COMMON STRUCTURED PRODUCTS

• The following hierarchy of structured products with respect to complexity of structure corresponds roughly to their historical development.
• Covered bonds are issued mainly by European banks, mainly in Germany and Denmark. In this structure, mortgage loans are aggregated into a cover pool, by which a bond issue is secured. The cover pool stays on the balance sheet of the bank, rather than being sold off-balance-sheet, and therefore, covered bonds are not considered full fledged securitizations. Bond owners have higher priority than general creditors of the bank in case of default. Also, the principal and interest on the secured bond issue are paid out of the general cash flows of the issuer, rather than out of the cash flows generated by the cover pool.
• Mortgage pass-through securities are true off-balance sheet securitizations. Investors receive cash flows based entirely on the performance of the pool less associated fees paid to the servicer. Since most of them are agency MBS, issued under an explicit or implicit U.S. federal guarantee of the performance of the underlying loans, so there is little default risk.

The main risk is prepayment risk.

• Collateralized mortgage obligations (CMOs) are MBSs that were developed to deal with prepayment risk, and also as a way to create both longer- and shorter-term bonds out of a pool of mortgage loans. Such loans amortize over time, creating cash flow streams that diminish over time. CMOs are divided into tranches, that are paid down on a specified schedule. The simplest structure is sequential pay, in which the tranches are ordered, with “Class A” receiving all principal repayments from the loan until it is paid off and retired, then “Class B”, and so on. The higher tranches in the sequence have less prepayment risk, while the lower ones tranches bear more prepayment risk.
• Structured credit products introduce one more innovation: the sequential distribution of credit losses. Structured products are backed by credit risky loans or bonds. Tranching is done in a way so that different tranches have different degrees of credit risk. As losses occur, the tranches are gradually written down. Junior tranches are written down first, and more senior tranches only begin to bear credit losses once the junior tranches have been written down to zero.

 STRUCTURED PRODUCTS AND SPV

• A structured product can be thought of as a “robot” corporate entity with a balance sheet, but no other business.
• Structured products are usually set up as special purpose entities (SPE) or vehicles (SPV), also known as a trust. This arrangement is intended to legally separate the assets and liabilities of the structured product from those of the original creditors and of the company that manages the payments. That is, it makes the SPE bankruptcy remote. This permits investors to focus on the credit quality of the loans themselves rather than that of the original lenders in assessing the credit quality of the securitization. The underlying debt instruments in the SPV are the robot entity’s assets, and the structured credit products built on it are its liabilities.

TYPES OF SECURITIZATION

• Depending on the type of the underlying assets, securitizations are of following types:
  • Generically called asset-backed securities (ABS) or mortgage-backed securities (MBS), or collateralized loan obligations (CLOs).
  • Securitizations that repackage other securitizations are called collateralized debt obligations (CDOs, issuing bonds against a collateral pool consisting of ABS, MBS, or CLOs), collateralized mortgage obligations (CMOs), or collateralized bond obligations (CBOs).
  • Third-level securitizations, in which the collateral pool consists of CDO liabilities, which themselves consist of bonds backed by a collateral pool, called CDO-squareds.

CLASSIFICATION OF STRUCTURED PRODUCTS

• There are several other dimensions along which we can classify structured credit products:
  • Underlying asset classes -The collateral is typically composed of residential or commercial real estate loans, consumer debt such as credit cards balances and auto and student loans, and corporate bonds. But many other types of debt, and even nondebt assets such as recurring fee income, can also be packaged into securitizations.
  • Type of structure – A key dimension is tranching, the number and size of the bonds carved out of the liability side of the securitization. Another is how many levels of securitization are involved, that is, whether the collateral pool consists entirely of loans or liabilities of other securitizations.
  • How much the pool changes over time – Each type of pool has its own risk management challenges
    • Static pools – are amortizing pools in which a fixed set of loans is placed in the trust. As the loans amortize, are repaid, or default, the deal, and the bonds it issues, gradually wind down. Static pools are common for such asset types as auto loans and residential mortgages, which generally themselves have a fixed and relatively long term at origination but pay down over time.
    • Revolving pools – specify an overall level of assets that is to be maintained during a revolving period. As underlying loans are repaid, the size of the pool is maintained by introducing additional loans from the balance sheet of the originator. Revolving pools are common for bonds backed by credit card debt. Once the revolving period ends, the loan pool becomes fixed, and the deal winds down gradually as debts are repaid or become delinquent and are charged off.
    • Managed pools – are pools in which the manager of the structured product has discretion to remove individual loans from the pool, sell them, and replace them
    • with others. Managed pools have typically been seen in CLOs.

