.S., the U.K., France, Germany, and Japan. We present evidence that cash flow growth rates contain a small predictable long-run component; this feature, in conjunction with time-varying systematic risk, can justify key empirical characteristics of observed equity prices. Our model also has direct implications for the level of equity prices and specific versions of the model can, in many cases, capture observed price levels. Our evidence suggests that the ex ante risk premium on the global market portfolio has dropped considerably—we show that this fall in the risk premium is related to a decline in the conditional variance of global real cash flow growth rates.     

Estimating the effect of smoking on birth outcomes using a matched panel data approach

Estimating the casual effect of smoking on birth outcomes is difficult since omitted (unobserved) variables are likely to be correlated with a mother's decision to smoke. While some previous work has dealt with this endogeneity problem by using instrumental variables, this paper instead attempts to estimate the smoking effect from panel data (i.e., data on mothers with multiple births). Panel data sets are constructed with matching algorithms applied to federal natality data. The fixed effects regressions, which control for individual heterogeneity, yield significantly different results from ordinary least squares and previous instrumental variable approaches. The potential inconsistency caused by ‘false matches’ and other violations of the fixed effects strict exogeneity assumption are considered. Copyright © 2006 John Wiley & Sons, Ltd.     

Pricing the hedging factor in the cross-section of stock returns

We investigate the role of investors’ net hedging strategy (factor) in predicting stock returns and pricing the cross-section of individual stocks and equity portfolios. We estimate stock exposure to changes in the hedging factor and show that the hedging premium is driven by outperformance of stocks with large positive net hedging betas, which explains their higher average returns. We find the positive hedging premium indicates risk-averse investors demand extra compensation to hold stocks with higher equity risk premiums, and they are themselves willing to pay higher prices for stocks with positive hedging betas.     

The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts

The recent theoretical asset allocation literature has derived optimal dynamic investment strategies in various advanced models of asset returns. But how sensitive is investor welfare to deviations from the theoretically optimal strategy? Will unsophisticated investors do almost as well as sophisticated investors? This paper develops a general theoretical framework for answering such questions and applies it to three specific models of interest rate risk, stochastic stock volatility, and mean reversion and growth/value tilts of stock portfolios. Among other things, we find that growth/value tilts are highly valuable, but the hedging of time-varying stock risk premia is less important.