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Abstract:
This paper examines the cross-sectional relation between idiosyncratic volatility and expected stock returns. The results indicate that (i) data frequency used to estimate idiosyncratic volatility, (ii) weighting scheme used to compute average portfolio returns, (iii) breakpoints utilized to sort stocks into quintile portfolios, and (iv) using a screen for size, price and liquidity play a critical role in determining the existence and significance of a relation between idiosyncratic risk and the cross-section of expected returns. Portfolio-level analyses based on two different measures of idiosyncratic volatility (estimated using daily and monthly data), three weighting schemes (value-weighted, equal-weighted, inverse-volatility-weighted), three breakpoints (CRSP, NYSE, equal-market-share), and two different samples (NYSE/AMEX/NASDAQ and NYSE) indicate that there is no robust, significant relation between idiosyncratic volatility and expected returns.

idiosyncratic risk, expected stock returns, size, book-to-market, liquidity

Abstract:
This paper examines the cross-sectional relation between idiosyncratic volatility and expected stock returns. The results indicate that (i) data frequency used to estimate idiosyncratic volatility, (ii) weighting scheme used to compute average portfolio returns, (iii) breakpoints utilized to sort stocks into quintile portfolios, and (iv) using a screen for size, price and liquidity play a critical role in determining the existence and significance of a relation between idiosyncratic risk and the cross-section of expected returns. Portfolio-level analyses based on two different measures of idiosyncratic volatility (estimated using daily and monthly data), three weighting schemes (value-weighted, equal-weighted, inverse-volatility-weighted), three breakpoints (CRSP, NYSE, equal-market-share), and two different samples (NYSE/AMEX/NASDAQ and NYSE) indicate that there is no robust, significant relation between idiosyncratic volatility and expected returns.

idiosyncratic risk, total risk, expected stock returns, size, liquidity

Abstract:
We examine the relation between expected future volatility (options' implied volatility) and the cross-section of expected returns. A trading strategy buying stocks in the highest implied volatility quintile and shorting stocks in the lowest implied volatility quintile generates insignificant returns. A similar strategy using one-month lagged realized volatility generates significantly negative returns. To investigate the differences and interactions between alternative measures of total risk, we estimate three principal components based on realized volatility, call implied and put implied volatility. Long-short trading strategies generate significant returns only for the second and the third principal components. We find that the second principal component is related to the realized-implied volatility spread which can be viewed as a proxy for volatility risk. We find that the third principal component is related to the call-put implied volatility spread that reflects future price increase of the underlying stock.

expected returns, implied volatility, realized volatility, volatility spread

Abstract:
Using two large hedge fund databases, this paper empirically tests the presence and significance of a cross-sectional relation between hedge fund returns and value at risk (VaR). The univariate and bivariate portfolio-level analyses as well as the fund-level regression results indicate a significantly positive relation between VaR and the cross-section of expected returns on live funds. During the period of January 1995 to December 2003, the live funds with high VaR outperform those with low VaR by an annual return difference of 9%. This risk-return tradeoff holds even after controlling for age, size, and liquidity factors. Furthermore, the risk profile of defunct funds is found to be different from that of live funds. The relation between downside risk and expected return is found to be negative for defunct funds because taking high risk by these funds can wipe out fund capital, and hence they become defunct. Meanwhile, voluntary closure makes some well performed funds with large assets and low risk fall into the defunct category. Hence, the risk-return relation for defunct funds is more complicated than what implies by survival. We demonstrate how to distinguish live funds from defunct funds on an ex ante basis. A trading rule based on buying the expected to live funds and selling the expected to disappear funds provides an annual profit of 8-10% depending on the investment horizons.

hedge funds, value at risk, cross-section of expected returns, liquidity

Abstract:
Due to the near unit-root behavior of interest rates, the movements of individual interest-rate series are inherently difficult to forecast. In this paper, we propose an innovative way of applying dynamic term structure models to forecast interest-rate movements. Instead of directly forecasting the movements based on the estimated factor dynamics, we use the dynamic term structure model as a decomposition tool and decompose each interest-rate series into two components: a persistent component captured by the dynamic factors, and a strongly mean-reverting component given by the pricing residuals of the model. With this decomposition, we form interest-rate portfolios that are first-order neutral to the persistent dynamic factors, but are fully exposed to the strongly mean-reverting residuals. We show that the predictability of these interest-rate portfolios is significant both statistically and economically, both in sample and out of sample.

Term structure, Predictability, Interest rates, Factors, Pricing errors, Expectation hypotheses

Abstract:
This paper examines derivatives use of foreign exchange, interest rate and commodities risk by non-financial firms across multiple industries, using data from 1995 to 2001. This paper considers the interaction of a firm's risk exposures, derivatives use, and real operations simultaneously, and considers how these factors change over time using a consistent data base. Hedging with derivatives is only significantly related to commodity risk exposure during most years of the study, and to a more limited degree to interest rate exposure. Further, we find a strong correlation between risk exposures for some years using a new technique, suggesting that univariate modeling is not always appropriate. The implications are that hedging with derivatives is not always important to a firm's rate of return and is linked to other non-financial and economic factors.

hedging, derivatives use, risk management, risk exposure

Abstract:
This paper examines the returns to investment strategies based on the interactions between value-to-market indicators and corporate financing transactions that increase or decrease the firm's outstanding equity, i.e., equity issues and repurchases. Portfolio-level analyses and firm-level cross-sectional regressions indicate that the well-documented contrarian profits soar when value stocks which repurchase shares (value repurchasers) and growth stocks which issue shares (growth issuers) are considered. The results also show that value-to-market ratios cannot capture the cross-sectional variation in expected stock returns when value issuers and growth repurchasers are considered. Based on various risk measures, we find that value repurchasers are not riskier than growth issuers. Furthermore, value repurchasers (growth issuers) experience the highest increase (decrease) in future growth rates. Our findings are consistent with the misvaluation explanation for the superior returns of value stocks.

