Robust Forecasting and Backtesting of Value at Risk (VaR) and Expected Shortfall (ES) risk measures

Recent financial turmoil has set in motion changes that include the switch from the Value at Risk (VaR) risk measure to the Expected Shortfall (ES). Although ES seems superior to VaR, both measures are statistical quantities estimated using historical data. This basis in historical data raises numerous concerns regarding their implementation. This thesis focuses on the estimation, evaluation and applications of the Value at Risk and Expected Shortfall risk measures. It consists of four main chapters corresponding to four research papers.

The first chapter evaluates the utility of the forecast combination approach in risk forecasting. We implement a forecast combination approach aiming to improve the accuracy of the freight rate VaR forecasts. In addition, we utilize an augmented statistical evaluation approach accompanied by the relevant evaluation of the forecasts. This is done in order to acquire a thorough understanding of the performance of the forecasts. Our findings suggest that the combination approach significantly improves the accuracy of the VaR forecasts.

In the second chapter we evaluate the performance of the backtesting methods and their reliability. Specifically, through a simulation exercise and a financial data application, we evaluate the size and power properties of the major VaR and ES backtesting methods. In addition, we examine the impacts of the regulatory specifications and estimation risk on the tests performance. The simulation results suggest that the size of the tests is distorted and the power of the tests is low, especially for the regulatory specifications. Finally, the empirical application results suggest that misspecified methods are not rejected.

In the third chapter we focus on the relevant evaluation of the density forecasts. Specifically, we propose a new rule that aims to capture the performance of the methods at specific regions of the tail. In order to evaluate the performance of the proposed scoring rule, we conduct a simulation exercise and a financial data application. Our findings suggest that the tests of equal performance based on the newly proposed scoring rule have a robust size and power profile. In addition, the financial data application results suggest that the proposed rule provides a more clear insight into the tail performance of the forecasting methods.

Finally, in the fourth chapter we utilize the VaR and ES risk measures in order to evaluate the risk-return relationship of the hedge funds and the fund of funds. In addition, we propose an optimal portfolio strategy that aims to outperform the hedge funds and their portfolio benchmarks. Our findings suggest that there are small gains from investing in fund of funds when compared to low risk hedge funds. More importantly, the optimal portfolios outperform all the fund of funds benchmarks.