The answer to the TVaR calculation for portfolio A is as follows: TVaR97.5%A = (-20 * 0.5% * 5,000 + 20 * 2% * 100,000) / 2.5% Can I confirm that the percentages in the numerator are allocated: an expected default in one year’s time (assuming a binomial distribution) of 2% and the remaining probability of 0.5% that the bond will not default? Why is this assumption made?
The Tail VaR can be found by considering the possible losses (gains) if the VaR is exceeded. A profit of £5,000 per bond applies up to the 98% level (ie 0.5% above the 97.5% VaR level) and then a loss of £100,000 per bond applies thereafter (default with no recovery). Alternatively, for the TVaR, it can be argued that, as all the bonds are identical, the losses are binary and that if losses exceed the 97.5% point, then we will lose everything – ie TVaR = £2m.