Share issues, share repurchases, contrarian investment, expected stock returns, value-to-market ratios

Abstract:
Using equity returns for financial institutions we estimate both catastrophic and operational risk measures over the period 1973-2003. We find evidence of cyclical components in both the catastrophic andoperational risk measures obtained from the Generalized Pareto Distribution and the Skewed Generalized Error Distribution. Our new, comprehensive approach to measuring operational risk shows that approximately 18% of financial institutions returns represent compensation for operational risk. However,depository institutions are exposed to operational risk levels that average 39% of the overall equity risk premium. Moreover, operational risk events are more likely to be the cause of large unexpected catastrophiclosses, although when they occur, the losses are smaller than those resulting from a combination of market risk, credit risk or other risk events.

operational risk, catastrophic risk, value at risk, extreme value theory, skewed fat tailed distribution

Abstract:
A natural point of departure for all elements of business risk measurement is the past. Future trends and current metrics are often extrapolated from an historical data series. However, this process is fundamentally flawed if there are cyclical factors that impact business measures of risk or performance. Historical data on operational risk gathered during an economic expansion may not be relevant for a period of recession. Estimates of default risk and recovery rates incorporate cyclical components that are correlated to systematic risk factors, such as macroeconomic fluctuations and regulatory shifts. All too frequently, however, researchers and practitioners alike ignore these cyclical factors and blithely extend an unadjusted trend line into the future. The metrics obtained using this methodology are fundamentally flawed. By aggregating across different macroeconomic regimes, these historical estimates do not accurately reflect either time period. It is the goal of this paper to demonstrate the importance of developing models to adjust for systematic and cyclical risk factors in business metrics. This is the first paper, to our knowledge, to test the cyclicality of catastrophic and operational risk measures. Using equity returns for financial institutions we estimate both catastrophic and operational risk measures over the period 1973-2003. We utilize an extreme value approach (Generalized Pareto Distribution, GPD), as well as a generalized distributional approach (Skewed Generalized Error Distribution, SGED) to obtain estimates of catastrophic risk parameters and 1% value at risk (VaR). We find evidence of procyclicality in the catastrophic VaR for financial institutions. We define a new, residual operational risk measure and estimate the risk parameters using both the GPD and SGED. We use these operational risk parameters to determine the 1% operational VaR. Using our measure, we find that operational risk is quite significant, comprising approximately 18% of the total equity returns of financial institutions. This paper presents the first evidence of procyclicality in operational risk measures. Our results are robust to alternative distributional specifications, conditionality in downside risk measures, and simulated databases. Thus, we conclude that macroeconomic, systematic and environmental factors play a considerable role in influencing the risk of financial institutions. Models that ignore these factors are therefore fundamentally flawed. These results provide encouragement for further research into both catastrophic and operational risk measures that are conditioned on cyclical factors.

operational risk, catastrophic risk, value at risk, extreme value theory, skewed fat tailed distribution.

Abstract:
This paper examines the intertemporal relation between expected return and risk for 30 stocks in the Dow Jones Industrial Average. The mean-reverting dynamic conditional correlation model of Engle (2002) is used to estimate a stock s conditional covariance with the market and test whetherthe conditional covariance predicts time-variation in the stock s expected return. The risk-aversion coefficient, restricted to be the same across stocks in panel regression, is estimated to be betweentwo and four and highly significant. This result is robust across different market portfolios, different sample periods, alternative specifications of the conditional mean and covariance processes, and including a wide variety of state variables that proxy for the intertemporal hedging demand component of the ICAPM. Risk premium induced by the conditional covariation of individual stocks with the market portfolio remains economically and statistically significant after controlling for risk premiums induced by conditional covariation with macroeconomic variables (federal funds rate, default spread, and term spread), financial factors (size, book-to-market, and momentum), and volatility measures (implied, GARCH, and range volatility).

ICAPM, Dynamic conditional correlation, ARCH, Risk aversion, Dow Jones

Abstract:
This paper examines the intertemporal relation between expected return and risk for 30 stocks in the Dow Jones Industrial Average. The mean-reverting dynamic conditional correlation model of Engle (2002) is used to estimate a stock's conditional covariance with the market and test whether the conditional covariance predicts time-variation in the stock's expected return. The risk-aversion coefficient, restricted to be the same across stocks in panel regression, is estimated to be between two and four and highly significant. This result is robust across different market portfolios, different sample periods, alternative specifications of the conditional mean and covariance processes, different data sets including book-to-market portfolios and stocks in the S&P 100 index, and including a wide variety of state variables that proxy for the intertemporal hedging demand component of the ICAPM. The risk premium induced by the conditional covariation of individual stocks with the market portfolio remains economically and statistically significant after controlling for risk premia induced by conditional covariation with macroeconomic variables (federal funds rate, default spread, and term spread), financial factors (size, book-to-market, and momentum), and volatility measures (implied, GARCH, and range volatility).

