Volatility estimates and their robustness are addressed in this issue of The Journal of Risk. In one case, low–high price ranges are used for estimation. In two others, second-order risk and chaos theory are adopted to assess estimation bias and sensitivity to initial conditions, respectively. This issue concludes with a paper that contrasts two regulatory effects: one based on short-sales restrictions and the other based on capital requirements.
A central challenge in the implementation of any portfolio strategy is the estimation of parameters such as covariance of asset returns. As strategies are concerned with ex ante estimates of variance, the notion of second-order risk (SOR), which measures the discrepancy between ex ante and ex post variances, is also helpful in quantifying model risk. In “Second-order risk of alternative risk parity strategies”, Simone Bernardi, Markus Leippold and Harald Lohre apply the concept of SOR to compare risk parity strategies driven by principal component analysis of the covariance matrix of asset returns. Among their findings, they discover that the principal risk parity strategy, which invests equally in each eigenvector, is immune to SOR bias.
The volatility of major markets has been studied using a number of approaches. In “Chaotic behavior in financial market volatility”, Houda Litimi, Ahmed BenSa¨ıda, Lotfi Belkacem and Oussama Abdallah propose the use of chaos theory and neural networks to assess the chaotic nature of volatility. Their objective is to determine whether volatility can endogenously be significantly affected by small initial conditions. The authors’ empirical analysis suggests the presence of low-level chaos in all major stock market volatilities, which, however, differ in their chaotic maps.
Haibin Xie and Xinyu Wu use low–high price ranges in “Range-based volatility forecasting: an extended conditional autoregressive range model” to estimate volatility. In particular, the authors employ an extended conditional autoregressive model to capture the dynamic evolution of low–high price ranges. They show that it improves on the forecast accuracy of the standard conditional autoregressive range model and its asymmetric and gamma variants.
In the midst of the financial crisis of 2008, regulators rushed to adopt short- selling rules in addition to existing value-at-risk (VaR) considerations for capital requirements. In “The implications of value-at-risk and short-selling restrictions for portfolio manager performance", Fulbert Tchana Tchana and Georges Tsafack con duct a study to evaluate the effects of both when portfolio managers have some private information, Their empirical analysis shows that in highly volatile mar kets, VaR restrictions are more constraining on portfolio performance than short-sale regulations.
Warrington College of Business, University of Florida
In this paper, the authors provide theoretical and empirical evidence of the contribution of second-order risk to realized volatility for alternative risk parity strategies.
In this paper, the authors present a robust method for the detection of chaos based on the Lyapunov exponent, which is consistent even for noisy and finite scalar time series.
This paper proposes an extended conditional autoregressive range (EXCARR) model to describe the range-based volatility dynamics of financial assets.
This paper provides a framework to analyze the performance of a portfolio manager under a value-at-risk (VaR) constraint, in a Markowitz setup.