FIRE SALES FORENSICS: MEASURING ENDOGENOUS RISK

We propose a tractable framework for quantifying the impact of loss‐triggered fire sales on portfolio risk, in a multi‐asset setting. We derive analytical expressions for the impact of fire sales on the realized volatility and correlations of asset returns in a fire sales scenario and show that our results provide a quantitative explanation for the spikes in volatility and correlations observed during such deleveraging episodes. These results are then used to develop an econometric framework for the forensic analysis of fire sales episodes, using observations of market prices. We give conditions for the identifiability of model parameters from time series of asset prices, propose a statistical test for the presence of fire sales, and an estimator for the magnitude of fire sales in each asset class. Pathwise consistency and large sample properties of the estimator are studied in the high‐frequency asymptotic regime. We illustrate our methodology by applying it to the forensic analysis of two recent deleveraging episodes: the Quant Crash of August 2007 and the Great Deleveraging following the default of Lehman Brothers in Fall 2008.     

Asymmetric Correlations in Predicting Portfolio Returns*

Rigorous statistical tests have been designed to detect the existence of asymmetric correlations. However, these tests can hardly further facilitate future investment or risk management because asymmetric correlations are time‐varying and difficult to predict. In this paper, we construct a unified state‐space model, which not only measures in‐sample asymmetric correlations, but also exploit out‐of‐sample asymmetric correlations in the context of predicting portfolio returns. First, we regard time‐varying correlation between market returns and portfolio returns as a state variable and model it as an AR(1) process. Then, we measure future asymmetric correlations based on correlation coefficients between two unpredictable components in market returns and correlation, respectively. Third, we clarify the intuition, calculate asymmetric correlations for two portfolio sets and estimate the economic value of applying our model in asset allocation. Finally, we try to search for potential variables that can explain future asymmetric correlations. The results show that market‐wide liquidity, variance, earning price ratio, and investor sentiment can partially explain the asymmetry correlation phenomenon.     

Timing the Market with a Combination of Moving Averages

A combination of simple moving average trading strategies with several window lengths delivers a greater average return and skewness as well as a lower variance and kurtosis compared with buying and holding the underlying asset using daily returns of value‐weighted US decile portfolios sorted by market size, book‐to‐market, momentum, and standard deviation as well as more than 1000 individual US stocks. The combination moving average (CMA) strategy generates risk‐adjusted returns of 2% to 16% per year before transaction costs. The performance of the CMA strategy is driven largely by the volatility of stock returns and resembles the payoffs of an at‐the‐money protective put on the underlying buy‐and‐hold return. Conditional factor models with macroeconomic variables, especially the market dividend yield, short‐term interest rates, and market conditions, can explain some of the abnormal returns. Standard market timing tests reveal ample evidence regarding the timing ability of the CMA strategy.     

Market Timing With Moving Averages

I present evidence that a moving average (MA) trading strategy has a greater average return and skewness as well as a lower variance compared to buying and holding the underlying asset using monthly returns of value‐weighted US decile portfolios sorted by market size, book‐to‐market, and momentum, and seven international markets as well as 18,000 individual US stocks. The MA strategy generates risk‐adjusted returns of 3–7% per year after transaction costs. The performance of the MA strategy is driven largely by the volatility of stock returns and resembles the payoffs of an at‐the‐money protective put on the underlying buy‐and‐hold return. Conditional factor models with macroeconomic variables, especially the default premium, can explain some of the abnormal returns. Standard market timing tests reveal ample evidence regarding the timing ability of the MA strategy.     

PORTFOLIO LIQUIDATION IN DARK POOLS IN CONTINUOUS TIME

We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0, T] and can trade continuously at a traditional exchange (the “primary venue”) and in a dark pool. At the primary venue, trading yields a linear price impact. In the dark pool, no price impact costs arise but order execution is uncertain, modeled by a multidimensional Poisson process. We characterize the costs of trading by a linear‐quadratic functional which incorporates both the price impact costs of trading at the primary exchange and the market risk of the position. The solution of the cost minimization problem is characterized by a matrix differential equation with singular boundary condition; by means of stochastic control theory, we provide a verification argument. If a single‐asset position is to be liquidated, the investor slowly trades out of her position at the primary venue, with the remainder being placed in the dark pool at any point in time. For multi‐asset liquidations this is generally not the case; for example, it can be optimal to oversize orders in the dark pool in order to turn a poorly balanced portfolio into a portfolio bearing less risk.     