ICAPM, Dynamic conditional correlation, ARCH, Risk aversion, Dow Jones

Abstract:
This paper introduces a conditional extreme value volatility estimator (EVT) based on high-frequency returns. The relative performance of the extreme value volatility estimator is compared with the discrete-time GARCH and implied volatility models for 1-day and 20-day-ahead forecasts of realized volatility. This is also a first attempt towards detecting any time-series variation in extreme value distributions using high-frequency intraday data. The information content of EVT is examined in the context of forecasting S&P 100 index volatility. Adjusted-R2 values imply superior performance of the implied volatility index (VIX) and EVT in capturing time-series variation in realized volatility. The forecasting ability of various discrete time GARCH models turns out to be inferior to VIX and EVT. According to the Theil inequality coefficient and the heteroscedasticity-adjusted root mean squared and mean absolute errors, (1) EVT provides more accurate forecasts than the VIX and GARCH volatility models; (2) VIX generally yields a less accurate characterization of realized volatility than EVT and GARCH models. These results have implications for financial risk management, and are thus relevant to both regulators and practitioners.

extreme value, realized volatility, high-frequency returns, GARCH, implied volatility

Abstract:
This paper examines the intertemporal relation between risk and return for the aggregate stock market using high-frequency data. We use daily realized, GARCH, implied, and range-based volatility estimators to determine the existence and significance of a risk-return tradeoff for several stock market indices. We find a positive and statistically significant relation between the conditional mean and conditional volatility of market returns at the daily level. This result is robust to alternative specifications of the volatility process, across different measures of market return and sample periods, and after controlling for macroeconomic variables associated with business cycle fluctuations. We also analyze the risk-return relationship over time using rolling regressions, and find that the strong positive relation persists throughout our sample period. The market risk measures adopted in the paper add power to the analysis by incorporating valuable information, either by taking advantage of high frequency intraday data (in the case of realized, GARCH, and range volatility) or by utilizing the market's expectation of future volatility (in the case of implied volatility index).

ICAPM, intraday data, stock market volatility, stock market returns, risk-return tradeoff

Abstract:
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.

conditional value at risk, GARCH, skewed generalized t distribution, conditional skewness and kurtosis

Abstract:
The intertemporal capital asset pricing model of Merton (1973) states that the expected excess return on an asset is proportional to the expected covariance of the excess return on this asset with the excess return on the market portfolio. The proportionality coefficient measures the average relative risk aversion of investors. When the investment opportunity is stochastic, the expected excess return is also proportional to the covariance of the excess return with the state variables that govern the state of the investment opportunity. The proportionality coefficients on these covariance terms measure the investors' average aversion to unfavorable shifts in these state variables. In this paper, we use GARCH-type models to estimate the conditional covariance of a wide array of industry and Fama-French size/book-to-market portfolios with the market portfolio and with the Fama-French size (SMB) and book-to-market (HML) risk factors. We then estimate the system of simultaneous equations that links the excess returns on these portfolios to the corresponding conditional covariances with the market portfolio and the common risk factors. We obtain a positive and highly significant estimate for the relative risk aversion coefficient. The coefficient is about three for the long sample from July 1926 to December 2002, and is around six for the more recent period from July 1963 to December 2002. Furthermore, the expected excess returns are negatively related to their conditional covariance with the Fama-French size risk factor, suggesting that an increase in the size factor predicts an unfavorable shift in the investment opportunity. However, we do not find any consistent loading on the covariance with the book-to-market risk factor. Our findings are robust to different ways of forming portfolios and estimating conditional covariances. Most of the existing literature estimates the intertemporal risk-return relation using one single series of the market portfolio return. We show that the estimates from a single return series have low statistical significance and large sample variation. Our key contribution here is to direct the attention of the literature to the cross-sectional consistency of the intertemporal asset pricing relation and the universal proportionality underlying the risk-return relation. By exploiting this universal relation, we obtain positive and highly significant estimates on the relative risk aversion coefficient. We also gain a better understanding on how different risk factors predict future movements in investment opportunities.

ICAPM, risk-return tradeoff, risk aversion, intertemporal hedging demand, conditional covariance

Abstract:
This paper provides a comprehensive analysis of the short-term interest-rate dynamics based on three different data sets and two flexible parametric specifications. The significance of nonlinearity in the short-rate drift declines with increasing maturity for the interest-rate series used in the study. Using a flexible diffusion specification and incorporating GARCH volatility and non-normal innovation reduce the need for a nonlinear drift specification. Finally, the nonlinear drift specification performs better than the linear drift specification only when the short-term interest-rate levels reach historical highs.

