# Transaction Exposure

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At a high level, under the GMRA, if one party has “Transaction Exposure” to its counterparty, the counterparty must make a “Margin Transfer” to the party with “Transaction Exposure” in order to extinguish that “Transaction Exposure”.

Conceptually, “Transaction Exposure” is best understood by asking the question “In relation to a particular Repurchase Transaction, if we terminated this Repurchase Transaction today, who would owe whom money?” The party that is OWED money has “Transaction Exposure” in an amount equal to the sum owed. That exposure is the risk that the party owing that money defaults and does not make payment when due, leaving the party which is owed the money to shoulder a loss. To that extent, “Transaction Exposure” is a measure of the extent to which an individual Repurchase Transaction is either under- or over- collateralised. It is worth noting that only one party can have “Transaction Exposure” in relation to a particular Repurchase Transaction at any one time. It is not possible for both parties to have “Transaction Exposure” in relation to the same transaction at the same time.

From a documentation point of view, the definition of “Transaction Exposure” is used to determine how much margin (if any) one of the parties is required to transfer to its counterparty.

The definitions of “Transaction Exposure” under the 1995 and 2000 Global Master Repurchase Agreements (“GMRAs”) are identical, but look quite different to that under the 2011 GMRA. In truth, however, the changes are not so great. Essentially, the real difference between the various forms of the GMRA is that the 1995 and 2000 GMRAs describe only “Method A” as a way of calculating “Transaction Exposure” (although it did not go by this name) whereas the 2011 GMRA provides the option between “Method A” and “Method B”, with the parties choosing which option they prefer. We will only consider “Transaction Exposure” as defined under the 2011 GMRA.

“Method A” is sometimes referred to as the “initial margin” approach. “Method B” is sometimes referred to as the “haircut” approach.

At a very high level, you can think of the “initial margin” approach as providing the answer to the question “If I wanted to borrow GBP 100, how much above this value would you require by way of collateral?” You can think of the “haircut” approach as providing the answer to the question “If I had GBP 100 worth of collateral, by how much would you discount my collateral and therefore, how much would you lend me off the back of that?” As you can see, they are both fundamentally driving at the same issue – making sure that there is a sufficient amount of collateral to ensure that market swings are covered – but they address this point via different routes.

Irrespective of whether “Method A” or “Method B” is selected, the underlying collateral must be valued in order to determine whether or not one party has “Transaction Exposure”. Both “Method A” and “Method B” use the definition of “Market Value” to do this.

The parties can choose whether they wish to adopt “Method A” or “Method B” within Annex 1, Paragraph 1(g) of the 2011 GMRA.

## Method A

“Method A” is sometimes referred to as the “initial margin” approach. This is because, essentially, the Seller pays a premium (in terms of the collateral that it has to transfer) over the cash which is paid over by the Buyer. The “initial margin” element of “Method A” is captured within the definition of the “Margin Ratio”.

Under “Method A”, “Transaction Exposure” (E) equals:

(R*MR) – MV

where:

“R” is the “Repurchase Price” (in other words, the amount of the ‘loan plus interest’ to be repaid);

“MR” is the applicable “Margin Ratio” (the “Margin Ratio” is equal to the “Market Value” of the Purchased Securities at the time when the Transaction was entered into divided by the Purchase Price (i.e., the amount of the ‘loan’). In other words, it is a number that represents how much excess collateral exists. The hope is that this number is greater than 1, otherwise there would be insufficient collateral to cover the ‘loan’; and

“MV” is the market value of Equivalent Securities at the time of calculation.

It is useful to consider this equation in a bit more detail. We will start by looking at the “(R*MR)” part of the equation first.

“R” is the “Repurchase Price” and represents the TOTAL AMOUNT of the ‘loan’ that needs to be repaid on a given day. It is important to bear in mind that “R” increases every day because interest accrues on the ‘loan’ every day.

“MR” is the applicable “Margin Ratio”. We discussed previously how this is typically a number GREATER THAN 1. As such, “MR” serves to INFLATE the value of “R” by the ‘collateral cushion’ that existed on execution of the relevant Repurchase Transaction.

Taking a step back, in essence “(R*MR)” asks the question “As of today, what is the correct amount of collateral that should be held in order to make sure that the then total amount of the ‘loan’ to be repaid is covered (to the same extent that it was at the outset of the transaction)?”

Let’s now turn to look at the “MV” portion of the “Transaction Exposure” equation under “Method A” (the market value of the securities which are held as collateral).

