The thesis finds evidence supporting that the assumptions surrounding the Basel framework are inadequate. Both risk measures applied in Basel, value-at-risk and expected shortfall, fails in their most standard form to provide estimates which are sufficiently reducing losses. In particular, the assumption of Gaussian distributed returns surrounding the Basel framework is found to be wrong. Both the homoscedastic volatility estimates provided by the model and the assumption of identically and independent returns are found to be violated.
The returns are found to be relatively stable from day-to-day over the whole period, but is at times quite volatile. Analyses of the observations show that, when divided into two subsamples, a normal and extreme market, the empirical distribution of the two differs significantly from each other and from a Gaussian distribution. Both are found to have high kurtosis and negative skewness, in addition to volatility clustering. The two market states differ the most in tail properties, as the extreme market is described by the large magnitude of the returns at each end of the distribution, whereas the normal market displays more moderate values. The findings suggest that it may not be suitable to use one single model to describe a market characterised by large differences in stability, but rather apply two models conditionally of the given market state.
To adjust the approach of the Basel framework, two models are proposed for the normal and extreme market respectively. A student’s t-distributed GARCH (1,1) model is used during normal market conditions to incorporate the distribution properties of the sample, while at the same time incorporating heteroskedastic volatility estimates. Extreme value theory is proposed applied for extreme market conditions in the form of a conditional peak-over-threshold model to account for both the extremity of the tails and to incorporate heteroskedastic volatility. The two models are also combined into one applicable model to provide a realistic setup for a portfolio manager. The models are found to violate the risk limits of VaR and ES far less than the Basel framework, during both normal and non-normal market conditions. In addition, the two models prove to be more adaptable to the state of the market, quickly incorporating changing volatility and thus effectively notifying a portfolio manager of adjusted risk exposure.
|Uddannelser||Cand.merc.fin Finance and Investments, (Kandidatuddannelse) Afsluttende afhandling|