Short-term interest rates, nonlinearity, drift, diffusion, jumps, GARCH, stochastic volatility

Abstract:
This paper presents a comprehensive study of continuous time GARCH modeling with the thin-tailed normal and the fat-tailed Student-t and generalized error distributions. The paper measures the degree of mean reversion in stock return volatility based on the relationship between discrete time GARCH and continuous time diffusion models. The convergence results based on the aforementioned distribution functions are shown to have similar implications for testing mean reversion in stochastic volatility. Alternative models are compared in terms of their ability to capture mean-reverting behavior of stock return volatility. The empirical evidence obtained from several stock market indices indicates that the conditional variance, log-variance, and standard deviation of stock market returns are pulled back to some long-run average level over time.

reversion, fat-tailed distributions, diffusion, GARCH, stochastic volatility

Abstract:
We show that stocks that experience a sudden increase in idiosyncratic volatility earn abnormally high contemporaneous returns but significantly underperform otherwise similar stocks in the future. Our findings indicate that volatility jumps can be traced to unusual firm-level news. We conjecture that these unusual news events increase the level of investor disagreement about firms' fundamental values. Because short-selling of highly volatile stocks is costly, prices rise to reflect the more optimistic views but then revert down as investors' opinions start to converge. The observed patterns of trade order imbalances and effective spreads lend support for this hypothesis.

unusual news events, volatility shocks, differences of opinion

Abstract:
We show that stocks that experience a sudden increase in idiosyncratic volatility earn abnormally high contemporaneous returns but significantly underperform otherwise similar stocks in the future. Our findings indicate that volatility jumps can be traced to unusual firm-level news. We conjecture that these unusual news events increase the level of investor disagreement about firms' fundamental values. Because short-selling of highly volatile stocks is costly, prices rise to reflect the more optimistic views but then revert down as investors' opinions start to converge. The observed patterns of trade order imbalances and effective spreads lend support for this hypothesis.

volatility shocks, unusual news events, divergence of opinion

Abstract:
We show that stocks that experience a sudden increase in idiosyncratic volatility earn abnormally high contemporaneous returns but significantly underperform otherwise similar stocks in the future. Our findings indicate that volatility jumps can be traced to unusual firm-level news. We conjecture that these unusual news events increase the level of investor disagreement about firms' fundamental values. Because short-selling of highly volatile stocks is costly, prices rise to reflect the more optimistic views but then revert down as investors' opinions start to converge. The observed patterns of trade order imbalances and effective spreads lend support for this hypothesis.

volatility shocks, unusual news events, divergence of opinion

Abstract:
This paper examines the proportion of wealth invested in stock and bond portfolios as a function of the investors' age, i.e., investment horizon. It has become increasingly popular to advice investors to relocate their funds from a primarily stock portfolio to a primarily bond portfolio as they get older. However, the existing theory does not support this advice: the well-known decision rules such as Mean-Variance (MV) or Stochastic Dominance (SD) rules are unable to explain this common practice. In this paper, we utilize the recently developed Almost Stochastic Dominance (ASD) and Almost Mean Variance (AMV) approaches and employ various datasets to examine the dominance of stock and bond portfolios as a function of the investment horizon. We find that, for short investment horizons, all portfolios are efficient. However, for medium and longer horizons, only the portfolios with higher stock proportions are efficient. The results indicate that ASD and AMV rules unambiguously support the popular practice of advising higher stock to bond ratio for long investment horizons. Hence, we provide an explanation to the practitioners' recommendation within the expected utility paradigm.

Asset Allocation, Life-Cycle Funds, Almost Stochastic Dominance, Almost Mean-Variance

Abstract:
This paper introduces a model-independent measure of aggregate idiosyncratic risk based on the mean-variance portfolio theory and the concept of gain from portfolio diversification. With the new approach, there is no need to estimate the covariance terms or the industry-level or firm-level beta coefficients when constructing the average idiosyncratic risk at the industry- or firm-level. Since there is no gain from diversification when the correlations among individual stocks equal one, the variance of the portfolio with perfectly correlated securities contains systematic risk and idiosyncratic risk of the securities in the portfolio. We also think that the stock market index can be viewed as a fully diversified portfolio, which does not contain any idiosyncratic risk. Since the market portfolio contains a large number of stocks, enough diversification gains are achieved and the idiosyncratic risk contributes nothing to the total risk of the market portfolio. That is, the risk of this well-diversified portfolio is due solely to the systematic risk of the securities in the portfolio. The new measure of average idiosyncratic volatility is defined as the difference between the variance of the non-diversified portfolio and the variance of the fully diversified portfolio. We present two versions of the new methodology; one decomposing total risk into firm and market variance, and the other decomposing total risk into firm, industry, and market variance. The statistical results and graphical analyses provide strong evidence that there are significant level and trend differences between the average idiosyncratic volatility measures of Campbell, Lettau, Malkiel, and Xu (2001, CLMX) and the new methodology. Although both approaches indicate a noticeable increase in the firm-level idiosyncratic risk, the volatility measure of CLMX is greater and has a stronger upward trend than the new idiosyncratic volatility measure. The analytical and empirical results show that the significant upward trend in the differences of the two idiosyncratic volatility measures is related to the increase in the cross-sectional dispersion of the volatility of individual stocks.

idiosyncratic risk, total risk, average stock risk, stock market volatility, stock returns

Abstract:
Motivated by existing evidence of a preference among investors for assets with lottery-like payoffs and that many investors are poorly diversified, we investigate the significance of extreme positive returns in the cross-sectional pricing of stocks. Portfolio-level analyses and firm-level cross-sectional regressions indicate a negative and significant relation between the maximum daily return over the past one month (MAX) and expected stock returns. Average raw and risk-adjusted return differences between stocks in the lowest and highest MAX deciles exceed 1% per month. These results are robust to controls for size, book-to-market, momentum, short-term reversals, liquidity, and skewness. Of particular interest, including MAX reverses the puzzling negative relation between returns and idiosyncratic volatility recently documented in Ang et al. (2006, 2008).

expected stock returns, maximum returns, idiosyncratic volatility, skewness

Abstract:
This paper examines the intertemporal relation between downside risk and expected stock returns. Value at risk (VaR), expected shortfall, and tail risk are used as measures of downside risk to determine the existence and significance of a risk-return tradeoff. We find a positive and significant relation between downside risk and the portfolio returns on NYSE/AMEX/Nasdaq stocks. VaR remains a superior measure of risk when compared to the traditional risk measures. These results are robust across different stock market indices, different measures of downside risk, loss probability levels, and after controlling for macroeconomic variables and volatility over different holding periods as originally proposed by Harrison and Zhang (1999).

