Hello everyone,
Computing Question 5 ii) a) (parts b) & c) have the same issue) from https://www.actuaries.org.uk/studying/curriculum-2019/actuarial-mathematics I arrive at stochastic return r_A as follows:
r_A = -1 (i.e. loosing all the investment) if company A defaults (probability q=0.01887)
r_A = 0.06 if company A survives (prob 1-q)
Hence
P(r_A<x) = 0 for x<=-1
P(r_A<x) = q for 1<x<=0.06
P(r_A<x) = 1 for 0.06<x
As q < 0.05 (95% confidence is required) is is evident that max { x : P(X<x) <= 0.05} = 0.06. So VaR_95% = - 0.06. I.e. in monetary terms noting 100 original investment the maximum loss on a 95% degree of confidence are -6 pounds. However the official solution (available via https://www.actuaries.org.uk/studying/curriculum-2019/actuarial-mathematics) says that VaR_95% = 0.
Then the TailVar is also calculated in the official solution in my opininion as a conditional TailVar (conditioned that there is a shorfall). According to my calculations the TailVar should be as follows:
A) using my VaR_95%
TailVar = (0.06 - (-1))q=0.02 so the expected loss in excess of the VaR_95% is 100x0.02 = 2. In absolute thinking the loss is -6+2 = -4 (still a profit).
B)
Using theii zero VaR_95%
TailVar = (0 - (-1))q=q=0.01887 so the expected loss in excess of the VaR_95% is 1.887. In absolute thinking the loss is -6+2 = -4 (still a profit).
Could anybody reinforce me in thinking that something went wrong in their official calculation?
Side comment: in the CMP VaR's are calculated always for returns (then as an answer the monetary approach is prefered). I thought I will work accordingly also during the exam. But I start to feel here that in some cases it is better to directly work in monetary terms.
For your convenience, I also attached the mentioned paper and the corresponding solution file.
Thx. in advance for your help,
S.
