Value-at-risk: A coherent measure of risk?
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Value-at-risk is an instrument which is widely used by financial institutions for calculating risk. It has been known since the late nineties that this tool lacks an important logical property: subadditivity. This can cause major errors, leading to systematic underestimation of risk when multiple portfolios are combined. It is known to be caused by coarseness in the return distribution and is thus most problematic when using historical simulation. This thesis investigates the severity of subadditivity violations from historical simulation, using the oil markets as a source of data. In order to measure this, a variant of the standard backtest has been used. The amount of subadditivity is found to be strongly dependent on the correlation between the individual portfolios, but independent of the choice of confidence level and sample size. A negative correlation virtually eliminates non-subadditivity altogether.
Master's thesis in Industrial economics