Collateral Debt Obligations. Thought of the Day 111.0

A CDO is a general term that describes securities backed by a pool of fixed-income assets. These assets can be bank loans (CLOs), bonds (CBOs), residential mortgages (residential- mortgage–backed securities, or RMBSs), and many others. A CDO is a subset of asset- backed securities (ABS), which is a general term for a security backed by assets such as mortgages, credit card receivables, auto loans, or other debt.

To create a CDO, a bank or other entity transfers the underlying assets (“the collateral”) to a special-purpose vehicle (SPV) that is a separate legal entity from the issuer. The SPV then issues securities backed with cash flows generated by assets in the collateral pool. This general process is called securitization. The securities are separated into tranches, which differ primarily in the priority of their rights to the cash flows coming from the asset pool. The senior tranche has first priority, the mezzanine second, and the equity third. Allocation of cash flows to specific securities is called a “waterfall”. A waterfall is specified in the CDO’s indenture and governs both principal and interest payments.

1: If coverage tests are not met, and to the extent not corrected with principal proceeds, the remaining interest proceeds will be used to redeem the most senior notes to bring the structure back into compliance with the coverage tests. Interest on the mezzanine securities may be deferred and compounded if cash flow is not available to pay current interest due.

One may observe that the creation of a CDO is a complex and costly process. Professionals such as bankers, lawyers, rating agencies, accountants, trustees, fund managers, and insurers all charge considerable fees to create and manage a CDO. In other words, the cash coming from the collateral is greater than the sum of the cash paid to all security holders. Professional fees to create and manage the CDO make up the difference.

CDOs are designed to offer asset exposure precisely tailored to the risk that investors desire, and they provide liquidity because they trade daily on the secondary market. This liquidity enables, for example, a finance minister from the Chinese government to gain exposure to the U.S. mortgage market and to buy or sell that exposure at will. However, because CDOs are more complex securities than corporate bonds, they are designed to pay slightly higher interest rates than correspondingly rated corporate bonds.

CDOs enable a bank that specializes in making loans to homeowners to make more loans than its capital would otherwise allow, because the bank can sell its loans to a third party. The bank can therefore originate more loans and take in more origination fees. As a result, consumers have more access to capital, banks can make more loans, and investors a world away can not only access the consumer loan market but also invest with precisely the level of risk they desire.

1: To the extent not paid by interest proceeds.

2: To the extent senior note coverage tests are met and to the extent not already paid by interest proceeds. If coverage tests are not met, the remaining principal proceeds will be used to redeem the most senior notes to bring the structure back into compliance with the coverage tests. Interest on the mezzanine securities may be deferred and compounded if cash flow is not available to pay current interest due.

The Structured Credit Handbook provides an explanation of investors’ nearly insatiable appetite for CDOs:

Demand for [fixed income] assets is heavily bifurcated, with the demand concentrated at the two ends of the safety spectrum . . . Prior to the securitization boom, the universe of fixed-income instruments issued tended to cluster around the BBB rating, offering neither complete safety nor sizzling returns. For example, the number of AA and AAA-rated companies is quite small, as is debt issuance of companies rated B or lower. Structured credit technology has evolved essentially in order to match investors’ demands with the available profile of fixed-income assets. By issuing CDOs from portfolios of bonds or loans rated A, BBB, or BB, financial intermediaries can create a larger pool of AAA-rated securities and a small unrated or low-rated bucket where almost all the risk is concentrated.

CDOs have been around for more than twenty years, but their popularity skyrocketed during the late 1990s. CDO issuance nearly doubled in 2005 and then again in 2006, when it topped $500 billion for the first time. “Structured finance” groups at large investment banks (the division responsible for issuing and managing CDOs) became one of the fastest-growing areas on Wall Street. These divisions, along with the investment banking trading desks that made markets in CDOs, contributed to highly successful results for the banking sector during the 2003–2007 boom. Many CDOs became quite liquid because of their size, investor breadth, and rating agency coverage.

Rating agencies helped bring liquidity to the CDO market. They analyzed each tranche of a CDO and assigned ratings accordingly. Equity tranches were often unrated. The rating agencies had limited manpower and needed to gauge the risk on literally thousands of new CDO securities. The agencies also specialized in using historical models to predict risk. Although CDOs had been around for a long time, they did not exist in a significant number until recently. Historical models therefore couldn’t possibly capture the full picture. Still, the underlying collateral could be assessed with a strong degree of confidence. After all, banks have been making home loans for hundreds of years. The rating agencies simply had to allocate risk to the appropriate tranche and understand how the loans in the collateral base were correlated with each other – an easy task in theory perhaps, but not in practice.

The most difficult part of valuing a CDO tranche is determining correlation. If loans are uncorrelated, defaults will occur evenly over time and asset diversification can solve most problems. With low correlation, an AAA-rated senior tranche should be safe and the interest rate attached to this tranche should be close to the rate for AAA-rated corporate bonds. High correlation, however, creates nondiversifiable risk, in which case the senior tranche has a reasonable likelihood of becoming impaired. Correlation does not affect the price of the CDO in total because the expected value of each individual loan remains the same. Correlation does, however, affect the relative price of each tranche: Any increase in the yield of a senior tranche (to compensate for additional correlation) will be offset by a decrease in the yield of the junior tranches.

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Haircuts and Collaterals.

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{y₀ > 0 : Pr(y > y₀) ≤ 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 C₀,

h_EC = inf{h ∈ R⁺: EC[L|h] ≤ C₀} —– (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 L₀,

h_EL = inf{h ∈ R⁺: E[L|h] ≤ L₀} —– (5)

The expected loss target L₀ 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 L₀ 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.