TRANCHING AND DISTRIBUTION OF CREDIT LOSSES

• Tranching refers to how the liabilities of the securitization SPV are split into a capital structure. Each type of bond within the capital structure has its own coupon or spread, and depending on its place in the capital structure, its own priority or seniority with respect to losses.
• There may be many dozen, or only a small handful of tranches in a securitization, but they can be categorized into three groups:
  • Equity Tranche: It typically receives no fixed coupon payment, but is fully exposed to defaults in the collateral pool. It is entitled to the residual cash flows after all the other obligations of the SPE have been satisfied. It is a “thin” tranche i.e. it is the smallest part of the capital structure.
  • Mezzanine Tranche (or Junior debt) is typically also thin. This earns a relatively high fixed coupon or spread, but if the equity tranche is exhausted by defaults in the collateral pool, it is next in line to suffer default losses.
  • Senior Tranche earns a relatively low fixed coupon or spread, but is protected by both the equity and mezzanine tranches from default losses. Senior bonds are typically the bulk of the liabilities in a securitization.

CAPITAL STRUCTURE AND CREDIT LOSSES

• The capital structure is sometimes called the “capital stack,” with senior bonds at the top of the stack. The boundary between two tranches, expressed as a percentage of the total of the liabilities, is called the attachment point of the more senior tranche and detachment point of the more junior tranche. The equity tranche only has a detachment point, and the most senior only has an attachment point.
• The part of the capital structure below a bond tranche is called its subordination or credit enhancement. It is the fraction of the collateral pool that must be lost before the bond takes any loss. Credit protection to one class implies shifting risk to other parts of capital structure.
• Credit enhancement can be internal or external credit enhancement. External credit enhancement is like insurance purchased from a third party.
• Two main techniques of internal credit enhancements are overcollateralization (hard credit enhancement) and excess spread (soft credit enhancement).

WATERFALL STRUCTURE

• The waterfall refers to the rules about how the cash flows from the collateral are distributed to the various securities in the capital structure. The term “waterfall” arose because generally the capital structure is paid in sequence, “top down”, with the senior debt receiving all of its promised payments before any lower tranche receives any money.
• A typical structured credit product begins life with a certain amount of hard overcollateralization, since part of the capital structure is an equity note, and the debt tranches are less than 100 percent of the deal. Soft overcollateralization mechanisms may begin to pay down the senior debt over time with part of the collateral pool interest, or divert part of it into a reserve that provides additional credit enhancement for the senior tranches. That way, additional credit enhancement is built up at the beginning of the life of the product, when collateral cash flows are strongest. Typically, there is a detailed set of overcollateralization triggers that state the conditions under which excess spread is to be diverted into various reserves.

WATERFALL STRUCTURE – EXAMPLE FROM SCHWESER

• Consider a CLO, the underlying assets of which are 1000 identical leveraged loans, with a par value of $1,000,000 each, and priced at par.
• The loans are floating rate obligations that pay a fixed spread of 3%, reset annually. Assume that there are no upfront, management, or trustee fees. :_ INFLOW
• The senior, junior, and equity tranches are 80%, 15%, and 5% of the pool, respectively.
• The spreads on the senior and mezzanine tranches are 1% and 5%. :- OUTFLOW
• There is one overcollateralization trigger where the equity holders are entitled to a maximum of $ 15 million and any excess is diverted to the excess trust account.:
• The previous information is summarized in the following tables

Inflows

8% of $1B = $80M

Composition

Senior (A) :

• 80% of $1B = $800M
• Outflow on Senior Tranche = 6% of $800M = $48M

Mezzanine (B) :

• 15% of $1B = $150M
• Outflow on Mezzanine Tranche = 10% of $150M = $15M

Total Outflow on Senior + Mezzanine

= $48M + $15M = $63M

Net Inflows

= $80M – $63M
= $17M

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Allocation

Out of this $17M, equity tranche receives $15M.

