Forecasting expected shortfall: Should we use a multivariate model for stock market factors?

Is univariate or multivariate modeling more effective when forecasting the market risk of stock portfolios? We examine this question in the context of forecasting the one-week-ahead expected shortfall of a stock portfolio based on its exposure to the Fama–French and momentum factors. Applying extensive tests and comparisons, we find that in most cases there are no statistically significant differences between the forecasting accuracy of the two approaches. This result suggests that univariate models, which are more parsimonious and simpler to implement than multivariate factor-based models, can be used to forecast the downside risk of equity portfolios without losses in precision.     

Testing forecast accuracy of expectiles and quantiles with the extremal consistent loss functions

Forecast evaluations aim to choose an accurate forecast for making decisions by using loss functions. However, different loss functions often generate different ranking results for forecasts, which complicates the task of comparisons. In this paper, we develop statistical tests for comparing performances of forecasting expectiles and quantiles of a random variable under consistent loss functions. The test statistics are constructed with the extremal consistent loss functions of Ehm et al. (2016). The null hypothesis of the tests is that a benchmark forecast at least performs equally well as a competing one under all extremal consistent loss functions. It can be shown that if such a null holds, the benchmark will also perform at least equally well as the competitor under all consistent loss functions. Thus under the null, when different consistent loss functions are used, the result that the competitor does not outperform the benchmark will not be altered. We establish asymptotic properties of the proposed test statistics and propose to use the re-centered bootstrap to construct their empirical distributions. Through simulations, we show that the proposed test statistics perform reasonably well. We then apply the proposed method to evaluations of several different forecast methods.     

Assessing value at risk with CARE, the Conditional Autoregressive Expectile models

In this paper we propose a downside risk measure, the expectile-based Value at Risk (EVaR), which is more sensitive to the magnitude of extreme losses than the conventional quantile-based VaR (QVaR). The index θ of an EVaR is the relative cost of the expected margin shortfall and hence reflects the level of prudentiality. It is also shown that a given expectile corresponds to the quantiles with distinct tail probabilities under different distributions. Thus, an EVaR may be interpreted as a flexible QVaR, in the sense that its tail probability is determined by the underlying distribution. We further consider conditional EVaR and propose various Conditional AutoRegressive Expectile models that can accommodate some stylized facts in financial time series. For model estimation, we employ the method of asymmetric least squares proposed by Newey and Powell [Newey, W.K., Powell, J.L., 1987. Asymmetric least squares estimation and testing. Econometrica 55, 819–847] and extend their asymptotic results to allow for stationary and weakly dependent data. We also derive an encompassing test for non-nested expectile models. As an illustration, we apply the proposed modeling approach to evaluate the EVaR of stock market indices.     

VaR模型及其在金融风险管理中的应用

风险价值(简称VaR)是目前国际金融风险管理领域广泛使用的工具,也是度量金融风险的一种新的技术标准。本文着重介绍了VaR的概念、计算及其应用,并指出VaR模型作为衡量金融市场风险的标准在我国的应用前景。     

REAL OPTIONS AND THE CROSS‐SECTION OF EXPECTED STOCK RETURNS

This paper surveys the theoretical literature investigating the effect of firms’ investment flexibility on the cross‐section of expected stock returns. Real options analysis derives firms’ value‐maximizing investment policies as functions of exogenous fundamental drivers of profitability and calculates firms’ market values as functions of the same variables. These functions yield the relationship between expected stock returns and firm fundamentals. Several plausible explanations for the value premium – the high average stock returns earned by firms with high book‐to‐market ratios – emerge from this literature.     

Alternative measures of homeownership gaps across segregated neighborhoods

The dramatic rise in the U.S. homeownership rate from 64% in 1996 to almost 70% in 2005 has prompted increased attention to the relation between homeownership and demographic characteristics of households. The recent rise and sharp decline of subprime lending will likely spur further interest in homeownership gaps. Statistical analysis of these differences or “gaps” in homeownership between white and minority households has evolved into a highly stylized comparison of differences in homeownership at the mean or the conditional mean. This study implements a quantile decomposition technique that identifies the unexplained portion of the gap not only at the mean, but at every percentile of the homeownership distribution. Results suggest that differences in homeownership gaps at the mean reflect a combination of small differences at the upper end and much larger gaps at the lowest end of the distribution of homeowners. This study also adds credit history to the factors that are used to explain homeownership gaps.     

Estimation of the mean of the selected population under asymmetric loss function

This paper is concerned with the comparison of seven estimators of the mean of the selected population from two normal populations with unknown means and common known variance under an asymmetric loss namely the LINEX loss function. The proposed estimators are invariant under location transformation. The bias and risks of the seven estimators are computed and compared. The conclusion recommend the use of δ_P (σ) which is simple to use and it is minimax. Received: January 1999     

Herding behavior,market sentiment and volatility: Will the bubble resume?

This paper aims to investigate herding behavior and its impact on volatility under uncertainty. We apply a cross-sectional absolute deviation approach as well as Quantile Regression methods to capture the herding behavior in daily and monthly frequencies in US markets over several time-periods including the global financial crisis. In a novel attempt we modify the empirical CSAD herding modeling by introducing implied volatility as a measure of agent risk expectations. Our findings indicate that herding tends to be intense under extreme market conditions, as depicted in the upper high quantile range of the conditional distribution of returns. During crisis periods herding is observed at the beginning of the crisis and becomes insignificant towards the end. The US market herding behavior exhibits time-varying dynamic trading patterns that can be attributed e.g., to overconfidence or excessive “flight to quality” features, mostly observed in the aftermath of the global financial crisis. Moreover, implied volatility reveals asymmetric patterns and plays a key role in enforcing irrational behavior.