Downside risk, skewed fat-tail distributions, extreme stock returns, tail risk.

Abstract:
This paper provides a cross-sectional investigation of the conditional and unconditional intertemporal capital asset pricing model (ICAPM). The results indicate that estimating the conditional ICAPM with a pooled panel of time series and cross-sectional data in a multivariate GARCH-in-mean framework iscrucial in identifying the positive risk-return tradeoff. Different from the traditional literature, the paper decomposes the aggregate stock market portfolio into ten book-to-market portfolios and then estimates a cross-sectionally consistent slope coefficient on the conditional variance-covariance matrix. The risk aversion coefficient, restricted to be the same across all portfolios, is estimated to be positive and highly significant. This is the first study testing the cross-sectional consistency of the intertemporal relation by estimating the multivariate GARCH-in-mean model with different slopes. The statistical results indicate theequality of slope coefficients across all portfolios, supporting the empirical validity and sufficiency of the conditional ICAPM. The paper also provides evidence that the time-varying conditional covariances can explain the value premium because the average risk-adjusted return difference between the value and growth portfolios is economically and statistically insignificant within the conditional ICAPM framework.

Abstract:
This paper provides a cross-sectional investigation of the conditional and unconditional intertemporal capital asset pricing model (ICAPM). The results indicate that estimating the conditional ICAPM with a pooled panel of time series and cross-sectional data in a multivariate GARCH-in-mean framework is crucial in identifying the positive risk-return tradeoff. Different from the traditional literature, the paper decomposes the aggregate stock market portfolio into ten book-to-market portfolios and then estimates a cross-sectionally consistent slope coefficient on the conditional variance-covariance matrix. The risk-aversion coefficient, restricted to be the same across all portfolios, is estimated to be positive and highly significant. This is the first study testing the cross-sectional consistency of the intertemporal relation by estimating the multivariate GARCH-in-mean model with different slopes. The statistical results indicate the equality of slope coefficients across all portfolios, supporting the empirical validity and sufficiency of the conditional ICAPM. The paper also provides evidence that the time-varying conditional covariances can explain the value premium because the average risk-adjusted return difference between the value and growth portfolios is economically and statistically insignificant within the conditional ICAPM framework.

G12; G13; C51

Abstract:
This paper provides an analysis of the predictability of stock returns using market, industry, and firm-level earnings. Contrary to Lamont (1998), we find that neither dividend payout ratio nor the level of aggregate earnings can forecast the excess market return. We show that these variables do not have robust predictive power across different stock portfolios and sample periods. In contrast to the aggregate-level findings, earnings yield has significant explanatory power for the time-series and cross-sectional variation in firm-level stock returns and 48-industry portfolio returns. It is the mean-reversion of stock prices as well as the earnings' correlation with expected stock returns that are responsible for the forecasting power of earnings yield. These results are robust after controlling for book-to-market, size, price momentum and post-earnings announcement drift. At the aggregate-level, the information content of firm-level earnings about future cash flows is diversified away and higher aggregate earnings do not forecast higher returns.

earnings, dividends, stock returns, market returns, predictability, business cycle

Abstract:
This paper investigates the risk versus mispricing explanation of superior returns to contrarian strategies using the interactions between value-to-market indicators and corporate financing transactions that increase or decrease a firm's outstanding equity. Portfolio-level analyses and firm-level cross-sectional regressions indicate that the well-documented contrarian profits soar when value stocks which repurchase shares (value repurchasers) and growth stocks which issue shares (growth issuers) are considered. Various risk measures indicate that value repurchasers are not riskier than growth issuers. Furthermore, time-series of realized growth rates, analysts' long-term growth estimates, and sensitivity of portfolio returns to investor sentiment support the misvaluation explanation.

Abstract:
The literature has so far focused on the risk-return tradeoff in equity markets and ignored alternative risky assets. This paper is the first to examine the presence and significance of an intertemporal relation between expected return and risk in the foreign exchange market. The paper provides new evidence on the intertemporal capital asset pricing model by using high-frequency intraday data on currency and by presenting significant time-variation in the risk aversion parameter. Five-minute returns on the spot exchange rates of the U.S. dollar vis-a-vis six major currencies (the Euro, Japanese Yen, British Pound Sterling, Swiss Franc, Australian Dollar, and Canadian Dollar) are used to test the existence and significance of a daily risk-return tradeoff in the FX market based on the GARCH, realized, and range volatility estimators. The results indicate a positive, but statistically weak relation between risk and return on currency.