Dispersion in Analysts’ Earnings Forecasts and Market Efficiency

Recent studies show that firms with higher analysts’ earnings forecasts dispersion subsequently have lower returns than firms with lower forecasts dispersion. This paper evaluates alternative explanations for the dispersion–return relation using a stochastic dominance approach. We aim to discriminate between the hypothesis that some asset pricing models can explain the puzzling negative relation between dispersion and stock returns, and the alternative hypothesis that the dispersion effect is mainly driven by investor irrationality and thus is an evidence of a failure of efficient markets. We find that low dispersion stocks dominate high dispersion stocks by second‐ and third‐order stochastic dominance over the period from 1976 to 2012. Our results imply that any investor who is risk‐averse and prefers positive skewness would unambiguously prefer low dispersion stocks to high dispersion stocks. We conclude that the dispersion effect is more likely evidence of market inefficiency, rather than a result of omitted risk factors.     

Market Excess Returns,Variance and the Third Cumulant

In this paper, we develop an equilibrium asset pricing model for market excess returns, variance and the third cumulant by using a jump‐diffusion process with stochastic variance and jump intensity in Cox et al. (1985) production economy. Empirical evidence with the S&P 500 index and options from January, 1996 to December, 2005 strongly supports our model prediction that the lower the third cumulant, the higher the market excess returns. Consistent with existing literature, the theoretical mean–variance relation is supported only by regressions on risk‐neutral variance. We further demonstrate empirically that the third cumulant explains significantly the variance risk premium.     

Asymmetric pricing of implied systematic volatility in the cross‐section of expected returns

Assuming a symmetric relation between returns and innovations in implied market volatility, Ang, A., Hodrick, R., Xing, Y., and Zhang, X. (2006) find that sensitivities to changes in implied market volatility have a cross‐sectional effect on firm returns. Dennis, P., Mayhew, S., and Stivers, C. (2006), however, find an asymmetric relation between firm‐level returns and implied market volatility innovations. We incorporate this asymmetry into the cross‐sectional relation between sensitivity to volatility innovations and returns. Using both portfolio sorting and firm‐level regressions, we find that sensitivity to VIX innovations is negatively related to returns when volatility is rising, but is unrelated when it is falling. The negative relation is robust to controls for other variables, suggesting only the increase in implied market volatility is a priced risk factor. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:34–54, 2011     

The performance of alternative futures buy‐write strategies

This study compares the performance of a conventional buy‐write (or covered call writing) and a dynamic buy‐write strategy. The conventional strategy generally enhances portfolio returns in low volatility conditions but underperforms the underlying cash asset in sharply rising markets. The dynamic strategy adjusts the moneyness of the option according to market conditions. The study extends Hill, J. M., Balasubramanian, V., Gregory, K., and Tierens, I. ( 2006 ) and tests how and to what extent market volatility and market direction affect the performance of these two strategies. The study finds that both strategies offer significant positive α, higher returns and lower standard deviations than the market. Consistent with prior research, the abnormal returns of the buy‐write strategies can be attributed to a volatility premium embedded in the options prices. The buy‐write returns from the Hong Kong market appear to be lower than those found in the U.S. and U.K. markets. The conventional buy‐write outperforms the dynamic strategy in both high and low volatility environments, and in sharply falling markets. However, by targeting exercise probability, the dynamic strategy provides a greater upside in sharply rising markets. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Pitfalls of Downside Performance Measures with Arbitrary Targets

Downside performance measures relate above target returns with lower partial moments. They were developed to resolve restrictive assumptions of the classical Sharpe ratio. While the Sharpe ratio evaluates whether portfolios of a mutual fund and the risk‐free asset dominate passive portfolios of the benchmark and the risk‐free asset, this characteristic cannot be transferred to downside performance measures with arbitrary targets. We show that downside performance measures assign different values to passive benchmark strategies if the target differs from the risk‐free rate. This effect can lead to reverse rankings of financial assets. Therefore, downside performance measures are only applicable in asset management if the target is set equal to the risk‐free rate.     

