Book 2. Credit Risk

FRM Part 2

CR 22. Structured Credit Risk

Presented by: Sudhanshu

Module 1. Structured Products

Module 2. Securitization

Module 3. Simulation, Probability of Default and Default Correlation, Default Sensitivities and Structured Products

Module 1. Structured Products

Topic 1. Types of Structured Products

Topic 2. Capital Structure in Securitization

Topic 3. Waterfall Structure

Topic 1. Types of Structured Products

• Securitization: The process of pooling credit-sensitive assets, like mortgages or auto loans, and creating new securities. The cash flows from these new securities are backed by the cash flows from the original assets. The primary goal is to transform illiquid assets into liquid ones and to redistribute risk.

• Structured Products: These are the new securities created through the securitization process. Each structured product has its own unique risk and return characteristics, which can differ significantly from the underlying assets.

• Covered Bonds: These are on-balance sheet securitizations. A pool of assets, typically mortgages, is kept on the originator's balance sheet and serves as security for the bonds. Unlike true securitizations, investors have recourse against the originating bank if it defaults, and the principal and interest are guaranteed by the originator.

• Mortgage Pass-Through Securities: These are true off-balance sheet securitizations. The investors receive cash flows (principal and interest) that are "passed through" from the underlying mortgage pool, less any fees paid to the servicer. Default risk is usually low, especially for agency MBSs with implicit or explicit government guarantees. The main risk is prepayment of principal by homeowners.

• Collateralized Mortgage Obligations (CMOs): A type of MBS where cash flows are divided into different tranches based on a predetermined schedule. This allows for the creation of securities with varying maturities and cash flow profiles, which can appeal to a wider range of investors with different risk appetites. A common example is the "waterfall" or sequential pay structure.

• Structured Credit Products: This is a broad category of structured products where the underlying assets are risky debt instruments. The key feature is the creation of tranches with different levels of credit risk. The most junior tranches (equity) absorb the first losses, protecting the more senior tranches.

• Asset-Backed Securities (ABS): This is the most general class of securitizations. An ABS can be backed by any cash-flow generating assets, such as credit card receivables, auto loans, or even toll collections. MBSs are a specific type of ABS. Other varieties include Collateralized Bond Obligations (CBOs), Collateralized Debt Obligations (CDOs), and Collateralized Loan Obligations (CLOs).

Practice Questions: Q1

Q1. How many of the following statements concerning the capital structure in a securitization are most likely correct?
I. The mezzanine tranche is typically the smallest tranche size.
II. The mezzanine and equity tranches typically offer fixed coupons.
III. The senior tranche typically receives the lowest coupon.
A. No statements are correct.
B. One statement is correct.
C. Two statements are correct.
D. Three statements are correct.

Practice Questions: Q1 Answer

Explanation: B is correct.

Senior tranches are perceived to be the safest, so they receive the lowest coupon. The equity tranche receives residual cash flows and no explicit coupon. Although the mezzanine tranche is often thin, the equity tranche is typically the thinnest slice.

Topic 2. Capital Structure in Securitization

• Tranching: This is the core principle of structured finance. It's the process of slicing a pool of assets into different layers, or tranches, based on their seniority in receiving cash flows and absorbing losses. This allows a single pool of assets to be used to create multiple securities with widely different risk profiles, appealing to a broader range of investors.

• Senior Tranche: This is the safest and highest-rated tranche. It has first priority on all cash flows from the underlying assets. It receives the lowest interest rate (coupon) because it bears the least amount of credit risk. Defaults in the underlying asset pool must be significant enough to wipe out all junior tranches before the senior tranche is affected.

• Mezzanine Tranche: This tranche sits between the senior and equity tranches in the capital stack. It has a lower priority than the senior tranche but a higher priority than the equity tranche. It is designed to absorb losses from the underlying assets after the equity tranche has been completely depleted. In return for taking on this higher level of risk, mezzanine investors receive a higher coupon or interest spread compared to the senior tranche.

• Equity Tranche: Also known as the "first-loss" or "unrated" tranche. It is the riskiest part of the securitization, as it is the first to absorb losses from defaulted assets. Equity investors receive the residual cash flow from the asset pool after all senior and mezzanine obligations have been met. Because its cash flow is variable and non-guaranteed, its returns are highly volatile but also have the potential for the highest returns.