foreign exchange market, ICAPM, high-frequency data, time-varying risk aversion

Abstract:
This paper provides new evidence on the time-series predictability of stock market returns by introducing a test of nonlinear mean reversion. The performance of extreme daily returns is evaluated in terms of their power to predict short- and long-horizon returns on various stock market indices and size portfolios. The paper shows that the speed of mean reversion is significantly higher during the large falls of the market. The parameter estimates indicate a negative and significant relation between the monthly portfolio returns and the extreme daily returns observed over the past one to eight months. Specifically, in a quarter in which the minimum daily return is -2% the expected excess return is 37 basis points higher than in a month in which the minimum return is only -1%. This result holds for the value-weighted and equal-weighted stock market indices and for each of the size decile portfolios. The findings are also robust to different sample periods, different indices, and investment horizons.

mean reversion, extreme returns, time-varying risk aversion, stock market returns, market efficiency

Abstract:
Motivated by existing evidence of a preference among investors for assets with lottery-like payoffs and that many investors are poorly diversified, we investigate the significance of extreme positive returns in the cross-sectional pricing of stocks. Portfolio-level analyses and firm-level cross-sectional regressions indicate a negative and significant relation between the maximum daily return over the past one month (MAX) and expected stock returns. Average raw and risk-adjusted return differences between stocks in the lowest and highest MAX deciles exceed 1% per month. These results are robust to controls for size, book-to-market, momentum, short-term reversals, liquidity, and skewness. Of particular interest, including MAX reverses the puzzling negative relation between returns and idiosyncratic volatility recently documented in Ang et al. (2006, 2008).

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
Motivated by existing evidence of a preference among investors for assets with lottery-like payoffs and that many investors are poorly diversified, we investigate the significance of extreme positive returns in the cross-sectional pricing of stocks. Portfolio-level analyses and firm-level cross-sectional regressions indicate a negative and significant relation between the maximum daily return over the past one month (MAX) and expected stock returns. Average raw and risk-adjusted return differences between stocks in the lowest and highest MAX deciles exceed 1% per month. These results are robust to controls for size, book-to-market, momentum, short-term reversals, liquidity, and skewness. Of particular interest, including MAX generally subsumes or reverses the puzzling negative relation between returns and idiosyncratic volatility recently documented in Ang et al. (2006, 2008).

Abstract:
This paper investigates whether realized and implied volatilities of individual stocks can predict the cross-sectional variation in expected returns. Although the levels of volatilities from the physical and risk-neutral distributions cannot predict future returns, there is a significant relation between volatility spreads and expected stock returns. Portfolio level analyses and firm-level cross-sectional regressions indicate a negative and significant relation between expected returns and the realized-implied volatility spread that can be viewed as a proxy for volatility risk. The results also provide evidence for a significantly positive link between expected returns and the call-put options’ implied volatility spread that can be considered as a proxy for jump risk. The parameter estimates from the VAR-bivariate- GARCH model indicate significant information flow from individual equity options to individual stocks, implying informed trading in options by investors with private information.

realized volatility, implied volatility, volatility risk, jump risk, stock returns

Abstract:
Investment bankers focus on narrow, industry-based peer groups for individual stock valuation. And some market-neutral equity hedge fund managers restrict their portfolios to be sector-neutral as well. Yet, academic research into contrarian strategy investment performance has typically invoked full universe valuation and ignored industry effects. Here, we find in favor of the bankers’ and hedge fund managers’ approach. Industry effects matter. Narrow industry-based peer groups improve stock valuation precision for three key valuation ratios. While our analysis of the dynamics of these ratios indicates substantial inertia in relative value rankings, we find that average returns to industry-based contrarian portfolio strategies are positive, statistically significant, and persistent. And over a sample that extends through the “new economy/old economy” and boom/bust period of the late 1990s, contrarian strategies were particularly profitable for NASDAQ-listed stocks. Most importantly, using our full sample of stocks, we show that an industry-neutral strategy is far superior to an industry-exposed, full universe strategy in Sharpe ratio terms over every horizon for each valuation ratio. Thus, contrarian strategy portfolio performance is significantly improved in risk-adjusted terms when implemented in its industry-neutral hedging form.

Abstract:
This paper investigates the predictability of variance and value at-risk (VaR) measures in international stock markets. We use daily stock market returns for G7 countries (the United States, the United Kingdom, Germany, Japan, Canada, France, Italy) and generate the realized variance and VaR estimates. We then compute the proportion of the one month ahead variance and VaR that can be explained by the variance and VaR obtained from the past one month to six months of daily data to determine the persistency of these risk measures. We find that for all G7 countries considered in the paper persistency in variance is significantly higher than that in VaR. Variance of the stock market indices for Germany and Italy has the highest persistence, whereas the persistence is low for the US and Canada. However, different than the case of variance, the strongest predictability of VaR is obtained for Japan. We conclude that although the second moment of stock return distributions is highly predictable for Germany and Italy, tails of the distribution are more persistent for Japan.

Abstract:
There exists a small sample bias in predictive regressions, when a rate of return is regressed on a lagged stochastic regressor, and the regression disturbance is correlated with the regressors’ innovations. Although this bias can be a serious concern in time-series predictive regressions, it is not significant in panel data setting. By using simulations and stock level data, we document that as the number of cross sections used in the panel data increases the bias in coefficient estimates becomes negligible.

