This issue of The Journal of Risk starts by looking at risk capital allocation within a firm in the context of two prominent risk measures: value-at-risk (VaR) and expected shortfall (ES). Next, the associated issue of efficiently backtesting ES is addressed. Two empirical papers based on Chinese data complete the set, with one focused on systemic risk and the other focused on the effects of stock price risk and split share reform on the cost of equity capital.
A financial institution’s risk capital is assessed using the risk exposure across its divisions. In “Static and dynamic risk capital allocations with the Euler rule”, the first paper in this issue, Tim J. Boonen highlights some pitfalls of the Euler rule, a common allocation approach. It is used to determine the amount a division will contribute to the risk capital of the whole firm. The author shows that this rule is more sensitive to empirical measurement errors than an alternative proportional rule, whether VaR or ES is used, with the latter resulting in a diminished impact.
Our second paper, “Backtesting expected shortfall: a simple recipe?”, sees Felix Moldenhauer and Marcin Pitera specifically focusing on an important issue related to ES that has become increasingly prominent in a regulatory capital setting. The authors propose a backtesting approach that is much simpler than current ones, which are often challenging to implement due to their complexity or hefty data requirements. Their approach monitors negative breaches of cumulative secured positions, which account for both capital reserves and realized financial positions. This approach can be viewed in the same manner as the traffic-light thresholds adopted in the current regulatory framework. In addition to being model independent, the approach requires neither the joint estimation of VaR and ES nor the standard reference-benchmark procedure found in elicitability-based backtests.
In the issue’s third paper, “Measuring the systemic risk of China’s banking sector: an application of differential DebtRank”, Wenjie Yin, Faqi Jin, Meiyu Tian and Fenghua Wen conduct an empirical study based on differential DebtRank, a ranking method akin to PageRank – central to search engines – to assess the systemic risk of banking in the second-largest economy in the world. Their analysis confirms the presence of systemically important banks as well as significant contributions to systemic risk by banks with high returns on assets and low liquidity. The authors further highlight the amplification of risk contributions made by small-scale banks and shadow banking during periods of high systemic stress.
Quanxi Liang’s and Wei Mao’s “Crash risk exposure, diversification and cost of equity capital: evidence from a natural experiment in China”, our fourth and final paper, is another empirical study based on Chinese data, this time with a focus on exposure to stock price crashes. The latter is further evaluated within the context of an exogenous shock: namely, the split share structure reform. The authors find that crash risk exposure is significantly and positively associated with the ex ante cost of equity capital, and this relation is not affected by the reform even after controlling for idiosyncratic volatility and its interaction with the reform. Additional tests show that the positive association between a higher cost of equity and price crash risk was most pronounced during the 2008 global financial crisis.
Warrington College of Business, University of Florida
This paper studies the volatility of the Euler rule for capital allocation in static and dynamic empirical applications with a simulated history.
In this paper, the authors introduce a new ES backtesting framework based on the duality between coherent risk measures and scale-invariant performance measures.
This paper investigates the systemic risk of China’s banking sector via network analysis and differential DebtRank from 2007 to 2016.
Crash risk exposure, diversification and cost of equity capital: evidence from a natural experiment in China
Based on a broad sample of Chinese listed firms for the period 2001–10, this study investigates the effect of stock price crash risk exposure on the cost of equity capital and uses the split share structure reform as an exogenous shock to test whether…