In a repo-style securities financing transaction, the repo buyer or lender is exposed to the borrower’s default risk for the whole duration with a market contingent exposure, framed on a short window for default settlement. A margin period of risk (MPR) is a time period starting from the last date when margin is met to the date when the defaulting counterparty is closed out with completion of collateral asset disposal. MPR could cover a number of events or processes, including collateral valuation, margin calculation, margin call, valuation dispute and resolution, default notification and default grace period, and finally time to sell collateral to recover the lent principal and accrued interest. If the sales proceeds are not sufficient, the deficiency could be made a claim to the borrower’s estate, unless the repo is non-recourse. The lender’s exposure in a repo during the MPR is simply principal plus accrued and unpaid interest. Since the accrued and unpaid interest is usually margined at cash, repo exposure in the MPR is flat.

A flat exposure could apply to OTC derivatives as well. For an OTC netting, the mark-to-market of the derivatives could fluctuate as its underlying prices move. The derivatives exposure is formally set on the early termination date which could be days behind the point of default. The surviving counterparty, however, could have delta hedged against market factors following the default so that the derivative exposure remains a more manageable gamma exposure. For developing a collateral haircut model, what is generally assumed is a constant exposure during the MPR.

The primary driver of haircuts is asset volatility. Market liquidity risk is another significant one, as liquidation of the collateral assets might negatively impact the market, if the collateral portfolio is illiquid, large, or concentrated in certain asset sectors or classes. Market prices could be depressed, bid/ask spreads could widen, and some assets might have to be sold at a steep discount. This is particularly pronounced with private securitization and lower grade corporates, which trade infrequently and often rely on valuation services rather than actual market quotations. A haircut model therefore needs to capture liquidity risk, in addition to asset volatility.

In an idealized setting, we therefore consider a counterparty (or borrower) C’s default time at t, when the margin is last met, an MPR of u during which there is no margin posting, and the collateral assets are sold at time t+u instantaneously on the market, with a possible liquidation discount g.

Let us denote the collateral market value as B(t), exposure to the defaulting counterparty C as E(t). At time t, one share of the asset is margined properly, i.e., E(t) = (1-h)B(t), where h is a constant haircut, 1 >h ≥0. The margin agreement is assumed to have a zero minimum transfer amount. The lender would have a residual exposure (E(t) – B(t+u)(1-g))^{+}, where g is a constant, 1 > g ≥ 0. Exposure to C is assumed flat after t. We can write the loss function from holding the collateral as follows,

L(t + u) = E_{t}(1 – B_{t+u}/B_{t} (1 – g)/(1 – h))^{+} = (1 – g)B_{t}(1 – B_{t+u}/B_{t} (h – g)/(1 – g))^{+} —– (1)

Conditional on default happening at time t, the above determines a one-period loss distribution driven by asset price return B(t+u)/B(t). For repos, this loss function is slightly different from the lender’s ultimate loss which would be lessened due to a claim and recovery process. In the regulatory context, haircut is viewed as a mitigation to counterparty exposure and made independent of counterparty, so recovery from the defaulting party is not considered.

Let y = (1 – B_{t+u}/B_{t}) be the price decline. If g=0, Pr(y>h) equals to Pr(L(u)>0). There is no loss, if the price decline is less or equal to h. A first rupee loss will occur only if y > h. h thus provides a cushion before a loss is incurred. Given a target rating class’s default probability p, the first loss haircut can be written as

h_{p} = inf{h > 0:Pr(L(u) > 0) ≤ p} —– (2)

Let VaR_{q} denote the VaR of holding the asset, an amount which the price decline won’t exceed, given a confidence interval of q, say 99%. In light of the adoption of the expected shortfall (ES) in BASEL IV’s new market risk capital standard, we get a chance to define haircut as ES under the q-quantile,

h_{ES} = ES_{q} = E[y|y > VaR_{q}]

VaR_{q} = inf{y_{0} > 0 : Pr(y > y_{0}) ≤ 1 − q} —– (3)

Without the liquidity discount, h_{p} is the same as VaR_{q}. If haircuts are set to VaR_{q} or h_{ES}, the market risk capital for holding the asset for the given MPR, defined as a multiple of VaR or ES, is zero. This implies that we can define a haircut to meet a minimum economic capital (EC) requirement C_{0},

h_{EC} = inf{h ∈ R^{+}: EC[L|h] ≤ C_{0}} —– (4)

where EC is measured either as VaR or ES subtracted by expected loss (EL). For rating criteria employing EL based target per rating class, we could introduce one more definition of haircuts based on EL target L_{0},

h_{EL} = inf{h ∈ R^{+}: E[L|h] ≤ L_{0}} —– (5)

The expected loss target L_{0} can be set based on EL criteria of certain designated high credit rating, whether bank internal or external. With an external rating such as Moody’s, for example, a firm can set the haircut to a level such that the expected (cumulative) loss satisfies the expected loss tolerance L_{0} of some predetermined Moody’s rating target, e.g., ‘Aaa’ or ‘Aa1’. In (4) and (5), loss L’s holding period does not have to be an MPR. In fact, these two definitions apply to the general trading book credit risk capital approach where the standard horizon is one year with a 99.9% confidence interval for default risk.

Different from VaR_{q}, definitions h_{p}, h_{EL}, and h_{EC} are based on a loss distribution solely generated by collateral market risk exposure. As such, we no longer apply the usual wholesale credit risk terminology of probability of default (PD) and loss given default (LGD) to determine EL as product of PD and LGD. Here EL is directly computed from a loss distribution originated from market risk and the haircut intends to be wholesale counterparty independent. For real repo transactions where repo haircuts are known to be counterparty dependent, these definitions remain fit, when the loss distribution incorporates the counterparty credit quality.