Abstract:
This paper provides a cross-sectional investigation of the conditional and unconditional intertemporal capital asset pricing model (ICAPM). The results indicate that estimating the conditional ICAPM with a pooled panel of time series and cross-sectional data in a multivariate GARCH-in-mean framework is crucial in identifying the positive risk-return tradeoff. Different from the traditional literature, the paper decomposes the aggregate stock market portfolio into ten book-to-market portfolios and then estimates a cross-sectionally consistent slope coefficient on the conditional variance-covariance matrix. The risk-aversion coefficient, restricted to be the same across all portfolios, is estimated to be positive and highly significant. This is the first study testing the cross-sectional consistency of the intertemporal relation by estimating the multivariate GARCH-in-mean model with different slopes. The statistical results indicate the equality of slope coefficients across all portfolios, supporting the empirical validity and sufficiency of the conditional ICAPM. The paper also provides evidence that the time-varying conditional covariances can explain the value premium because the average risk-adjusted return difference between the value and growth portfolios is economically and statistically insignificant within the conditional ICAPM framework.

ICAPM, Risk-return tradeoff, Risk aversion, Multivariate GARCH-in-mean

Abstract:
This paper investigates the significance of an intertemporal relation between expected return and risk for the futures markets. The paper not only takes a look at the domestic futures, but the relationship between conditional risk and return is examined in international futures markets as well. We test the significance of a daily risk-return tradeoff in stock index futures for G8 countries (US, Canada, UK, Germany, France, Italy, Japan, and Australia). We use GARCH modeling with the thin-tailed normal and the fat-tailed Student t, generalized error, and generalized t distributions to simultaneously generate risk measures and forecast expected futures returns. The maximum likelihood parameter estimates indicate that the relation between risk and return is flat in futures markets. This result is robust across eight different countries.

stock index futures, international futures markets, risk-return tradeoff, GARCH-in-mean.

Abstract:
Recent theoretical models based on dynamic human capital formation, or social influence, suggest an inverse relationship between criminal activity and economic opportunity and between criminal activity and deterrence, but predict an asymmetric response of crime. In this paper we use three different data sets and three different empirical methodologies to document this previously-unnoticed regularity. Using nonparametric methods we show that the behavior of property crime is asymmetric over time, where increases are sharper but decreases are gradual. Using aggregate time-series U.S. data as well as data from New York City we demonstrate that property crime reacts more (less) strongly to increases (decreases) in the unemployment rate, to decreases (increases) in per capita real GDP and to decreases (increases) in the police force. The same result is obtained between unemployment and property crime in annual state-level panel data. These results suggest that it may be cost effective to implement mechanisms to prevent crime commission rates from rising in the first place.

Abstract:
This paper determines whether the world market risk, country-specific total risk, and country-specific idiosyncratic risk are priced in an international capital asset pricing model (ICAPM). The paper also tests if the price of risk associated with each factor is common across countries.

Portfolio-level analyses, country-level cross-sectional regressions, stacked time-series, and pooled panel regressions indicate that the world market risk is not, but country-specific total and idiosyncratic risks are significantly priced in an ICAPM framework with partial integration. In addition, the prices of total and idiosyncratic risks are significantly different across 37 countries considered in the paper. This result is robust to different methods for estimating risk measures, different investment horizons, and after controlling for the countries’ aggregate dividend yield, earnings-to-price ratios, inflation risk, aggregate volatility risk, and past return characteristics. The main findings turn out to be insensitive to the choice of one-factor versus multifactor models used to estimate systematic and idiosyncratic risk measures.

international equity returns, country-specific risk, idiosyncratic risk, systematic risk

Abstract:
This paper evaluates the performance of three extreme value distributions, i.e., generalized Pareto distribution (GPD), generalized extreme value distribution (GEV), and Box-Cox-GEV, and four skewed fat-tailed distributions, i.e., skewed generalized error distribution (SGED), skewed generalized t (SGT), exponential generalized beta of the second kind (EGB2), and inverse hyperbolic sign (IHS) in estimating conditional and unconditional value at risk (VaR) thresholds. The results provide strong evidence that the SGT, EGB2, and IHS distributions perform as well as the more specialized extreme value distributions in modeling the tail behavior of portfolio returns. All three distributions produce similar VaR thresholds and perform better than the SGED and the normal distribution in approximating the extreme tails of the return distribution. The conditional coverage and the out-of-sample performance tests show that the actual VaR thresholds are time varying to a degree not captured by unconditional VaR measures. In light of the fact that VaR type measures are employed in many different types of financial and insurance applications including the determination of capital requirements, capital reserves, the setting of insurance deductibles, the setting of reinsurance cedance levels, as well as the estimation of expected claims and expected losses, these results are important to financial managers, actuaries, and insurance practitioners.

Abstract:
This paper tests the empirical performance of a model-independent measure of aggregate idiosyncratic risk introduced by Bali and Cakici (2004) in ICAPM framework. The results indicate a significantly positive relation between the equal-weighted average stock volatility and the value-weighted portfolio returns on the NYSE/AMEX/Nasdaq stocks for the sample period of 1963:08-1999:12. We show that this result is driven by small stocks traded on the NASDAQ. In addition, the positive risk-return tradeoff does not exist for the extended sample of 1963:08-2004:12 and for portfolios of NYSE/AMEX and NYSE stocks. More importantly, we find almost no evidence of a significant link between the value-weighted portfolio returns and various measures of the value-weighted average idiosyncratic volatility.

