Comparing different explanations of the volatility trend

We analyze the puzzling behavior of the volatility of individual stock returns over the past few decades. The literature has provided many different explanations to the trend in volatility and this paper tests the viability of the different explanations. Virtually all current theoretical arguments that are provided for the trend in the average level of volatility over time lend themselves to explanations about the difference in volatility levels between firms in the cross-section. We therefore focus separately on the cross-sectional and time-series explanatory power of the different proxies. We fail to find a proxy that is able to explain both dimensions well. In particular, we find that Cao et al. [Cao, C., Simin, T.T., Zhao, J., 2008. Can growth options explain the trend in idiosyncratic risk? Review of Financial Studies 21, 2599-2633] market-to-book ratio tracks average volatility levels well, but has no cross-sectional explanatory power. On the other hand, the low-price proxy suggested by Brandt et al. [Brandt, M.W., Brav, A., Graham, J.R., Kumar, A., 2010. The idiosyncratic volatility puzzle: time trend or speculative episodes. Review of Financial Studies 23, 863-899] has much cross-sectional explanatory power, but has virtually no time-series explanatory power. We also find that the different proxies do not explain the trend in volatility in the period prior to 1995 (R-squared of virtually zero), but explain rather well the trend in volatility at the turn of the Millennium (1995-2005).     

The Risk Map: A new tool for validating risk models

This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is defined as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR defined at an extremely low probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.     

When more is less: Using multiple constraints to reduce tail risk

Financial institutions suffered large trading losses during the 2007–2009 global financial crisis. These losses cast doubt on the effectiveness of regulations and risk management systems based on a single Value-at-Risk (VaR) constraint. While some researchers have recommended using Conditional Value-at-Risk (CVaR) to control tail risk, VaR remains popular among practitioners and regulators. Accordingly, our paper examines the effectiveness of multiple VaR constraints in controlling CVaR. Under certain conditions, we theoretically show that they are more effective than a single VaR constraint. Furthermore, we numerically find that the maximum CVaR permitted by the constraints is notably smaller than with a single constraint. These results suggest that regulations and risk management systems based on multiple VaR constraints are more effective in reducing tail risk than those based on a single VaR constraint.     

Basel’s value-at-risk capital requirement regulation: An efficiency analysis

We analyze the optimal portfolio policies of expected utility maximizing agents under VaR Capital Requirement (VaR-CR) regulation in comparison to the optimal policy under exogenously-imposed VaR Limit (VaR-L) and Limited-Expected-Loss (LEL) regulations. With VaR-CR regulation the agent strategy consists of simultaneous decisions on both the portfolio VaR and on the implied amount of required eligible capital. As a result, the performance of VaR-CR regulation depends on its design (the parameter n) and the agent preferences. We show that an optimal VaR-CR regulation allows the regulator on the one hand, to completely eliminate the exposure to the largest losses, which may jeopardize the existence of the institution, and on the other hand, to restrain the portfolio exposure to all other losses. These results rationalize the current Basel regulations. However, the analysis shows also that there is an optimal level of required eligible capital from the regulator standpoint. Counter-intuitively, any requirement above this optimal level is inefficient as it leads to a smaller amount of actually maintained eligible capital and thereby to a larger exposure to the most adverse states of the world. Unfortunately, the current Basel’s range of required levels (n = 3–4) is within this inefficient range. Moreover, with an inefficient regulation the agent might employ an inefficient reporting and disclosure procedure.     

Dynamic effects of idiosyncratic volatility and liquidity on corporate bond spreads

We study the dynamic impact of idiosyncratic volatility and bond liquidity on corporate bond spreads over time and empirically disentangle both effects. Using an extensive data set, we find that both idiosyncratic volatility and liquidity are critical mainly for the distress portfolios, i.e., low-rated and short-term bonds; for others only volatility matters. The effects of volatility and liquidity shocks on bond spreads were both exacerbated during the recent financial crisis. Liquidity shocks are quickly absorbed into bonds prices; however, volatility shocks are more persistent and have a long-term effect. Our results overall suggest significant differences between how volatility and liquidity dynamically impact bond spreads.     

Does information drive trading in option strategies?

We study trading in option strategies in the FTSE-100 index market. Trades in option strategies represent around 37% of the total number of trades and over 75% of the total trading volume in our sample. We find some evidence that order flow in volatility–sensitive option strategies contains information about future realized volatility. We do not find evidence that order flow in directionally–sensitive option strategies contains information about future returns. Overall, our evidence suggests that option strategies are used both by traders who possess non-public information about future volatility and by uninformed speculators who appear to follow unprofitable trend chasing strategies.     