• Credit Enhancement: These are mechanisms used to protect the more senior tranches from losses.

  • Internal: These enhancements are created from within the securitization structure itself. Examples include:

    • Overcollateralization: The par value of the collateral pool is greater than the par value of the bonds issued. For example, a $120 million pool of loans might only be used to back $100 million in issued securities, providing a $20 million buffer.

    • Excess Spread: The interest rate earned on the collateral pool is higher than the interest rate paid to the noteholders. This surplus is held in an account to cover potential future losses.

  • External: These enhancements are provided by a third party. An example is a guarantee or insurance policy purchased from a highly-rated institution, like a monoline insurer, which promises to make interest and principal payments if the underlying assets default.

Topic 3. Waterfall Structure

• Waterfall Structure: The waterfall structure is the most critical component of a securitization. It is a set of precise rules that dictates the order in which all cash flows from the underlying collateral pool are distributed to the various noteholders and other parties. The term "waterfall" is used because cash flows flow down from the top (most senior) to the bottom (most junior) of the capital structure.

• Cash Flow Priority: Cash flows are distributed in a strict hierarchy, ensuring that senior tranches are paid first, followed by mezzanine, and then equity.

  • Inflows from Collateral: The process begins with all cash inflows generated by the underlying assets, which include scheduled interest and principal payments, as well as any recovery proceeds from defaulted loans.

  • Payments to Senior Tranche: The senior noteholders are paid their full principal and interest before any other tranche receives a penny.

  • Payments to Mezzanine Tranche: After the senior tranche has been paid in full, the remaining cash flows are used to pay the principal and interest to the mezzanine noteholders.

  • Residual Cash Flow to Equity: Any cash flow remaining after all senior and mezzanine obligations are met flows to the equity tranche. This residual amount is highly volatile and represents their return on investment. In some structures, this excess spread may first be diverted to an overcollateralization account to provide further credit enhancement before being paid out to equity investors.

• Default Impact: When a loan in the underlying pool defaults, it reduces the total cash flow entering the waterfall.

  • The first impact is felt by the equity tranche, as their residual payment is reduced or eliminated entirely.

  • If the number of defaults is severe enough to exhaust the equity tranche's buffer, losses will then begin to "spill up" and impact the mezzanine tranche.

  • Only in the most catastrophic scenarios would losses extend to and impact the senior tranche, as it is protected by the buffers of both the equity and mezzanine tranches.

Practice Questions: Q2

Q2. Assume there are 100 identical loans with a principal balance of $500,000 each. Based on a credit analysis, a 300 basis point spread is applied to the borrowers. The market reference rate is currently 4% and the coupon rate will reset annually. The senior, junior, and equity tranches are 75%, 20%, and 5% of the pool, respectively. The spreads on the senior and mezzanine tranches are 2% and 6%.
Excess cash flow is diverted above $1,000,000. Assume the default rate is 2%. What are the cash flows to the mezzanine and excess trust account in the first period?

Practice Questions: Q2 Answer

Explanation: A is correct.

The interest rate on the loans = 4% (market reference rate) + 3% (spread) = 7%. Therefore, the total collateral cash flows in the first period = 100 × $500,000 × 7% × (1 − 0.02) = $3,430,000. The senior tranche receives $50million × 0.75 × (4% + 2%) = $2,250,000. Similarly, the mezzanine tranche receives $50million × 0.20 × (4% + 6%) = $1,000,000. Next, the residual cash flows are calculated: $3,430,000 − $2,250,000 − $1,000,000 = $180,000. Since $180,000 < $1,000,000, all cash flows are claimed by the equity investors and there is no diversion to the trust account.

Module 2. Securitization

Topic 1. Securitization Participants

Topic 2. Three-Tiered Securitization Structure

Topic 1. Securitization Participants

• Originator/Sponsor: This entity, typically a bank or financial institution, is responsible for originating the loans and creating the pool of assets to be securitized. Their motivation is to remove the assets from their balance sheet to free up regulatory capital and generate fee income from the securitization process itself.

• Underwriter: The underwriter, usually an investment bank, designs the structure of the securitization. This includes determining the size and credit rating of each tranche, setting the coupon rates, and establishing the rules for the waterfall. They also market and sell the new securities to investors.