Idiosyncratic Risk, total risk, average stock risk, stock market volatility, stock returns

Abstract:
Stock size, liquidity, and value at risk (VAR) can explain the cross-sectional variation in expected returns, but market beta and total volatility have almost no power to capture the cross-section of expected returns at the stock level. Furthermore, the strong positive relationship between average returns and VAR is robust for different investment horizons and loss-probability levels. In addition to the cross-sectional regressions at the stock level, this study used a time-series approach to test the empirical performance of VAR at the portfolio level. The results, based on 25 size/book-to-market portfolios, indicate that VAR has additional explanatory power after the characteristics of market return, size, book-to-market ratio, and liquidity are controlled for.

Equity Investments: Fundamental Analysis and Valuation Models; Portfolio Management: Equity Strategies; Risk Measurement and Management: Equity Portfolios

Abstract:
This paper analyzes one potential source of misspecification of existing models of the short-term interest rate and introduces a new class of discrete-time econometric specifications that nests many existing interest rate models as special cases. In existing continuous-time or time-series econometric models, the structural form of conditional means and variances is relatively inflexible in the sense that the existing models do not allow for departures from linearity in the conditional mean and they do not parameterize the diffusion function flexible enough to incorporate serially correlated unexpected news, asymmetry and level effects into the definition of conditional volatility. This study attempts to model the conditional distribution of interest rates by specifying a more general econometric framework, which allows for nonlinear effects in the dynamics of the short rate and defines the conditional volatility as a nonlinear function of unexpected information shocks and interest rate levels. The empirical results point to the presence of nonlinearity in the conditional mean, and serial correlation, asymmetry and level effects in the conditional variance of the short rate. In addition, the relative performance of the new class of models in predicting the future level and variance of interest rate changes is found to be superior to the moving-average, diffusion, and GARCH models.

Abstract:
This paper compares the empirical performance of a wide variety of well-known diffusion models - with particular emphasis on the Black, Derman, and Toy (1990) term structure model - in capturing the dynamic behavior of interest rate volatility. Many popular models are nested within a more flexible time-varying BDT framework that allows us to determine the appropriate specification of the spot rate process. The empirical results for the one-month Treasury yields indicate that the equilibrium models that do not allow the drift and diffusion parameters to vary over time and parameterize the volatility only as a function of interest rate levels fail to model adequately the serial correlation in conditional variances. On the other hand, the serial-correlation-based arbitrage-free models with time-dependent parameters in the drift and diffusion functions may fail to capture adequately the relationship between interest rate levels and volatility. The results also suggest that time-varying volatilities within the BDT framework may lead to non-recombining binomial trees that increase the storage requirements and computational cost substantially in pricing interest rate contingent claims.

Abstract:
This paper proposes an extreme value approach to estimating the term structure of interest rate volatility, and shows that the volatility of interest rate changes is overestimated by the standard approach that uses the thin-tailed normal distribution. The volatility of maximal and minimal changes in three-, six-, and twelve-month T-bill rates is estimated over the late 1950s through the end of 1999. The empirical results indicate that the volatility of daily changes in short rates obtained from the fat-tailed generalized error distribution is almost the same as the volatility of the extremes obtained from the generalized Pareto distribution.

Volatility, extremes, term structure of interest rates

Abstract:
This paper focuses on pricing Eurodollar futures options using the single-factor Black, Derman, and Toy (1990) term structure model with particular emphasis on yield curve smoothing. Of the various approaches, the maximum smoothness forward rate approach developed by Adams and van Deventer (1994), cubic yield spline and linear interpolation are used to produce finely spaced binomial trees. We compare the pricing accuracy associated with the use of yield curve smoothing techniques within the BDT framework. The findings provide the first supporting evidence that using a forward rate curve with maximum smoothness together with a time-varying volatility structure improves best the
performance of the BDT model. The empirical results are found to be robust across factors affecting the option price such as time-to-expiration, moneyness, and trading volume.

Abstract:
This paper concentrates on the effects of different class of volatility estimators in pricing interest rate sensitive options using the single-factor Black, Derman, and Toy [1990] model. We employ the moving average, such as constantly-weighted and exponentially-weighted moving average, and the time-series models, such as Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and the integrated GARCH (IGARCH), in estimating the volatility of short rates. Empirical results, based on 4,228 estimated prices, indicate that valuation of Eurodollar futures options is sensitive to the volatility model used and the time-series models provide a more accurate representation of the underlying time-varying volatility structure than the moving average models.

Abstract:
I introduce two-factor discrete time stochastic volatility models of the short-term interest rate to compare the relative performance of existing and alternative empirical specifications. I develop a nonlinear asymmetric framework that allows for comparisons of non-nested models featuring conditional heteroskedasticity and sensitivity of the volatility process to interest rate levels. A new class of stochastic volatility models with asymmetric drift and nonlinear asymmetric diffusion process is introduced in discrete time and tested against the popular continuous time and symmetric and asymmetric GARCH models. The existing models are rejected in favor of the newly proposed models because of the asymmetric drift of the short rate, and the presence of nonlinearity, asymmetry, GARCH, and level effects in its volatility. I test the predictive power of nested and non-nested models in capturing the stochastic behavior of the risk-free rate. Empirical evidence on three-, six-, and 12-month U.S. Treasury bills indicates that two-factor stochastic volatility models are better than diffusion and GARCH models in forecasting the future level and volatility of interest rate changes.