Risk Measures - from theory to an empirical study over time

Sammanfattning: This thesis concerns risk measures in theory and an empirical study of their accuracy in predicting future risks, back-testing them using an out-of-sample study with a rolling window scheme. The theoretical part includes a general presentation of risk, covers various risk measures – dispersion measures and safety measures – and attempts to sort out their advantages and disadvantages. The coherent risk measure Conditional Value at Risk should, in theory, be an adequate tool to measure risk. However, the important thing is to know what to do and most likely, one needs to include several measures to get a complete picture of the risk. The results of the empirical study indicate that the chosen safety risk measures and time periods do not succeed in predicting the amount of risk very well, even though they in some periods do perform quite well. However, if one calls a successful prediction a prediction which falls below the outcome, the methodology succeeds quite well. Also, especially for Maximum Draw-down, instable periods seem to affect the accuracy significantly. Future research might include other risk measures and other time periods – longer prediction windows than one year and shorter or longer estimation periods. Furthermore, one could also look at other time periods for the risk measure definitions (e.g. a week instead of a day).