Jump tails,extreme dependencies,and the distribution of stock returns

We provide a new framework for estimating the systematic and idiosyncratic jump tail risks in financial asset prices. Our estimates are based on in-fill asymptotics for directly identifying the jumps, together with Extreme Value Theory (EVT) approximations and methods-of-moments for assessing the tail decay parameters and tail dependencies. On implementing the procedures with a panel of intraday prices for a large cross-section of individual stocks and the S&P 500 market portfolio, we find that the distributions of the systematic and idiosyncratic jumps are both generally heavy-tailed and close to symmetric, and show how the jump tail dependencies deduced from the high-frequency data together with the day-to-day variation in the diffusive volatility account for the “extreme” joint dependencies observed at the daily level.     

How Do Alphas and Betas Move? Uncertainty,Learning and Time Variation in Risk Loadings*

I employ a parsimonious model with learning, but without conditioning information, to extract time‐varying measures of market‐risk sensitivities, pricing errors and pricing uncertainty. The evolution of these quantities has interesting implications for macroeconomic dynamics. Parameters estimated for US equity portfolios display significant low‐frequency fluctuations, along patterns that change across size and book‐to‐market stocks. Time‐varying betas display superior predictive accuracy for returns against constant and rolling‐window OLS estimates. As to the relationship of betas with business‐cycle variables, value stocks’ betas move pro‐cyclically, unlike those of growth stocks. Investment growth, rather than consumption, predicts the betas of value and small‐firm portfolios.     

The extension from independence to dependence between jump frequency and jump size in Markov-modulated jump diffusion models

We set out in this study to investigate the relationship between jump frequency and jump size for the 30 component stocks of the Dow Jones Industrial Average (DJIA) index, extending the Markov-modulated jump diffusion model from independence to dependence between jump frequency and jump size. We propose an estimation method for the parameters of the Markov-modulated jump diffusion model based upon dependence between jump frequency and size, with our results indicating that when abnormal events occur, the Markov-modulated jump diffusion models with both state-independent jump sizes (MJMI) and state-dependent jump sizes (MJMD) outperform the pure jump diffusion (JD) model in terms of capturing the risks of jump frequency and jump size. Based upon Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC), our results further indicate that for 23 of the component stocks, the MJMD model may be better suited, as compared to the MJMI model. Finally, our empirical observations reveal that the behavior of jump risks in the stock markets, including jump frequency and jump size, is not independent, since these phenomena are found to coincide during both financial crisis periods and stock market crashes, with the largest jump size risks, during certain periods, being accompanied by either systematic or idiosyncratic risks.     

Risk,jumps, and diversification

We test for price discontinuities, or jumps, in a panel of high-frequency intraday stock returns and an equiweighted index constructed from the same stocks. Using a new test for common jumps that explicitly utilizes the cross-covariance structure in the returns to identify non-diversifiable jumps, we find strong evidence for many modest-sized, yet highly significant, cojumps that simply pass through standard jump detection statistics when applied on a stock-by-stock basis. Our results are further corroborated by a striking within-day pattern in the significant cojumps, with a sharp peak at the time of regularly scheduled macroeconomic news announcements.     

Threshold bipower variation and the impact of jumps on volatility forecasting

This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous components using estimators which are not only consistent, but also scarcely plagued by small sample bias. With the aim of achieving this, we introduce the concept of threshold bipower variation, which is based on the joint use of bipower variation and threshold estimation. We show that its generalization (threshold multipower variation) admits a feasible central limit theorem in the presence of jumps and provides less biased estimates, with respect to the standard multipower variation, of the continuous quadratic variation in finite samples. We further provide a new test for jump detection which has substantially more power than tests based on multipower variation. Empirical analysis (on the S&P500 index, individual stocks and US bond yields) shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump.     

Is a co-jump in prices a sparse jump?

Systematic co-jumps in asset prices are generally thought to account for only a small proportion of overall jumps. In actual observations, however, jumps in asset prices are often persistent, and the time of persistence varies. In this context, we develop a new rule to identify co-jumps and improve traditional tests by considering different sampling frequencies and different sampling starting points to re-evaluate the occurrence rate of systematic co-jumps in financial assets. We conduct a simulation experiment to show that the current test procedures generally underestimate the number of co-jumps when considering persistence, but that the proposed procedure can identify co-jumps more accurately. We also perform an empirical analysis using price data from the Shanghai 50 Index and its 25 constituent stocks in China’s stock market. The average proportion of systematic co-jumps detected by the improved s-BNS is approximately 30%, which shows that the co-jump and even the systematic co-jump are not sparse jumps. The results also reveal the shortcomings of traditional jump tests in estimating persistent jumps and demonstrate that the proposed method can better detect the possible nondiversifiable risks between market indices and their constituent stocks, thereby contributing to financial risk management.     