Regulation fair disclosure and the market’s reaction to analyst investment recommendation changes

Previous research has shown that affiliated analysts (those who are working for investment banks that underwrite securities for companies) have an incentive to provide optimistically biased recommendations from selective information they are given by the firm. In an effort to halt such activities, as of October 2000, Regulation Fair Disclosure (RegFD) prohibits selective disclosure of material non-public information by public companies to privileged individuals (such as favored research analysts) and requires broad, non-exclusionary disclosure of such information. We examine firms’ stock price reactions to investment recommendation changes from affiliated analysts versus unaffiliated analysts from October 1998 to November 2002, around the passage of RegFD. Similar to previous research, we find that investors reacted more significantly to recommendation downgrades by affiliated analysts than to those by unaffiliated analysts prior to the passage of RegFD. However, we find that the difference in the reactions to recommendation changes is not present after the passage of RegFD. We also find that stock price reactions to analysts’ (both affiliated and unaffiliated) recommendation changes decreased significantly after the passage of RegFD. Thus, RegFD appears to have curbed the selective disclosure of information (particularly negative information) by firms to affiliated analysts. Further, the smaller reactions to recommendation changes by all analysts after RegFD may reflect a change in analysts’ behavior (irrespective of information that is available) or a response by corporate managers to withhold information rather than risking a violation of fair disclosure rules.     

High-frequency financial data modeling using Hawkes processes

Intraday Value-at-Risk (VaR) is one of the risk measures used by market participants involved in high-frequency trading. High-frequency log-returns feature important kurtosis (fat tails) and volatility clustering (extreme log-returns appear in clusters) that VaR models should take into account. We propose a marked point process model for the excesses of the time series over a high threshold that combines Hawkes processes for the exceedances with a generalized Pareto distribution model for the marks (exceedance sizes). The conditional approach features intraday clustering of extremes and is used to calculate instantaneous conditional VaR. The models are backtested on real data and compared to a competitor approach that proposes a nonparametric extension of the classical peaks-over-threshold method. Maximum likelihood estimation is computationally intensive; we use a differential evolution genetic algorithm to find adequate starting values for the optimization process.     

The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR

This paper investigates the role of high-order moments in the estimation of conditional value at risk (VaR). We use the skewed generalized t distribution (SGT) with time-varying parameters to provide an accurate characterization of the tails of the standardized return distribution. We allow the high-order moments of the SGT density to depend on the past information set, and hence relax the conventional assumption in conditional VaR calculation that the distribution of standardized returns is iid. The maximum likelihood estimates show that the time-varying conditional volatility, skewness, tail-thickness, and peakedness parameters of the SGT density are statistically significant. The in-sample and out-of-sample performance results indicate that the conditional SGT-GARCH approach with autoregressive conditional skewness and kurtosis provides very accurate and robust estimates of the actual VaR thresholds.     

Does SEC FRR No. 48 disclosure communicate risk management effectiveness?

We hypothesize that the quality of market risk disclosure mandated by the U.S. Securities and Exchange Commission Financial Reporting Release No. 48 (FRR No. 48) provides useful information for assessing risk management effectiveness. Measuring risk disclosure quality as the degree of modification, we find that higher-than-expected disclosure modification is associated with lower future cash flow volatility. On average, an increase in risk disclosure modification from the lowest to the highest decile is associated with a 5.34 percent decrease in cash flow volatility. Given the significant impact of cash flow volatility on firm value and capital investment, our results highlight the importance of market risk disclosures and should be of interest to investors and analysts.     

Mandatory and Voluntary Disclosures: Dynamic Interactions

Firms sometimes obtain soft private information about growth prospects along with hard information about current or past performance. In this environment, we find that optimizing disclosures over multiple periods yields nonlinear stock price reactions following both voluntary and mandatory disclosures. Further, we derive several predictions about distinct short‐run and long‐run effects of disclosures and nondisclosures on security prices. Under specified conditions, when the volatility of the firm's earnings increases, the average contemporaneous and prospective post‐mandatory‐disclosure market premia (for voluntary disclosures over nondisclosures) rise, while farther‐in‐future market discounts (for such voluntary disclosures) also become larger. Our analysis moreover predicts that both the disclosure probability and the information content of nondisclosures can increase in the persistence of earnings.     

DOES IT PAY TO DISCLOSE MANAGERIAL EARNINGS INFORMATION EARLY?

Does it pay to voluntarily disclose the manager's private information about the firm's earnings prospects before the mandatory announcement date? This question has been a subject of much debate because prior research establishes both benefits and costs of early information disclosure. We provide evidence on the net effect of such disclosure by examining its impact on firm value. Using a large sample and correcting for self‐selection bias, we find that early disclosure of the manager's private earnings information enhances the end‐of‐period value of the firm.     

Voluntary Disclosure with Informed Trading in the IPO Market

We examine voluntary disclosure and capital investment by an informed manager in an initial public offering (IPO) in the presence of informed and uninformed investors. We find that in equilibrium, disclosure is more forthcoming—and investment efficiency is lower—when a greater fraction of the investment community is already informed. Moreover, managers disclose more information when the likelihood of an information event is higher, more equity is issued, or the cost of information acquisition is lower. Investment efficiency and the expected level of underpricing are non‐monotonic in the likelihood that the manager is privately informed.     

