## Value at Risk Quiz 2

vandana.jain
Finance Junkie
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Joined: Tue Jul 24, 2012 4:56 pm

### Value at Risk Quiz 2

Hi,

Under usually accepted rules of market behaviour, the relationship between parametric delta-normal VAR and historical VAR will tend to be
a. St1: Parametric VaR will be higher.
b. St2: Parametric VaR will be lower.
c. St3: It depends on the correlations.
d. St4: None of the statements are correct.
Ans is b, How?

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

If you use delta-VAR for a portfolio of options, which of the following statements is always correct?
a. St1: It necessarily understates the VaR because it uses a linear approximation.
b. St2: It can sometimes overstate the VaR.
c. St3: It performs most poorly for a portfolio of deep-in-the money options.
d. St4: It performs most poorly for a portfolio of deep-out-of-the money options

Tags:

shreyas
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Joined: Thu Jul 19, 2012 6:49 pm

### Re: Value at Risk Quiz 2

Question: Parametric and historical VAR

Solution:Parametric VAR assumes normal distribution of returns, but in reality returns are skewed thus Delta normal VAR underestimates the risk.

shreyas
Finance Junkie
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Joined: Thu Jul 19, 2012 6:49 pm

### Re: Value at Risk Quiz 2

Question: Binary Options

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

shreyas
Finance Junkie
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Joined: Thu Jul 19, 2012 6:49 pm

### Re: Value at Risk Quiz 2

Question: Delta VAR on options

Solution: The delta-VAR could understate or overstate the true VAR, depending on whether the position is net long or short options, so St1) is incorrect. The delta-VAR is generally better for in-the-money options, because these have low gamma, so St2) is false for out-of-the-money options, delta is close to zero, so the delta-VAR method would predict zero risk. The risk could indeed be very small, so St4) is incorrect. So, St2) is the most general statement.

d2syh
Good Student
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Joined: Fri Aug 17, 2012 3:27 pm

### Re: Value at Risk Quiz 2

Can I check for the actual calculation on this payoff?

"Pay off of joint position Probability -200 0.0016 = 0.042 -100 0.0768 = 2x0.96x0.4 0 0.9216 = 0.962"

shreyas
Finance Junkie
Posts: 83
Joined: Thu Jul 19, 2012 6:49 pm

### Re: Value at Risk Quiz 2

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..