LVAR

[higaurav]

Hi David,

Need your help on this question given below, this is taken from the 2008 practice set.

Q Consider an asset worth USD 1 million whose 95th percentile VaR is USD 100,000 (computed using the
parametric method assuming the normal distribution). Suppose the bid-ask spread on the asset has a
mean of USD 0.10 and a standard deviation of USD 0.30. What is the 95th percentile liquidity adjusted
VaR assuming the market risk VaR and the liquidity risk piece are uncorrelated?
a. USD 200,000
b. USD 344,000
c. USD 444,000
d. USD 688,000

Explanation: If the VaR is USD100,000, the liquidity piece can be estimated from the mean and std
dev of the spread as V (μ - 1.96σ) = USD1,000,000 (USD0.10 - (1.96)(USD0.30)) = USD344,000
With no correlation to the market risk piece, we add to get (b).
Reference:
Christopher L. Culp, he Risk Management Process: Business Strategy and Tactics (Hoboken: John Wiley &
Sons, Inc, 2001)., Chapter 17 – Identifying, Measuring, and Monitoring Liquidity Risk

How can we arrive at the ans given the formula that we learned to add the 1/2 spread to the absolute VAR. I could not understand the formula used in the explanation and also if you notice 1.96 is used at 95th percentile (two tailed ?).. Pls advice, appreciate your guidance on this..thanks

 

[David Harper CFA FRM]

Hi OM

I need help with this question, too! John previously raised the issue of one- versus two-tailed test. I don't see any two-tailed tests here...

I completely disagree with the answer here. Maybe I am mistaken, but I think it is incorrect to add the 0.1 to negative volatility. This is a repeating error in Culp. Culp has the signs (+/-) wrong. In the spread, you want the mean spread plus (+) the dispersion; this result is offsetting them. e.g., a +0.1 with standard deviation of 0.1 results in zero, but that's not right!?

Here i put them both in an XLS. My answer is to the right:
https://www.editgrid.com/bt/admin/sample_2008_q36

David

 

[chih22]

I am confused by the answer GARP gave because they said the answer is C.) 444,000 when their explanation results in B.) 344,000.

I don't understand how they come up with 444,000? Is this a typo?

I understand how they calc 344,000...

100,000 + 1,000,000 x (1/2(.10 - 1.96 x .30))

Not sure what to do if something like this actually appears on the exam?

 

[David Harper CFA FRM]

I believe the entire answer is an error, for reasons cited above (e.g, + mean - volatilty makes no sense here, the 344 makes no sense). So, I disagree with both the signs (+/-) which, IMO, repeats Culp's error and also the one-tailed (1.96)

They got 444 by adding 344 to $100 VaR. Conceptually, that's okay: LVAR adds (on increases) VaR by one-half the spread. LVAR should increase the VaR, the method here is to use 1/2 the spread.

David