ANALYTIC APPROXIMATIONS FOR MULTI‐ASSET OPTION PRICING

We derive general analytic approximations for pricing European basket and rainbow options on N assets. The key idea is to express the option’s price as a sum of prices of various compound exchange options, each with different pairs of subordinate multi‐ or single‐asset options. The underlying asset prices are assumed to follow lognormal processes, although our results can be extended to certain other price processes for the underlying. For some multi‐asset options a strong condition holds, whereby each compound exchange option is equivalent to a standard single‐asset option under a modified measure, and in such cases an almost exact analytic price exists. More generally, approximate analytic prices for multi‐asset options are derived using a weak lognormality condition, where the approximation stems from making constant volatility assumptions on the price processes that drive the prices of the subordinate basket options. The analytic formulae for multi‐asset option prices, and their Greeks, are defined in a recursive framework. For instance, the option delta is defined in terms of the delta relative to subordinate multi‐asset options, and the deltas of these subordinate options with respect to the underlying assets. Simulations test the accuracy of our approximations, given some assumed values for the asset volatilities and correlations. Finally, a calibration algorithm is proposed and illustrated.     

CORRELATION UNDER STRESS IN NORMAL VARIANCE MIXTURE MODELS

We investigate correlations of asset returns in stress scenarios where a common risk factor is truncated. Our analysis is performed in the class of normal variance mixture (NVM) models, which encompasses many distributions commonly used in financial modeling. For the special cases of jointly normally and t‐distributed asset returns we derive closed formulas for the correlation under stress. For the NVM distribution, we calculate the asymptotic limit of the correlation under stress, which depends on whether the variables are in the maximum domain of attraction of the Fréchet or Gumbel distribution. It turns out that correlations in heavy‐tailed NVM models are less sensitive to stress than in medium‐ or light‐tailed models. Our analysis sheds light on the suitability of this model class to serve as a quantitative framework for stress testing, and as such provides valuable information for risk and capital management in financial institutions, where NVM models are frequently used for assessing capital adequacy. We also demonstrate how our results can be applied for more prudent stress testing.     

Bank risk-taking and market discipline: Evidence from CoCo bonds in Korea

We investigate whether the risk profile of contingent convertible (CoCo) bonds is well-priced by testing the sensitivity of bond spreads to bank asset volatility. While equity holders (bankers) have an incentive to make riskier investments to trigger the write-off, such risk-taking behavior can be contained if CoCo bond investors punish it by demanding higher returns. We have found that investors in the Korean financial market understand the risk profile of CoCo bonds and require higher returns for the additional bank risk, which suggests the presence of market discipline with regard to CoCo bonds.     

基于VaR和两基金分离的投资组合模型

本文使用VaR来度量投资组合的市场风险,构造了一个在可接受期末财富约束条件下,使VaR达到最小的投资组合模型,同时,发现该模型发生了两基金分离现象,因此存在多风险资产情形下的投资组合模型可以退化成为单风险资产情形下的投资组合模型。最后,本文使用简化的单风险模型对我国上海股票市场进行了实证分析,探讨投资者如何在股票和银行借贷中进行最优资产分配。     

International asset pricing with time-varying risk premia

Recent empirical evidence that forward exchange rates are biased predictors of future spot rates can also be interpreted as evidence against the hypothesis of a constant risk premium. Consequently, reconciliation of this evidence with efficient international capital markets requires the existence of time-varying risk premia. This paper modifies Kouri's (1977) asset pricing model to allow time-varying exected returns on assets, eliminates the assumption of a risk-free real asset and derives the characteristics of the risk premia in the forward market as well as the equilibrium yield relationships among the equities and riskless nominal bonds of all countries.     