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Excess

= $17M – $15M = $2M
→ Trust Account (Overcollateralization)

• Now in the same example, if we change the default rate to 4%

Loss Due to Default

4% of $80M = $3.2M

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Inflows from Loans

$80M – $3.2M = $76.8M

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Outflows

• Senior: $48M
• Mezzanine: $15M
  Total = $63M

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Remaining

$76.8M – $63M = $13.8M

The entire $13.8M goes to Equity.
OC = 0

KEY SECURITIZATION PARTICIPANTS

• Loan Originator – The loan originator is the original lender who creates the debt obligations in the collateral pool. This is often a bank, for example, when the underlying collateral consists of bank loans or credit card receivables. But it can also be a specialty finance company or mortgage lender. If most of the loans have been originated by a single intermediary, the originator may be called the sponsor or seller.
• Underwriter – The underwriter or arranger is often, but not always, a large financial intermediary. Typically, the underwriter aggregates the underlying loans, designs the securitization structure and markets the liabilities. Hence, the underwriter is also the issuer of the securities. A somewhat technical legal term, depositor, is also used to describe the issuer. 

During this aggregation phase, the underwriter bears warehousing risk, the risk that the deal will not be completed and the value of the accumulated collateral still on its balance sheet falls. This risk became important in the early days of the subprime crisis, as the market grew aware of the volumes of “hung loans” on intermediaries’ balance sheets. Underwriting is a “classical” broker-dealer function, i.e., to hold the finished securitization liabilities until investors purchase them, and to take the risk that not all the securities can be sold at par.

• Rating Agencies –  The rating agencies are engaged to assess the credit quality of the liabilities and assign ratings to them. An important part of this process is determining attachment points and credit subordination. In contrast to corporate bonds, in which rating agencies opine on creditworthiness, but have little influence over it, ratings of securitizations involve the agencies in decisions about structure.

Rating agencies are typically compensated by issuers, creating a potential conflict of interest between their desire to gain rating assignments and expand their business, and their duty to provide an objective assessment.

The potential conflict is exacerbated by the rating agencies’ inherent role in determining the structure. The rating agency may tell the issuer how much enhancement is required, given the composition of the pool and other features of the deal, to gain an investment-grade rating for the top of the capital stack. These senior-most bonds have lower spreads and a wider investor audience, and are therefore uniquely important in the economics of securitizations.

The rating agency has an incentive to require less enhancement, permitting the issuer to create a larger set of investment grade tranches. Investors can cope with the potential conflict by either demanding a wider spread or carrying out their own credit review of the deal.

• Managers – Managers are responsible for actively managing loan pools.

Potential conflict of interest for managers: Investors delegate the task of monitoring the credit quality of pools to the managers. The manager naturally would like to minimize their effort to continually monitor the credit quality of the collateral. Hence, there is a need for  mechanisms to align incentives. One such mechanism that has been applied to managed as well as static pools is to require the manager to own a first-loss portion of the deal. This mechanism has been enshrined in the Dodd-Frank Act changes to financial regulatory policy. Such conflicts can be more severe for asset types, especially mortgages, in which servicing is not necessarily carried out by the loan originator. Third-party servicing also adds an entity whose soundness must be verified by investors in the bonds.

• Servicers – The servicer collects principal and interest from the loans in the collateral pool and disburses principal and interest to the liability holders, as well as fees to the underwriter and itself. The servicer may be called upon to make advances to the securitization liabilities if loans in the trust are in arrears.