In deducting “MV” from “(R*MR)” we are effectively asking the question “do we have ACTUALLY have sufficient collateral coverage as of today?” If the result of this equation is:

- A positive number – it means that “(R*MR)” is GREATER THAN “MV”. In these circumstances, the outstanding amount of the loan (increased to include the ‘collateral cushion’) is GREATER THAN the market value of the collateral provided. As such, the
has “Transaction Exposure” and is entitled to receive a transfer of “Margin”.__BUYER__ - Zero – it means that “(R*MR)” is EQUAL TO “MV”. In other words, the outstanding amount of the loan (increased to include the ‘collateral cushion’) is EQUAL TO the market value of the collateral provided. In these circumstances,
has “Transaction Exposure” and no transfers of “Margin” will be made.__NEITHER PARTY__ - A negative number – it means that “(R*MR)” is LESS THAN “MV”). In these circumstances, the outstanding amount of the loan (increased to include the ‘collateral cushion’) is LESS THAN the market value of the collateral provided. As such, the
has “Transaction Exposure” and is entitled to a ‘return’ of “Margin”.__SELLER__

### A more detailed look at “Method A”

Let’s look at the fully expanded equation for “Transaction Exposure”. Hopefully, this will give us a more detailed understanding of how it works.

Let’s start with the fact that we know that “Transaction Exposure” (“E”) under “Method A” is:

E = (R*MR) – MV.

However, we also know that “R” (the “Repurchase Price”) is equal to “the Purchase Price PLUS the Price Differential). Therefore, “Method A” can be restated as:

E = ((PP + PD_{t})*MR) – MV

We also know that the “Price Differential” is equal to the “Pricing Rate” multiplied by the Purchase Price (calculated on a daily basis). In other words, the “Price Differential” equals PR*PP*(n/360 (or 365)). Therefore, “Method A” can be restated further as:

Finally, we know that the “Margin Ratio” is equal to the “Market Value” of the securities on execution of the Repurchase Transaction divided by the Purchase Price. In other words, the “Margin Ratio” is equal to:

Therefore, “Method A” can be restated again as:

Whilst it may look complicated, most of the inputs into this equation are known already, so it is really not that hard to work out. The thing to note at this stage is that if the result of this equation produces:

- A number GREATER than zero – then this means that the current market value of the securities is less than is needed in order to provide sufficient coverage for the ‘loan’. In these circumstances, the Buyer has exposure towards the Seller (because the ‘loan’ is under collateralised).
- A number LESS than zero – then this means that the current market value of the securities is greater than is needed in order to provide sufficient coverage for the ‘loan’. In these circumstances, the Seller has exposure towards the Buyer (because the loan is over-collateralised).

Of course, the AMOUNT of that exposure is whatever “E” is.

### “Method A” – a worked (and simplified) example

Consider the following scenario:

- On day 1
- A Seller has a need for GBP 100.

- The Seller has GBP denominated bonds worth GBP 105 to post as ‘collateral’.

- The Buyer agrees to ‘lend’ the Seller GBP 100 against that collateral and will charge interest of 2% per annum.

- On day 10, the value of the bonds has fallen to GBP 103.

What is the “Transaction Exposure” under “Method A” on day 10?

We will recall that the full equation for working out “Transaction Exposure” under “Method A” is:

The Seller had a need for GBP 100 – this was the “Purchase Price”. Substituting this into the equation gives us:

The Seller had GBP denominated bonds worth GBP 105 to post as ‘collateral’. This is the “Market Value” of the bonds at execution of the Repurchase Transaction (i.e. when t=0). Substituting this into the equation gives us:

The Buyer charged an ‘interest rate’ of 2% per annum. This is the “Pricing Rate”. Substituting this into the equation gives us:

As this is a Sterling denominated transaction, the day count fraction would be “365” rather than “360”. Substituting this into the equation give us:

We know that we need to calculate “Transaction Exposure” on day 10. Substituting this into the equation gives us:

Finally, we know that the market value of the securities on day 10 has fallen to GBP 103. Substituting this into the equation gives us:

We can now simply the equation:

As this number is GREATER than zero, it means that the Buyer has exposure towards the Seller. This makes sense as the current market value of the securities has fallen and is less than is needed in order to provide sufficient coverage for the ‘loan’.

Taking a step back, this result should make intuitive sense. The value of the collateral has fallen by GBP 2 in the 10-day window. In the meantime, a little bit of interest has also accrued on the ‘loan’ of GBP 100. When you add these two elements together, it means that the Buyer is exposed to the tune of about GBP 2.06.

## Method B

Under “Method B”, “Transaction Exposure” is:

E = R – V

where:

“R” is the “Repurchase Price” at the time of calculation (in other words, the amount of the ‘loan’ plus the interest that has accrued to date); and

“V” is the “Adjusted Value” of Equivalent Securities at such time, being:

V = (MV(1-H))

where:

“MV” is the Market Value of Equivalent Securities; and

“H” is the ‘haircut’ agreed for those securities.

Bringing these two elements together, “Transaction Exposure” under “Method B” is:

E = R – (MV(1-H)).

We can expand the brackets, which results in “Transaction Exposure” under “Method B” being equal to:

E = R – (MV – (MV*H))

Considering this equation, from a high-level point of view, we are looking, first, at the amount of the ‘loan plus accrued interest’. This is “R” – the “Repurchase Price”. We then deduct from this amount the haircutted value of collateral held against the ‘loan’. In doing so, we are effectively asking “does the haircutted value of the collateral exceed the current amount of the loan plus accrued interest?”