Realized jumps on financial markets and predicting credit spreads

This paper extends the jump detection method based on bipower variation to identify realized jumps on financial markets and to estimate parametrically the jump intensity, mean, and variance. Finite sample evidence suggests that the jump parameters can be accurately estimated and that the statistical inferences are reliable under the assumption that jumps are rare and large. Applications to equity market, treasury bond, and exchange rate data reveal important differences in jump frequencies and volatilities across asset classes over time. For investment grade bond spread indices, the estimated jump volatility has more forecasting power than interest rate factors and volatility factors including option-implied volatility, with control for systematic risk factors. The jump volatility risk factor seems to capture the low frequency movements in credit spreads and comoves countercyclically with the price–dividend ratio and corporate default rate.     

Low and high frequency macroeconomic forces in asset pricing

We use a frequency decomposition method to examine the differential pricing of low and high frequency movements in macroeconomic state variables that characterize systematic factor risks in the economy. We further examine whether the sensitivities to low and high frequency systematic risks differs by firm size. Results indicate that beta risk in low frequency cyclical periods of two years or more is priced with more significance than aggregate systematic risk, and that low frequency factor risks are relatively greater for small capitalization stocks while high frequency systematic factor risks are relatively greater for large capitalization stocks.     

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.     

Time-varying jump tails

We develop new methods for the estimation of time-varying risk-neutral jump tails in asset returns. In contrast to existing procedures based on tightly parameterized models, our approach imposes much fewer structural assumptions, relying on extreme-value theory approximations together with short-maturity options. The new estimation approach explicitly allows the parameters characterizing the shape of the right and the left tails to differ, and importantly for the tail shape parameters to change over time. On implementing the procedures with a panel of S&P 500 options, our estimates clearly suggest the existence of highly statistically significant temporal variation in both of the tails. We further relate this temporal variation in the shape and the magnitude of the jump tails to the underlying return variation through the formulation of simple time series models for the tail parameters.     

Does the information content of payout initiations and omissions influence firm risks?

We study the influence on firm risks of NASDAQ and NYSE firm payout initiations and omissions. These payout events can be interpreted as managerial signals of firm financial life-cycle maturation resulting in concomitant changes in firm risks. We remove confounding payout types and we match on the propensity to initiate or omit informed by determinants of payout known to investors in advance. For payout event and matched firms, we apply the difference-in-differences method to estimate the effect of the information content of actual initiations and omissions on firm risks. We find consistent significant declines in total, aggregate systematic, and idiosyncratic firm risks after cash dividend initiations and increases after dividend omissions, but only incidentally after share repurchase initiations and omissions.     

Testing for mutually exciting jumps and financial flights in high frequency data

We propose a new nonparametric test to identify mutually exciting jumps in high frequency data. We derive the asymptotic properties of the test statistics and show that the tests have good size and reasonable power in finite sample cases. Using our mutual excitation tests, we empirically characterize the dynamics of financial flights in forms of flight-to-safety and flight-to-quality. The results indicate that mutually exciting jumps and risk-off trades mostly occur in periods of high market stress. Flight-to-safety episodes (from stocks to gold) arrive more frequently than do flight-to-quality spells (from stocks to bonds). We further find evidence that reverse cross-excitations or seeking-return-strategies exhibit significant asymmetry over the business cycle, reflecting the fact that investors appear to be selling gold – rather than bonds – to invest in stocks during good market conditions.     

Press freedom and jumps in stock prices

Press freedom varies substantially across countries. In a free environment, any news immediately becomes public knowledge through mediums including various electronic media and published materials. However, in an unfree environment, (economic) agents would have more discretionary powers to disclose good news immediately, while hiding bad news or releasing bad news slowly. We argue that this discretion affects stock prices and that stock markets in countries with a free press should be better processors of economic information. Using an equilibrium asset-pricing model in an economy under jump diffusion, we decompose the moments of the returns of international stock markets into a diffusive risk and a jump risk part. Using stock market data for a balanced panel of 50 countries, our results suggest that in countries with a free press, the better processing of bad news leads to more frequent negative jumps in stock prices. As a result, stock markets in those countries are characterized by higher volatility, driven by higher jump risk and more negative return asymmetry. The results are robust to the inclusion of various controls for governance and other country- or market-specific characteristics. We interpret these as good stock market characteristics because a free press improves welfare and increases economic growth.     