Disagreement and asset prices

How do differences of opinion affect asset prices? Do investors earn a risk premium when disagreement arises in the market? Despite their fundamental importance, these questions are among the most controversial issues in finance. In this paper, we use a novel data set that allows us to directly measure the level of disagreement among Wall Street mortgage dealers about prepayment speeds. We examine how disagreement evolves over time and study its effects on expected returns, return volatility, and trading volume in the mortgage-backed security market. We find that increased disagreement is associated with higher expected returns, higher return volatility, and larger trading volume. These results imply that there is a positive risk premium for disagreement in asset prices. We also show that volatility in and of itself does not lead to higher trading volume. Instead, only when disagreement arises in the market is higher uncertainty associated with more trading. Finally, we are able to distinguish empirically between two competing hypotheses regarding how information in markets gets incorporated into asset prices. We find that sophisticated investors appear to update their beliefs through a rational expectations mechanism when disagreement arises.     

Dynamic factor Value-at-Risk for large heteroskedastic portfolios

We propose a methodology that can efficiently measure the Value-at-Risk (VaR) of large portfolios with time-varying volatility and correlations by bringing together the established historical simulation framework and recent contributions to the dynamic factor models literature. We find that the proposed methodology performs well relative to widely used VaR methodologies, and is a significant improvement from a computational point of view.     

Option pricing under time-varying risk-aversion with applications to risk forecasting

We present a two-factor option-pricing model, which parsimoniously captures the difference in volatility persistences under the historical and risk-neutral probabilities. The model generates an S-shaped pricing kernel that exhibits time-varying risk aversion. We apply our model for two purposes. First, we analyze the risk preference implied by S&P500 index options during 2001–2009 and find that risk-aversion level strongly increases during stressed market conditions. Second, we apply our model for Value-at-Risk (VaR) forecasts during the subprime crisis period and find that it outperforms several leading VaR models.     

A note on the importance of overnight information in risk management models

This paper examines the economic value of overnight information to users of risk management models. In addition to the information revealed by overseas markets that trade during the (domestic) overnight period, this paper exploits information generated via recent innovations in the structure of financial markets. In particular, certain securities (and associated derivative products) can now be traded at any time over a 24-h period. As such, it is now possible to make use of information generated by trading, in (almost) identical securities, during the overnight period. Of the securities that are available over such time periods, S&P 500 related products are by far the most actively traded and are, therefore, the subject of this paper. Using a variety of conditional volatility models that allow time-dependent information flow within (and across) three different S&P 500 markets, the results show that overnight information flow has a significant impact on the conditional volatility of daytime traded S&P 500 securities. Moreover (time-consistent) forecasts from models that incorporate overnight information are shown to have economic value to risk managers. In particular, Value-at-Risk (VaR) models based on these conditional volatility models are shown to be more accurate than VaR models that ignore overnight information.     

Forecasting oil price realized volatility using information channels from other asset classes

Motivated from Ross (1989) who maintains that asset volatilities are synonymous to the information flow, we claim that cross-market volatility transmission effects are synonymous to cross-market information flows or “information channels” from one market to another. Based on this assertion we assess whether cross-market volatility flows contain important information that can improve the accuracy of oil price realized volatility forecasting. We concentrate on realized volatilities derived from the intra-day prices of the Brent crude oil and four different asset classes (Stocks, Forex, Commodities and Macro), which represent the different “information channels” by which oil price volatility is impacted from. We employ a HAR framework and estimate forecasts for 1-day to 66-days ahead. Our findings provide strong evidence that the use of the different “information channels” enhances the predictive accuracy of oil price realized volatility at all forecasting horizons. Numerous forecasting evaluation tests and alternative model specifications confirm the robustness of our results.     

The day-of-the-week effect and conditional volatility: Sensitivity of error distributional assumptions

We test for reliable evidence of the day-of-the-week effect on both the mean and volatility for the S&P/TSX Canadian return index. Unlike previous studies, we permit several specifications for the error distribution — GARCH normal, Student's t, generalized error distribution, and double exponential distribution. Unlike other studies, we find that the day-of-the-week effect in both mean and conditional volatility is sensitive to the particular specification of the underlying distributions. We also find that using a regression analysis assuming a Student's t distribution is a better way to investigate this effect. Our evidence demonstrates the apparent fragility of previous empirical studies on calendar anomalies. Thus, our results serve as a warning that with financial data, the error distributional assumptions are critical to correctly identifying empirical regularities in the data.     

Long memory versus structural breaks in modeling and forecasting realized volatility

We explore the possibility of structural breaks in the daily realized volatility of the Deutschemark/Dollar, Yen/Dollar and Yen/Deutschemark spot exchange rates with observed long memory behavior. We find that structural breaks in the mean can partly explain the persistence of realized volatility. We propose a VAR-RV-Break model that provides superior predictive ability when the timing of future breaks is known. With unknown break dates and sizes, we find that a VAR-RV-I(d) long memory model provides a robust forecasting method even when the true financial volatility series are generated by structural breaks.