If E is GREATER than zero, then the ‘haircutted value of the collateral’ is less than the value of the ‘loan plus accrued interest’ and the Buyer (in other words, the lender) has exposure to the Seller (in other words, the borrower). Why? Because the amount to be repaid (“R”) EXCEEDS the haircutted value of the collateral held.

Conversely, if E is LESS than zero, then the ‘haircutted value of the collateral’ is greater than the value of the ‘loan plus accrued interest’ and the Seller (in other words, the borrower) has exposure to the Buyer (in other words, the borrower). Why? Because the haircutted value of the collateral held EXCEEDS the amount to be repaid.

### “Method B” – a worked (and simplified) example

Let’s consider a worked example of how “Method B” operates. For comparison purposes, we will deliberately try and stick as closely as possible to the factual scenario we looked at in relation to “Method A”:

- On day 1
- A Seller has a need for GBP 100.

- The Seller has GBP denominated bonds worth GBP 105 to post as ‘collateral’.

- The Seller and the Buyer agree to levy a 5% “haircut” on the value of the bonds.

- On that basis, the Buyer agrees to ‘lend’ the Seller 105*(1-5%) = GBP 99.75 (note that this is slightly less than the GBP 100 which the Buyer agreed to ‘lend’ to the Seller under “Method A”).

- The Buyer will charge interest interest of 2% per annum.

- On day 10, the value of the bonds has fallen to GBP 103.

What is the “Transaction Exposure” under “Method B” on day 10?

As with calculating “Transaction Exposure” under “Method A”, we are really only required to submit a series of already-known values into the equation for “Method B”, which is:

E = R – (MV – (MV*H))

Remember that “R” – the “Repurchase Price” at time “t” equals:

R_{t} = PP + PD_{t}

In other words, it is the sum of the “Purchase Price” and the “Price Differential” (as of the date of calculation). Therefore, “Transaction Exposure” under “Method B” can be restated as:

E = (PP + PD_{t}) – (MV – (MV*H))

We have also seen that the “Price Differential” is equal to:

PR*PP*(n/360 [or 365])

where:

“PR” is the “Pricing Rate” (in other words, the interest rate being charged on the money being ‘loaned’);

“PP” is the “Purchase Price” (in other words, the original the amount of the ‘loan’); and

“n” is the number of days from (and including) the Purchase Date to (but excluding) the date upon which the Price Differential is being calculated (or the Repurchase Date if this occurs earlier (i.e. the date upon which the ‘loan’ is repaid).

As such, “Transaction Exposure” under “Method B” can be restated again as being:

We know that the Purchase Price (in other words, the amount of the ‘loan’) is GBP 99.75. Substituting this into the equation gives us:

The “Pricing Rate” (in other words, the interest under the ‘loan’) is 2%. Substituting this into the equation gives us:

The Repurchase Transaction is Sterling-denominated, so the relevant day count fraction is “365”. Substituting this into the equation gives us:

The agreed haircut is 5%. Substituting this into the equation gives us:

We are performing the calculation on day 10. Substituting this into the equation gives us:

On day 10, the value of the collateral has fallen to GBP 103. Substituting this into the equation gives us:

We can now simply the equation:

We can see that “E” is GREATER than zero. This means that the “Buyer” (in other words, the lender) has exposure to the “Seller” (in other words, the borrower). More specifically, it means that the ‘haircutted value of the collateral’ is less than the value of the ‘loan plus accrued interest’.

## The difference between “Method A” and “Method B”

What is the difference between “Method A” and “Method B”?

At a very high level, you can think of the “initial margin” approach (in other words, “Method A”), as providing the answer to the question “If I wanted to borrow GBP 100, how much ABOVE this value would you require by way of collateral?” We also discussed how you can think of the “haircut” approach (in other words, “Method B”) as providing the answer to the question “If I had GBP 100 worth of collateral, how much would you lend me off the back of that?” It is clear that both “Methods” are trying to ensure that there is sufficient collateral to cover the ‘loan’ (taking into account market swings in the value of the collateral) but they adopt different approaches to achieving this objective.

Considering the matter in slightly closer detail, “Method A” looks at (a) the value of the ‘loan’ that has been advanced PLUS (b) the amount of the collateral cushion which was agreed at the outset of the Repurchase Transaction and asks whether this is greater than the market value of the collateral that has been taken as security for that ‘loan’.

In contrast, “Method B” looks at the value of the ‘loan plus interest’ to be repaid and asks whether this is greater than the haircutted value of the underlying securities taken as collateral. As previously mentioned, in many ways, it is looking at exactly the same issue – just from the opposite end of the lens.

Mathematically, the “initial margin” approach of “Method A” is a percentage of the Purchase Price, whereas the “haircut” approach of “Method B” is a percentage of the market value of the collateral. As such the arithmetic associated with the two approaches is slightly different.

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