The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange,stock, and bond markets

We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in our information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the heterogeneous autoregressive (HAR) model is applied with implied volatility as an additional forecasting variable. A vector HAR (VecHAR) model for the resulting simultaneous system is introduced, controlling for possible endogeneity issues. We find that implied volatility contains incremental information about future volatility in all three markets, relative to past continuous and jump components, and it is an unbiased forecast in the foreign exchange and stock markets. Out-of-sample forecasting experiments confirm that implied volatility is important in forecasting future realized volatility components in all three markets. Perhaps surprisingly, the jump component is, to some extent, predictable, and options appear calibrated to incorporate information about future jumps in all three markets.     

Continuous‐time models,realized volatilities,and testable distributional implications for daily stock returns

We provide an empirical framework for assessing the distributional properties of daily speculative returns within the context of the continuous‐time jump diffusion models traditionally used in asset pricing finance. Our approach builds directly on recently developed realized variation measures and non‐parametric jump detection statistics constructed from high‐frequency intra‐day data. A sequence of simple‐to‐implement moment‐based tests involving various transformations of the daily returns speak directly to the importance of different distributional features, and may serve as useful diagnostic tools in the specification of empirically more realistic continuous‐time asset pricing models. On applying the tests to the 30 individual stocks in the Dow Jones Industrial Average index, we find that it is important to allow for both time‐varying diffusive volatility, jumps, and leverage effects to satisfactorily describe the daily stock price dynamics. Copyright © 2009 John Wiley & Sons, Ltd.     

Jump-robust volatility estimation using nearest neighbor truncation

We propose two new jump-robust estimators of integrated variance that allow for an asymptotic limit theory in the presence of jumps. Specifically, our MedRV estimator has better efficiency properties than the tripower variation measure and displays better finite-sample robustness to jumps and small (“zero”) returns. We stress the benefits of local volatility measures using short return blocks, as this greatly alleviates the downward biases stemming from rapid fluctuations in volatility, including diurnal (intraday) U-shape patterns. An empirical investigation of the Dow Jones 30 stocks and extensive simulations corroborate the robustness and efficiency properties of our nearest neighbor truncation estimators.     

No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects,jumps and i.i.d. noise: Theory and testable distributional implications

We develop a sequential procedure to test the adequacy of jump-diffusion models for return distributions. We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and leverage effects. A novel robust-to-jumps approach is utilized to alleviate microstructure frictions for realized volatility estimation. Size and power of the procedure are explored through Monte Carlo methods. Our empirical findings support the jump-diffusive representation for S&P500 futures returns but reveal it is critical to account for leverage effects and jumps to maintain the underlying semi-martingale assumption.     

Mutual excitation in Eurozone sovereign CDS

We study self- and cross-excitation of shocks in the Eurozone sovereign CDS market. We adopt a multivariate setting with credit default intensities driven by mutually exciting jump processes, to capture the salient features observed in the data, in particular, the clustering of high default probabilities both in time (over days) and in space (across countries). The feedback between jump events and the intensity of these jumps is the key element of the model. We derive closed-form formulae for CDS prices, and estimate the model by matching theoretical prices to their empirical counterparts. We find evidence of self-excitation and asymmetric cross-excitation. Using impulse-response analysis, we assess the impact of shocks and a potential policy intervention not just on a single country under scrutiny but also, through the effect on cross-excitation risk which generates systemic sovereign risk, on other interconnected countries.     

Structural analysis of portfolio risk using beta impulse response functions

We estimate the data generating process of daily excess returns of 20 major German stocks in a CAPM framework with time varying betas. Our sample spans a 23 year period from 1974 to 1996. An asymmetric dependence of volatility on lagged innovations is taken into account. We introduce beta impulse response functions to shed light on the structural implications of systematic risk associated with competing volatility models. The dependence of beta on news is characterized with respect to different sources (asset specific vs. market general news). The empirical results suggest that negative news emerging from the market involve a stronger impact on beta relative to positive news. Concerning firm specific news the opposite relation is found for the majority of the analysed data sets.     

Non-parametric and semi-parametric asset pricing: An application to the Colombian stock exchange

We estimate non-parametrical one-factor and three-factor international Capital Asset Pricing Models (CAPM) and find strong evidence for rejecting the linear CAPM specification. Furthermore, we find inconsistent linear betas for a series of stocks in the Colombian stock exchange (BVC), supporting the hypothesis of better and consistent fit of non-parametrical versions of the CAPM.