Application of Risk Management Beyond the VaR in Insurance and Stock Investment

Value-at-risk has been broadly used in practice; however, it has some weaknesses. The most serious shortcoming is that it neglects risk exceeding the VaR value. Conditional Value-at-Risk (CVaR), the expected value of risk beyond the VaR, taking the whole loss distribution into account, considering the frequency and size of extreme events at the same time, will serve as a more suitable risk measure. In this article we investigate the differences from using VaR and CVaR as the risk measure. We conduct empirical study on the returns of eight industry indexes and the loss ratios of nine non-life insurance product lines. Some discoveries can be concluded as follows: 1. For the equity returns of industry indexes, the rankings of VaR and CVaR display divergent order in the long-term study period. It reveals that the most risky industry we suppose originally based on using VaR as the risk measure varies when we using CVaR as the risk measure instead. Furthermore, many loss distributions of industry indexes exhibit fat-tailed characteristic; this effect can be observed more obviously under CVaR computation. 2. In the short-run empirical analysis in returns of industry indexes, Based on the daily data, we find out the rankings of VaR and CVaR are similar, but if we convert daily computing frequency to weekly one, the rankings turn into different again. 3. Regarding the loss ratios of non-life insurance product lines, the differences “CVaR－VaR” based on historical simulation vary widely among the product lines. It implies that the loss distributions of non-life insurance may not be fat-tailed but have an extreme event, which produces huge loss with small probability. If we only use VaR to measure the risk, we would overlook this event. We suggest using CVaR as the risk measure, at least as a supplementary tool besides VaR to establish more comprehensive risk management.Contents I. Introduction……………………………………………...1 II. Methodology……………………………………………….6 2.1 Definition of Conditional Value-at-Risk 6 2.2 Research Targets 7 2.2.1 The Return of The Industry Indexes in Taiwan 7 2.2.2 The Loss Ratio of Non-Life Insurance by Product Line 10 III. Empirical Analysis………………………………………..11 3.1 The Empirical Results of Stock Market Returns by Industry Indexes in The Long-Run 12 3.1.1 Ranking of VaR and CVaR of Stock Market Returns by Industry in Different Confidence Level 12 3.1.2 Test of Fat-Tailed Distribution 14 3.2 The Empirical Results of Stock Market Returns by Industry Indexes in The Short-Run 17 3.2.1 Ranking of VaR and CVaR of Stock Market Returns by Industry in Different Confidence Level 17 3.2.2 Test of Fat-Tailed Distribution 21 3.2.3 Other Discoveries in Equity Investment Research 25 3.3 The Empirical Results of Loss Ratios of Non-Life Insurance by Product Lines 28 3.3.1 Ranking of VaR and CVaR of Loss Ratios by Product Line of Non-Life Insurance in Different Confidence Level 28 3.3.2 Test of Fat-Tailed Distribution 30 IV. Conclusion………………………………………………32 Reference……………………………………………………...35 Appendix………………………………………………………3