Confused on when to use one tail or two tail

[[email protected]]

Hi David,

While reviewing practice questions, I'm so confused about when to use the one-tailed or two tailed test.

For example in the 2008 FRM practice test 1 question #36 used
1.96 for the 95th percentile VaR
and in question #37
1.645 is used for the 95% surplus-at-risk.

Is there a way to remember when to use the one or two tailed?

Question 36 says:

Consider an asset with USD 1million whose 95th percentile VaR is USD 100,000.
Suppose the bid-ask spread on the asset has a mean of USD 0.10 and a std dev of USD 0.30.
What is the 95th percentile liquidity adjusted VaR assuming the market risk VaR and the
liquidity risk piece are uncorrelated?

Question 37 says:

Company XYZs pension fund has liabilities of USD 100M and assets of USD 120M.
The annual growth of the liabilities has an expected value of 5% with 3% volatility.
The annual return of the assets has an expected value of 8% with 12% volatility.
The correlation between asset return and liability growth is 0.3.
What is the 95% surplus-at-risk?


I would appreciate any guidance because this has been frustrating.

Thanks in advance.

John

 

[David Harper CFA FRM]

Hi John,

I think question 36 is confused, not you. I think Q 36 should use 1.645 per a worst-expected spread. As you say, the 1.96 implies a two-tailed 95% confidence but that's not the test: the LVaR cares about the spread that gets wider than mean, not the other tail where the spread gets narrower.

I'd say VaR, and the volatility-adjusted spread (as we care about the dispersion only on "one side," where it hurts us, not the other side, where it benefits us) are always one-tailed tests.

Note even the formula is incorrect. It repeats a formula error in Culp. It is incorrect to use LVAR = mean - (critical value)(volatility) + spread because then the spread is erroneously offsetting the volatility. As the spread needs to make LVaR worse than VaR, Culp should be either
mean - [(critical value)(volatility) + spread], or i prefer to follow Kevin Dowd with this formula which reduces the possibility for +/- sign errors:
- mean + [(critical value)(volatility) + spread]

David

append: John, I missed the bottom half where you quote the questions (maybe you edited the question, i do that too!). I still think the answer to q 36 is incorrect and I only see "one-tailed tests" here; i.e., VaR confidence is only one tailed, caring only about losses not gains. I've looked at the Culp source and i think that extends to the scaling the spread by volatility.

 

[[email protected]]

Hi David,

Thanks for the quick response! I thought so, that VaR is one-tailed. When q36 used 1.96 it confused me. I hope there aren't too many of these errors on the practice test.

John

 

[David Harper CFA FRM]

John,

FYI, Since question 36 was just posted in full, I got to take a look at the whole thing.
I think it's got even another mistake.
See here. ...David