VaR Calculation 2003 FRM Question

[ykho22]

Hello,

Try some past exam questions and came to the following. Can anyone explain the calculation?

Q (FRM 2003): Imagine a portfolio which holds two binary options, each with the same payoff and probability: USD -100 with a probability of 4% and USD 0 with a 96% probability. Assuming the underlying has uncorrelated returns, what is the VaR (95% confidence level, 1 day)?

Ans: The VaR of each position is zero. Assuming a 95% confidence interval, the joint positions has a VAR equal to 100.

Thanks.
Peach

 

[David Harper CFA FRM]

Hi Peach,

There are only four outcomes: both -100, both 0, -100/0 and 0/-100. (just like, how many permutations of two coin flips? Four)

Probability of both 0 = 96%^2 = 92.2%
Probability of both -100 (portfolio = -200) = 4% ^2 = 1.6%
Probability of 0/-100 or -100/0 equals 100% - 92.2% - 1.6% = 7.7% (but you don't really need this last part)

If you look at the distribution the 92.2% VaR = 0 and the 98.4% VaR (100% - 1.6%, the start of the extreme tail) = -200, so the 95% VaR is in between:

92.2% < 95% < [100% - 1.6%]

David

 

[cash king]

Hi david,

I think you made a calculation mistake there: 4%^2=0.16%, not 1.6%
Since VaR(92.16%)=0, VaR(99.84%)=-100, I think VaR(95%) has to be -$100, meaning we're confident that the chance of loss staying under -100 is at least 95%.

Correct me if I'm wrong.