Potential conflict of interest for servicer: If the servicer is tasked to managing underlying loans in distress and to determine whether to extend or refinance the loan, or to foreclose, the servicers is then involved in conflict of interest between itself and bondholders, or between different classes of bondholders.

• Trustee and Custodian – They are tasked with keeping records, verifying documentation, and moving cash flows among deal accounts and paying noteholders.

THREE TIERED SECURITIZATION STRUCTURE

• EXAMPLE FROM SCHWESER
• The original loan pool includes 100 loans with $ 1 million par value and a fixed coupon of 8%. The number of surviving loans is 90. The par for the senior and junior tranches is 75% and 20%, respectively. The equity investors contributed the remaining 5%. There are two defaults with recovery rate of 40% recovered at the end of the period. The value of the trust account at the beginning of the period is $16 million earning 4% per annum.

Total Pool Size (Loans)

= 100 × $1M
= $100M (Initially)

Current Pool Size

= 90 × $1M
= $90M

Composition

• Senior: $75M
• Junior: $20M
• Equity: $5M

EXAMPLE FROM SCHWESER – CONTINUED

Inflows

1️⃣ Coupon Received from Pool
= 8% of $90M = $7.2M

2️⃣ Defaulted Loans Recovery Amount
= 40% of ($1M × 2) = $0.8M

3️⃣ Non-Defaulting Loans Redemption Value
= 90 × $1M = $90M

4️⃣ Trust Account at the End of Period
= $16M + 4% of $16M = $16.64M

Total Inflows

= (1) + (2) + (3) + (4)
= $114.64M

EXAMPLE FROM SCHWESER – CONTINUED

Outflows

1️⃣ Senior Tranche – $75M
2️⃣ Junior Tranche – $20M

Equity Receives:
$114.64M – ($75M + $20M) = $19.64M

SIMULATION APPROACH

• The simulation process can be summarized in these steps:
  1. Estimate parameters – First we need to determine the parameters for the valuation, in particular, the default probabilities or default distribution of each individual security in the collateral pool, and the correlation used to tie the individual default distributions together.
  2. Generate default time simulations –  Using the estimated parameters and the copula approach, we simulate the default times of each security (here, the underlying loans) in the collateral pool. With the default times in hand, we can next identify, for each simulation thread and each security, whether it defaults within the life of the securitization, and if so, in what period.
  3. Compute the credit losses –  The default times can be used to generate a sequence of cash flows from the collateral pool in each period, for each simulation thread. This part of the procedure is the same as the cash flow analysis of the previous section. The difference is only that in the simulation approach, the number of defaults each period is dictated by the results of the simulation rather than assumed. The securitization capital structure and waterfall allocate the cash flows over time, for each simulation thread, to the securitization tranches. For each simulation thread, the credit loss, if any, to each liability and the residual cash flow, if any, to the equity tranche can then be computed. This gives us the entire distribution of losses for the bonds and of IRRs for the equity. The distributions can be used to compute credit statistics such as credit VaR for each tranche.

IMPACT OF PROBABILITY OF DEFAULT AND DEFAULT CORRELATION

• For a given correlation, an increase in default rate will be detrimental to the value of all  tranches. Increases in the default rate increase bond losses and decrease the equity IRR for all correlation assumptions.
• Increases in correlation can have a very different effect, depending on the level of defaults. At low default rates, the impact of an increase in correlation is relatively low. But when default rates are relatively high, an increase in correlation can materially increase the IRR of the equity tranche, but also increase the losses to the senior bond tranche. In other words, the equity benefits from high correlation, while the senior bond is hurt by it.
• The effect on the mezzanine bond is more complicated. At low default rates, an increase in correlation increases losses on the mezzanine bond, but decreases losses for high default rates. In other words, the mezzanine bond behaves more like a senior bond at low default rates, when it is unlikely that losses will approach its attachment point and the bond will be broken, and behaves more like the equity tranche when default rates are high and a breach of the attachment point appears likelier.

Equity Tranche Analysis

Case I: If ρ = 0

• Default probability (p) = 4%
• Number of loans (n) = 1000
• Expected number of defaults = 4% of 1000 = 40

Since defaults are independent:
→ Some loans default, others don’t.
→ Expected value of the equity tranche is lower.

