For part (ii) of the question, why is 95% VaR for AA zero and TailVaR = 106paa/paa ? More specifically how is VaR and TailVaR calculated in this question?
The 95% VaR is based on the point at the start of the lower 5% tail of the distribution. For Bond A, the probability of default (paa) is 0.0189. So the amount returned from an investment in Bond A is 0 (with prob 0.0189) or 106 (with prob 0.9801). The start of the lower 5% tail therefore corresponds to receiving 106, so this is the VaR. The examiners have expressed this as 0, ie there is no default. This is equivalent to saying the VaR is 0 relative to the no-default proceeds (or maximum return) of 106. Note that the examiners report indicates that full credit would have been given for answers relative to the maximum return, the expected return or the initial investment. The (unconditional) TailVaR is the expected loss beyond the value at risk. Here, this the amount of the loss beyond the value at risk (taken as a loss of 106 if default occurs) multiplied by the probability of this occurring (paa). This gives 106*paa. The (conditional) TailVar is the unconditional TailVaR divided by the probability of a loss occurring. Here this gives 106*paa/paa.