Cross‐commodity analysis and applications to risk management

The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. Although this is a well‐discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this study we are concerned with describing the joint return distribution of energy‐related commodities futures, namely power, oil, gas, coal, and carbon. The objective of the study is threefold. First, we conduct a careful analysis of empirical returns and show how the class of multivariate generalized hyperbolic distributions performs in this context. Second, we present how risk measures can be computed for commodity portfolios based on generalized hyperbolic assumptions. And finally, we discuss the implications of our findings for risk management analyzing the exposure of power plants, which represent typical energy portfolios. Our main findings are that risk estimates based on a normal distribution in the context of energy commodities can be statistically improved using generalized hyperbolic distributions. Those distributions are flexible enough to incorporate many characteristics of commodity returns and yield more accurate risk estimates. Our analysis of the market suggests that carbon allowances can be a helpful tool for controlling the risk exposure of a typical energy portfolio representing a power plant. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:197–217, 2009     

Time variation in the correlation structure of exchange rates: high‐frequency analyses

The correlation structure of asset returns is a crucial parameter in risk management as well as in theoretical finance. In practice, however, the true correlation structure between the returns of assets can easily become obscured by time variation in the observed correlation structure and in the liquidity of the assets. We employed a time‐stamped high‐frequency data set of exchange rates, namely, the US$–deutsche mark and the US$–yen exchange rates, to calibrate the observed time variation in the correlation structure between their returns. We also documented time variation in the liquidity structure of these rates. We then attempted to link the observed correlations with the liquidity via an application of an illiquid trading model first developed by Scholes and Williams (1976). We show that the observed correlation structure is strongly biased by the liquidity and that it is possible to effect at least a partial rectification of the otherwise downward‐biased observed correlation. The rectified sample correlation is, therefore, more appropriate for input into models used for forecasting, option pricing, and other risk management applications. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:127–144, 2001     

Is volatility risk priced in the securities market? Evidence from S&P 500 index options

The authors examine whether volatility risk is a priced risk factor in securities returns. Zero‐beta at‐the‐money straddle returns of the S&P 500 index are used to measure volatility risk. It is demonstrated that volatility risk captures time variation in the stochastic discount factor. The results suggest that straddle returns are important conditioning variables in asset pricing, and investors use straddle returns when forming their expectations about securities returns. One interesting finding is that different classes of firms react differently to volatility risk. For example, small firms and value firms have negative and significant volatility coefficients, whereas big firms and growth firms have positive and significant volatility coefficients during high‐volatility periods, indicating that investors see these latter firms as hedges against volatile states of the economy. Overall, these findings have important implications for portfolio formation, risk management, and hedging strategies. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:617–642, 2007     

Fama–French in China: Size and Value Factors in Chinese Stock Returns

We investigate the size and value factors in the cross‐section of returns for the Chinese stock market. We find a significant size effect but no robust value effect. A zero‐cost small‐minus‐big (SMB) portfolio earns an average premium of 0.61% per month, which is statistically significant with a t‐value of 2.89 and economically important. In contrast, neither the market portfolio nor the zero‐cost high‐minus‐low (HML) portfolio has average premiums that are statistically different from zero. In both time‐series regressions and Fama–MacBeth cross‐sectional tests, SMB represents the strongest factor in explaining the cross‐section of Chinese stock returns. Our results contradict several existing studies which document a value effect. We show that this difference comes from the extreme values in a few months in the early years of the market with a small number of stocks and high volatility. Their impact becomes insignificant with a longer sample and proper volatility adjustment.     

Wealth‐to‐Income Ratio and Stock Market Movements: Evidence from a Nonparametric Causality Test

We use a nonparametric causality‐in‐quantile test to analyze the predictive ability of the wealth‐to‐income ratio (wy) for excess stock returns and their volatility. Our results reveal that the wy is nonlinearly related with excess stock returns, and hence, results from linear Granger causality tests cannot be deemed robust. When we apply the nonparametric causality‐in‐quantile test, we find that the wy can predict excess stock returns over the majority of the conditional distribution, with the exception being the extreme ends, that is, when the market is in deep bear or bull phases. However, the wy has no predictability for the volatility of excess stock returns.