## VaR

Finance Junkie
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### VaR

Pls explain:

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)?
a. The VaR is USD 100
b. The VaR is zero
c. The VaR is USD 200
d. None of the above

Pristine Solution: The VaR of each position is zero. Assuming a 95% confidence interval, the joint positions has a VAR equal to 100.
Pay off of joint position Probability -200 0.0016 = 0.042 -100 0.0768 = 2x0.96x0.4 0 0.9216 = 0.962

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content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: VaR

The answer here, -100 is correct.

There are 3 possible payoffs of the 2 securities:
Both have a -100 payoff, total = -200, with a probability = 0.04* 0.04 = 0.16%
One has a -100 and the other 0 payoff, total = -100, with a probability = 2* 0.96* 0.04 = 7.68%
Both have a 0 payoff, total = 0, with a probability = 0.96* 0.96 = 92%

Now, take these 3 and plot a graph. The 95th percentile has a -100 payoff..

Hope this helps..

swarnendupathak
Finance Junkie
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Joined: Mon Sep 17, 2012 11:06 am

### Re: VaR

Hi,

Thanks
Swarnendu

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: VaR

As explained above:
Payoffs: -200, -100, 0
Probabilities: 0.16%, 7.68%, 92.16%
Cumulative Probability: 0.16%, 7.84%, 100%
The 5th percentile lies in the payoff region of -100.
Hence, that is the required VaR

Hope this helps!