Despite its limitations, value-at-risk (VaR) remains essential to risk management. In this issue of The Journal of Risk we present papers that show different facets of VaR, which is not only a foundation for portfolio management but also a device to help indirectly assess the accuracy of volatility estimators.
In the issue’s first paper, “Risk management for private equity funds”, Axel Buchner extends the concept of VaR to develop a risk management framework for private equity funds that accounts for market, liquidity and funding risks. The author provides an illustration of the calibration of his model to data for buyout funds; this is then paired with a Monte Carlo simulation showing the dynamic evolution of the associated risk measures.
Should one evaluate the quality of a volatility estimator based on that of another parameter it affects, such as VaR, or based on some accuracy criterion by comparing it with a benchmark value? In our second paper, “Comparing multivariate volatility forecasts by direct and indirect approaches”, Alessandra Amendola and Vincenzo Candila rely on VaR to indirectly evaluate, via backtesting, the accuracy of multivariate volatility forecasts. In a comparison with direct forecast assessment based on statistical loss functions, the authors show that, when using intraday returns, the latter is more reliable in helping to select from a variety of forecasting models.
One of the most expedient ways to incorporate kurtosis and skewness into a VaR estimate based on the normality assumption is through the Cornish–Fisher correction, resulting in the so-called modified VaR (mVaR). Similarly, asymptotic expansions lead to a modified expected shortfall (mES) expression. In “Inefficiency and bias of modified value-at-risk and expected shortfall”, the third paper in this issue, R. Douglas Martin and Rohit Arora show that such modifications can reduce bias but may also lead to inflated standard errors for these estimators.
In the final paper, “Estimating the tail shape parameter from option prices”, Kam Hamidieh makes use of extreme value theory and market-based option prices to estimate the tail shape parameter of the risk-neutral density. He shows in particular that only out-of-the money option prices are needed for this estimation. In contrast to alternative methods, this approach eschews the need for additional parameters such as spot value, dividend yield and risk-free rate.
This issue of The Journal of Risk is accompanied by a special online supplement that was edited separately. It consists of papers presented at the 8th International Finance Conference/Mediterranean Summit in Paris in March 2015.
University of Florida
This paper aims to fill a gap in the literature by developing the first comprehensive risk management framework for private equity fund investments.
This paper investigates direct and indirect volatility evaluations in the multivariate framework by means of a Monte Carlo simulation
This paper compares mVaR and mES estimators with VaR and ES under normal and fat tailed t-distributions.
In this paper, the author proposes a method to estimate the tail shape parameter of the risk-neutral density.