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# P2.T6.907. Collateral and the margin period of risk (Gregory Ch.6)

#### Nicole Seaman

Staff member
Subscriber
Learning objectives: Differentiate between a two-way and one-way CSA agreement and describe how collateral parameters can be linked to credit quality. Explain aspects of collateral including funding, rehypothecation and segregation. Explain how market risk, operational risk, and liquidity risk (including funding liquidity risk) can arise through collateralization.

Questions:

907.1. Acme Bank's position in a derivative contract has a current exposure of $100.0 million; i.e., the bank has a mark-to-market, unrealized gain of$100.0 million. The position's price volatility is 20.0%. Consider the following four scenarios:
• Scenario A. Acme leaves the exposure unhedged
• Scenario B. Acme hedges with $80.0 in collateral that itself has price volatility of 10.0% and is uncorrelated to the exposure • Scenario C. Acme hedges with$80.0 in collateral that itself has price volatility of 10.0% and has a negative correlation of -0.290 to the exposure
• Scenario D: Acme hedges with $70.0 in collateral that itself has price volatility of 10.0% and has a positive correlation of +0.420 to the exposure In which of the above scenarios is the DOLLAR volatility of Acme Bank's net position the highest? a. Scenario A; unhedged b. Scenario B;$80.0 million collateral with ρ = zero
c. Scenario C; $80.0 million collateral with ρ = -0.290 d. Scenario D;$70.0 million collateral with ρ = +0.420

907.2. Consider two counterparties who are about to enter into bilateral framework under an ISDA Master Agreement. They are currently negotiating the credit support annex (CSA) which will govern the terms of collateral posting. Each of the following is true EXCEPT which is inaccurate?

a. If the goal is to minimize funding costs, both parties prefer to avoid rehypothecation rights
b. With respect to VARIATION margin, both parties probably prefer rehypothecation rights; and probably will NOT require segregation
c. With respect to INITIAL margin, both parties probably are likely to insist on non-rehypothecation; and probably will require segregation
d. Whoever is the collateral poster (aka, collateral giver) prefers the method of Security Interest rather than the method of Title Transfer (which is preferred by the collateral receiver)

907.3. The margin period of risk (MRP) is a term that is specific to counterparty risk and refers to the effective time between a counterparty ceasing to post collateral and when the underlying transactions have been closed-out or replaced. Gregory explains that the MPR "is crucial since it defines the effective length of time without receiving collateral where any increase in exposure (including close-out costs) will remain collateralized." (Source: Jon Gregory, The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital, 3rd edition (West Sussex, UK: John Wiley & Sons, 2015))

Gregory further explains, "The MPR is the primary driver of the need for initial margin. Assuming only variation margin, the best-case reduction of counterparty risk can be shown to be approximately half the square root of the ratio of the maturity of the underlying portfolio to the MPR. For a five-year OTC derivatives portfolio, with a MPR of ten business days, this would lead to an approximate reduction of 0.5 × SQRT (5 * 250 /10) ≈ 5.6 times." (Source: Jon Gregory, The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital, 3rd edition (West Sussex, UK: John Wiley & Sons, 2015))

Put another way, where expected positive exposure (EPE) is the average exposure across all future time horizons, in this example where the MPR is presumed to be ten days, the ratio of uncollateralized EPE to collateralized EPE is about 5.6 such that the best-case reduction is about (1 - 1/5.6) or about 82.0%, which is still pretty good but shows how MPR yet implies some exposure.

If we assume 250 trading days, what is approximately the best-case reduction (in percentage terms) of a three-year OTC derivatives portfolio where the MPR is 23 days?

a. 44.2%
b. 65.0%
c. 77.9%
d. 93.0%

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#### nikic

##### Active Member
Will something like Q3 be tested at all in the exam? The formula to work out the answer is fully presented in the question.

On the flip side, the formula is super obscure if it weren't guided...in such a case will this even be tested if there's no guidance provided?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @nikic No, the MRP formula featured in 907.3 above would never realistically be tested (the LO verb is "Explain" not "Compute" or "Calculate"), which is precisely why the formula is included. But the calculation isn't really the point. Question 907.3 happens to be my designed question for the LO which is "Explain how market risk, operational risk, and liquidity risk (including funding liquidity risk) can arise through collateralization." Now, there are many (infinite?) ways to query, in addition to the question co-exists with other questions already linked to the chapter. But Gregory's heading is "6.6.2 Market risk and the margin period of risk," and the margin period of risk (MPR) is arguably the primary point is 6.6.2, so by providing the formula and asking for a calculation, I'm merely trying to give an application to the MPR concept. I've gotten some good questions about the MPR, it's yet another term that can be abstract, but I think parroting Gregory's numerical example is fine excuse to render the MPR a bit more concrete. That's how I think about it. Thanks,