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Case II: If ρ → 1

• Defaults are perfectly correlated.
  → Either no loss or total loss.
  → Expected value of the equity tranche is higher in this case.

Conclusion:
Overall, higher correlation is good for the equity tranche.

Senior Tranche Analysis

Case 1: ρ = 0
→ Almost certain or high chance of no impairment.

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Case 2: ρ = 1

→ No impairment when no defaults take place.
→ Guaranteed impairment when all loans default.
→ Overall, high correlation is bad for the senior tranche.

CONVEXITY

• At low correlations, the equity value is substantially positively convex in default rates. That is, the equity tranche loses value rapidly as default rates increase from a low level. But as default rates increase, the responsiveness of the equity value to further increases in the default rate drops off. In other words, you can’t beat a dead horse: If you are long the equity tranche, once you’ve lost most of your investment due to increases in default rates, you will lose a bit less from the next increase in default rates.
• For low correlations, the senior bond tranche has negative convexity in default rates; its losses accelerate as defaults rise. The mezzanine tranche, again, is ambiguous. It has negative convexity for low default rates, but is positively convex for high default rates. At high correlations, all the tranches are less convex; that is, they respond more nearly linearly to changes in default rates.

IMPACT ON CREDIT VaR OF THE TRANCHES

• Equity tranche –  The equity VaR actually falls for higher default probabilities and correlations, because the expected loss is so high at those parameter levels. Although the mean values of the equity tranche increase with correlation, so also does its risk.
• Mezzanine bond – The junior bond again shows risk characteristics similar to those of the equity at higher default rates and correlation and to those of the senior bond for lower ones.
• Senior bond –  Correlation is bad for the senior bond. At high correlations, the 99 percent Credit VaR of the senior bond is very high, while if defaults are uncorrelated, the bond is virtually risk-free even at high default probabilities.

IMPACT ON VALUE AND CREDIT VaR OF THE TRANCHES

IMPACT OF CORRELATIONS AND PD SUMMARIZED

MEASURING DEFAULT SENSITIVITIES

• The “default01” measures the impact of an increase of 1 basis point in the default probability. It is analogous to the DV01 and the spread01. To compute the default01, the default probability is increased and decreased 10 bps and each tranche is revalued at these new values of π. This requires repeating, twice, the entire valuation procedure from the point onward at which simulated default times are generated

• The default01 is computed for each combination of π and ρ. Each default01 is expressed as a positive number and expresses the decline in value or increase in loss resulting from a 1 basis point rise in default probability. For all tranches, in all cases, default01 is positive, as expected, regardless of the initial value of π and ρ, since equity and bond values decrease monotonically as the default probability rises. The default01 sensitivity converges to zero for all the tranches for very high default rates.
• The default01 varies most as a function of default probability when correlation is low. With ρ=0, the default01 changes sharply in a certain range of default probabilities, and then tapers off as the tranche losses become very large. The differences in the patterns for the different tranches are related to the locations of their attachment points. For each tranche, the range of greatest sensitivity to an increase in defaults, that is, the largest magnitude default01, begins at a default rate that brings losses in the collateral pool near that tranche’s attachment point.
• The above point implies that the peak default01 is at a default probability of zero for the equity tranche, and occurs at a lower default rate for the mezzanine than for the senior tranche because it has a lower attachment point. This introduces additional risk when structured credit exposures are put on in a low correlation environment, or correlation is underestimated. Underestimation of default correlation in structured credit products was an important factor in the origins of the subprime crisis.

