Oct 2011 Q8 Part iii

Very puzzled by the calculation for strategy A in part iii. I did it the following way, and I must be missing something obvious...

Investing 2M in single bond issue --> 20 units at 100,000 each.
In 1 year, entire portfolio will be worth either 0 (probability 2%) or 20*105,000 = 2.1M (probability 98%).
E[X] = (0.02)*0 + (0.98)*2.1M = 2.058M
Absolute VaR = 2.1M
Relative VaR = 2.058M - 2.1M = -42,000
Absolute TVaR = [0*.02+2.1M*.005]/.025 = 420,000
Relative TVaR = 2.058M - 420,000 = 1,638,000

Where am I going wrong?

Likewise, for strategy B I get:
Absolute VaR = 1.89M (2 defaults)
Relative VaR = 2.058M - 1.89M = 168,000
Absolute TVaR = [1.68M*0.0006+1.785M*0.0065+1.89M*(0.025-0.0006-0.0065)]/0.025 = 1,857,660
Relative TVaR = 2,058,000 - 1,857,660 = 200,340

The directions and orders of magnitude are consistent with the Examiners' Report but I'm not sure where the numbers are coming from (or if mine are completely wrong).

 

Sorry, I'm not following...

 

Ah, your last sentence about not suffering any losses at all caused me to realize something: I realized I was doing the VaR/TVaR of the value of the bonds, not the VaR/TVaR of the net loss to the investor. If I simply incorporate the initial cost to the investor ($2M) and then redo the calculations, I get the right answers. Thanks!

Strategy A VaR: Gain 100,000 98% of the time --> VaR = -100,000
Strategy A TVaR: [(2M-0)*.02+(2M-2.1M)*.005]/.025 = 1,580,000

Strategy B VaR: Lose 215,000 or more 0.71% of the time vs. lose 110,000 or more 5.99% of the time --> VaR = 110,000
Strategy B TVaR: [(2M-1.68M)*0.0006+(2M-1.785M)*0.0065+(2M-1.89M)*(0.025-0.0006-0.0065)]/0.025 = 142,340 (They rounded in the Examiners' Report)