Turan G. Bali

Idiosyncratic Volatility and the Cross-Section of Expected Returns

This paper examines the cross-sectional relation between idiosyncratic volatility and expected stock returns. The results indicate that i) the data frequency used to estimate idiosyncratic volatility, ii) the weighting scheme used to compute average portfolio returns, iii) the breakpoints utilized to sort stocks into quintile portfolios, and iv) using a screen for size, price, and liquidity play critical roles in determining the existence and significance of a relation between idiosyncratic risk and the cross section of expected returns. Portfoliolevel 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 no robustly significant relation exists between idiosyncratic volatility and expected returns.

An Extreme Value Approach to Estimating Volatility and Value at Risk

This article determines the type of asymptotic distribution for the extreme changes in U.S. Treasury yields. The thin-tailed Gumbel and exponential distributions are strongly rejected against the fat-tailed Frechet and Pareto distributions. The empirical results indicate that the volatility of maximal and minimal changes in interest rates declines as time-to-maturity rises, yielding a downward-sloping volatility curve for the extremes. The article proposes an extreme value approach to estimating value at risk and shows that the statistical theory of extremes provides a more accurate approach for risk management and value at risk (VaR) calculations than the standard models.

Is There an Intertemporal Relation between Downside Risk and Expected Returns

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 with 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).

A conditional-SGT-VaR approach with alternative GARCH models

This paper proposes a conditional technique for the estimation of VaR and expected shortfall measures based on the skewed generalized t (SGT) distribution. The estimation of the conditional mean and conditional variance of returns is based on ten popular variations of the GARCH model. The results indicate that the TS-GARCH and EGARCH models have the best overall performance. The remaining GARCH specifications, except in a few cases, produce acceptable results. An unconditional SGT-VaR performs well on an in-sample evaluation and fails the tests on an out-of-sample evaluation. The latter indicates the need to incorporate time-varying mean and volatility estimates in the computation of VaR and expected shortfall measures.

Testing the Empirical Performance of Stochastic Volatility Models of the Short-Term Interest Rate

I introduce two-factor discrete time stochastic volatility models of the short-term interest rate to compare the relative performance of existing and alternative empiricial specificattions. I develop a nonlinear asymmmetric framework that allows for comparisons of non-nested models featuring conditional heteoskedasticity and sensitivity of the volatility process to interest rate levels. A new class of stochastic volatility models with 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 but that two-factor stochastic volatility models are better than diffusion and GARCH models in forecasting the future level and volatility of interest rate changes.

Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns?

We investigate the pricing of risk-neutral skewness in the stock options market by creating skewness assets comprised of two option positions (one long and one short) and a position in the underlying stock. The assets are created such that exposure to changes in the underlying stock price (delta), and exposure to changes in implied volatility (vega) are removed, isolating the effect of skewness. We find a strong negative relation between risk-neutral skewness and the skewness asset returns, consistent with a positive skewness preference. The returns are not explained by well-known market, size, book-to-market, momentum, short-term reversal, volatility, or option market factors.

Cyclicality in Catastrophic and Operational Risk Measurements

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 and operational 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 catastrophic losses, although when they occur, the losses are smaller than those resulting from a combination of market risk, credit risk or other risk events.

Asymmetric Crime Cycles

Recent theoretical models underscore the potential asymmetric response of various behaviors, ranging from criminal activity to smoking. In this paper, we use state-level panel and individual-level panel data to document the previously unnoticed asymmetric response of crime to changes in the unemployment rate. The results have policy implications, and they have potentially widespread ramifications because similar asymmetries may also be prevalent in other domains, ranging from the relationship between income and health to peer quality and student outcomes.

Value at Risk and Expected Stock Returns

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. Although previous empirical studies have used a variety of stock characteristics and other factors, such as total risk and diversifiable risk, to explain the cross-section of expected returns, researchers have not investigated value at risk (VAR) as an alternative risk factor that can explain stock returns. In conducting this study, our goal was to test whether the maximum likely loss measured by VAR can explain cross-sectional and time-series differences in expected returns. Using monthly and annual regressions, we provide evidence that size, liquidity, and VAR could capture the cross-sectional variation in expected returns of NYSE, Amex, and Nasdaq stocks for the period January 1963 to December 2001. Furthermore, we show that market beta and total volatility have almost no power to explain average stock returns at the individual-stock level. We also compared the relative performance of size, beta, and VAR in explaining the cross-sectional variation in portfolio returns. The results show that all the risk factors considered in the article can capture the cross-sectional differences in portfolio returns but that VAR has the best performance in terms of R2 values. The strong positive relationship between stock (or portfolio) returns and VAR turns out to be robust over various investment horizons and loss-probability levels. In addition to using cross-sectional regressions in an asset-pricing framework, we also used time-series regressions to evaluate the empirical performance of VAR at the portfolio level. To mimic the risk factor in returns related to VAR, we devised an alternative factor, HVARL, the difference between the simple average of the high-VAR portfolio returns and the low-VAR portfolio returns. Using 25 portfolios, we investigated the relative performance of total volatility, VAR, and liquidity in terms of their ability to capture time-series variation in stock returns. When we regressed monthly returns for a stock portfolio on the returns for portfolios based on market return, company size, the book-to-market ratio, liquidity, and VAR, we found that VAR can capture substantial time-series variation in stock returns and provide additional explanatory power even after the characteristics of market return, size, book-to-market ratio, and liquidity are controlled for. The results also imply that the relationship between VAR and expected stock returns is not the result of a reversal in long-term returns, of liquidity, or of volatility. Modern portfolio theory determines the optimum asset mix by maximizing the expected risk premium per unit of risk in a mean–variance framework or the expected value of some utility function approximated by the expected return and variance of the portfolio. In both cases, market risk of the portfolio is defined in terms of the variance (or standard deviation) of expected portfolio returns. Modeling portfolio risk as defined by traditional volatility measures implies that investors are concerned only about the average variation (and covariation) of individual stock returns and does not allow investors to treat the negative and positive tails of the return distribution separately. The standard risk measures determine the volatility of unexpected outcomes under normal market conditions, which corresponds to the normal functioning of financial markets during ordinary periods. Neither the variance nor the standard deviation, however, can yield an accurate characterization of actual portfolio risk during highly volatile periods. Therefore, the set of mean–variance-efficient portfolios may lead to an inefficient strategy for maximizing expected portfolio return while minimizing risk. Our findings suggest a new approach to optimal portfolio selection in a VAR framework. A mean–VAR approach can be introduced to allocate financial assets by maximizing the expected value of some utility function approximated by the expected return and VAR of the portfolio, as well as the investors aversion to VAR.

Disturbing extremal behavior of spot rate dynamics

This paper presents a study of extreme interest rate movements in the U.S. Federal Funds market over almost a half century of daily observations from the mid 1950s through the end of 2000. We analyze the fluctuations of the maximal and minimal changes in short term interest rates and test the significance of time-varying paths followed by the mean and volatility of extremes. We formally determine the relevance of introducing trend and serial correlation in the mean, and of incorporating the level and GARCH effects in the volatility of extreme changes in the federal funds rate. The empirical findings indicate the existence of volatility clustering in the standard deviation of extremes, and a significantly positive relationship between the level and the volatility of extremes. The results point to the presence of an autoregressive process in the means of both local maxima and local minima values. The paper proposes a conditional extreme value approach to calculating value at risk by specifying the location and scale parameters of the generalized Pareto distribution as a function of past information. Based on the estimated VaR thresholds, the statistical theory of extremes is found to provide more accurate estimates of the rate of occurrence and the size of extreme observations.