MEASURING DEFAULT SENSITIVITIES

RISKS FOR STRUCUTURED PRODUCTS

• Based on an analysis of risk in the securitization liabilities, a few generalizations can be made about the risks of structured credit products:
  1. Systematic risk – Structured credit products can have a great deal of systematic risk, even when the collateral pools are well-diversified. The systematic risk shows up in the equity values and bond losses when default correlation is high. High default correlation is one way of expressing high systematic risk, since it means that there is a low but material probability of a state of the world in which an unusually large number of defaults occurs.  Even if the collateral is well-diversified, the senior bond has a risk of loss, and potentially a large loss, if correlation is high. While its expected loss may be lower than that of the underlying loan pool, the tail of the loss and the Credit VaR are high. In other words, they are very exposed to systematic risk. The degree of exposure depends heavily on the credit quality of the underlying collateral and the credit enhancement.
  2. Tranche thinness – Another way in which the senior bond’s exposure to systematic risk is revealed is in the declining difference between the senior bond’s Credit VaRs at the 99 and 95 percent confidence levels as default probabilities rise for high default correlations. For the mezzanine bond, the difference between Credit VaR at the 99 and 95 percent confidence levels is small for most values of π and ρ. The reason is that tranche is relatively thin. The consequence of tranche thinness is that, conditional on the tranche suffering a loss at all, the size of the loss is likely to be large.
  3. Granularity can significantly diminish securitization risks. In the last chapter, it was discussed that a portfolio of large loans has greater risk than a portfolio with equal par value of smaller loans, each of which has the same default probability, recovery rate, and default correlation to other loans. Similarly, “lumpy” pools of collateral have greater risk of extreme outliers than granular ones. A securitization with a more granular collateral pool can have a somewhat larger senior tranche with no increase in Credit VaR. A good example of securitizations that are not typically granular are the many CMBS deals in which the pool consists of relative few mortgage loans on large properties, or so-called fusion deals in which a fairly granular pool of smaller loans is combined with a few large loans. When the asset pool is not granular, and/ or correlation is high, the securitization is said to have high concentration risk.

IMPLIED CORRELATION

Implied credit correlation is as much a market-risk as a credit-risk concept. The value of each tranche has a distinct risk-neutral partial spread01, rather than a default01, that is, sensitivities to each of the constituents. The spread01 measures a market, rather than a credit risk, though it will be influenced by changing market assessments of each firm’s creditworthiness. Each of these sensitivities is a function of the implied correlation. Conversely, the implied correlation varies in its own right, as well as with the constituent and index credit spreads.

If default correlations are known, then the values of securitization tranches can be computed using a suitable model. Just like implied volatility, the other way round is also true here. If market prices are known and entered into the model, then the correlation which is obtained is known as implied correlation. So the implied correlation is the correlation implied from market prices.

The values, sensitivities, and other risk characteristics of a standard tranche can be computed using the copula techniques, but with one important difference.  Rather than using the default probabilities of the underlying firms to value the constituents, the market CDS spreads are used to obtain risk-neutral default probabilities. In many cases, there is not only an observation of the most liquid five-year CDS, but of spreads on other CDS along the term structure. There may also be a risk-neutral estimate of the recovery rate from recovery swaps. CDS indexes and their standard tranches are therefore typically valued, and their risks analyzed, using risk-neutral estimates of default probabilities.

The remaining key input into the valuation, using the copula technique is the constant pairwise correlation. While the copula correlation is not observable, it can be inferred from the market values of the tranches themselves, once the risk-neutral probabilities implied by the single-name CDS are accounted for. Not only the underlying CDS, but the tranches themselves, are relatively liquid products for which daily market prices can be observed. Given these market prices, and the risk-neutral default curves, a risk-neutral implied correlation can be computed for each tranche. Typically, the correlation computed in this fashion is called a base correlation, since it is associated with the attachment point of a specific tranche. Correlations generally vary by tranche, a phenomenon called correlation skew.

Since the implied correlation is computed using risk-neutral parameter inputs, the calculation uses risk-free rates rather than the fair market discount rates of the tranches. To compute the equity base correlation, the market equity tranche price is required (or is computed from the points up-front and running spread), and the spreads of the constituent CDS. Next, the risk-neutral default probabilities of each of the underlying CDS are computed. Given these default probabilities, and a copula correlation, the cash flows to the equity tranche can be simulated. There will be one unique correlation for which the present value of the cash flows matches the market price of the equity tranche. That unique value is the implied correlation.