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GARP 2013 Practice Exam Question 11

Roshan Ramdas

Active Member
Hi David,

Apologies for the last minute questions. I have 2 doubts with respect to the below question from GARP's 2013 sample questions.

Doubt 1 -
How do we infer from the below data if collateral increases or decreases current exposure ??
I understand that collateral in general reduces exposure,....although there are specific instances where it can increase exposure as well (example - collateral posted by counterpart A with counterpart B exceeds the actual exposure that counterpart B faces with respect to A).

Doubt 2 - With regards to the impact of collateral on exposure volatility between remargining periods, I have a concern with how GARP has presented the answer.

They calculate the worst case change in value of collateral and the worst case change in the value of exposure with collateral and then arrive at the conclusion that collateral increases volatility.

My approach was to calculate the worst case change in value of exposure without collateral and the worst case change in the value of exposure with collateral and then arrive at the conclusion that collateral increases volatility of exposure. Is there a logic behind GARP's way of approaching the question please ?

GARP Question
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11.
An underlying exposure with an effective annual price volatility of 6% is collateralized by a 10-year U.S.
Treasury note with an effective price volatility of 8%. The correlation between the exposure and the U.S.
Treasury note is zero. Changes in the value of the overall position (exposure plus collateral) are calculated for
a 10-day horizon at a 95% confidence interval (assume a year of 250 days). Which of the following would one
expect to observe from this analysis?
a. The presence of collateral increases the current exposure and increases the volatility of the exposure
between remargining periods.
b. The presence of collateral increases the current exposure, but decreases the volatility of the exposure
between remargining periods.
c. The presence of collateral decreases the current exposure, but increases the volatility of the exposure
between remargining periods.
d. The presence of collateral decreases the current exposure and decreases the volatility of the exposure
between remargining periods.

Explanation: Worse case change for the value of the collateral is: -1.96 * 8% * (10/250)0.5 = -3.136%
The overall volatility of the position: (.06^2 + .08^2)^0.5 = 10%
Thus the worst case change in the value of this position (exposure + collateral) is:
-1.96 * 10% * (10/250)0.5 = -3.92%
Thus, the collateral mitigates the exposure today while increasing the volatility of the position in the future.

ShaktiRathore

Well-Known Member
Subscriber
Hi there,if i may clarify
If current exposure is say 10 then if collateral is posted say then net exposure is 10-2=8.Thus our net current exposure is reduced by the collateral value.here we are talking about current exposure not potential future exposure(u r including also in the current exposure). If collateral is negatively correlated with exposure then collaterL posted would decrease in value and exposure may increase so that overall net exposure is increased by the collateral potentially in the future,this does make sense in the future but for current exposure position the collateral posted is decreasing the net current exposure.
Second doubt,i think Garp is trying to show that volatilty of combined collateral+exposure(total not just current) is greater when collateral is added to the exposure than we can take any base conclusion will be the same, i cant think it maked any difference but ur case is also valid where u r taking exposure as the base while for garp its collateral. Combined vol/base vol>1 for our 0 correlation case should be the conclusion i)collateral as base vol comb./vol coll=sqrt(vol coll^2+vol exp^2)/vol coll= sqrt(1+vol exp^2/vol coll^2)>1ii)exposure is base sqrt(vol coll^2+vol exp^2)/vol exp= sqrt(1+vol coll^2/vol exp^2)>1.
Thanks

Last edited:

Roshan Ramdas

Active Member
Hi there,if i may clarify
If current exposure is say 10 then if collateral is posted say then net exposure is 10-2=8.Thus our net current exposure is reduced by the collateral value.here we are talking about current exposure not potential future exposure(u r including also in the current exposure). If collateral is negatively correlated with exposure then collaterL posted would decrease in value and exposure may increase so that overall net exposure is increased by the collateral potentially in the future,this does make sense in the future but for current exposure position the collateral posted is decreasing the net current exposure.
Second doubt,i think Garp is trying to show that volatilty of combined collateral+exposure(total not just current) is greater when collateral is added to the exposure than we can take any base conclusion will be the same, i cant think it maked any difference but ur case is also valid where u r taking exposure as the base while for garp its collateral. Combined vol/base vol>1 for our 0 correlation case should be the conclusion i)collateral as base vol comb./vol coll=sqrt(vol coll^2+vol exp^2)/vol coll= sqrt(1+vol exp^2/vol coll^2)>1ii)exposure is base sqrt(vol coll^2+vol exp^2)/vol exp= sqrt(1+vol coll^2/vol exp^2)>1.
Thanks
Thank you

Gareth

New Member
Hi

I still don't understand the calc in the answer. Surely the worst case change in the value of the collateral should be compared with the worst case change in the value of the exposure (WITHOUT collateral) to show the former mitigates the latter.

Or am I being stupid?

Thanks