• Credit Rating Agencies (CRAs): CRAs, such as Moody's, S&P, and Fitch, play a crucial role by providing an independent credit rating for each tranche of the securitization. These ratings are essential for attracting investors, as they provide an opinion on the creditworthiness and expected loss of each tranche. A potential conflict of interest arises because the CRAs are paid by the underwriter or originator.

• Servicer: The servicer is the entity responsible for the ongoing administration of the securitized assets. Their duties include collecting principal and interest payments from the borrowers, managing delinquent accounts, and initiating foreclosure proceedings when necessary. The servicer receives a fee for these services and often provides a liquidity function by advancing payments in case of temporary delinquencies.

• Custodians and Trustees: These entities act as fiduciaries, holding the underlying collateral and overseeing the securitization trust. They ensure that the underwriter, servicer, and other parties operate in strict accordance with the legal documents governing the deal. The trustee's primary responsibility is to protect the interests of the investors.

• Conflicts of Interest: Conflicts of interest can arise between the different participants in the securitization process. For example, a servicer may have an incentive to delay foreclosure on a defaulted loan to continue collecting servicing fees, which could be detrimental to the investors who would prefer a swift resolution to a bad loan. Similarly, the fee-based relationship between underwriters/originators and rating agencies can be a source of conflict.

Topic 2. Three-Tiered Securitization Structure

• Inflows: The total cash available to the trust is a combination of interest on collateral (e.g., $90\times 8\%\times \$1,000,000$) and any recovery from defaulted assets (e.g., $2\times 40\%\times \$1,000,000$). This total amount, along with the starting value of the overcollateralization account, forms the pool of funds to be distributed.

• Outflows: The cash flows are distributed in a strict, sequential order to pay the coupon payments to senior and mezzanine noteholders first. Any remaining cash after these obligations are met goes to the equity holders.

• Overcollateralization Account: This is a key internal credit enhancement mechanism. It is a trust account that accumulates excess spread—the difference between the interest earned on the collateral and the interest paid to the noteholders. This account serves as an additional buffer to absorb losses before they can impact the rated tranches. Its value grows over time (e.g., from a starting value of $16 million to $16.64 million at the end of the year, assuming a 4% return).

• Cash Flow Tests: A custodian or trustee must perform regular tests to ensure the securitization is performing as expected. These tests determine if the current period's interest income is sufficient to cover the promised coupons and if the overcollateralization account can cover any shortfalls. If the tests fail, it can trigger events that change the waterfall's priority to protect senior tranches, such as diverting all cash flows to pay down the most senior debt.

• Terminal Cash Flows: In the final year of the securitization, the surviving loans mature and the principal is returned. This large influx of cash is distributed according to the waterfall to satisfy all remaining claims from the senior and mezzanine tranches. Any residual amount left over after all of these obligations have been met is paid to the equity tranche. This final payment is the ultimate return for the riskiest investors.

Practice Questions: Q1

Q1. Which of the following participants in the securitization process is least likely to face a conflict of interest?
A. Credit rating agency and servicer.
B. Servicer and underwriter.
C. Custodian and trustee.
D. Trustee and manager.

Practice Questions: Q1 Answer

Explanation: C is correct.

The custodian and trustee play the least important roles in the securitization process. The servicer, originator, underwriter, credit rating agency, and manager all face conflicts of interest to varying degrees.

Module 3. Simulation, Probability of Default and Default Correlation, Default Sensitivities and Structured Products

Topic 1. Simulation Approach

Topic 2. Impact of Probability of Default and Default Correlation

Topic 3. Measuring Default Sensitivities

Topic 4. Risks for Structured Products

Topic 5. Implied Correlation

Topic 6. Motivations for Using Structured Products

Topic 1. Simulation Approach

• Simulation: The simulation approach is a powerful tool used in structured credit risk analysis to model a wide range of potential outcomes for a securitization. It is particularly useful because of the complex interdependencies and non-linear relationships between the underlying risk factors. Instead of relying on simplified assumptions, a simulation runs thousands or even millions of scenarios to provide a more comprehensive view of potential losses and returns for each tranche.

• Methodology: The simulation involves generating random, but realistic, scenarios of default and recovery for the underlying collateral pool. For each scenario, the cash flows are run through the waterfall structure to determine the payments to each tranche. By repeating this process many times, a distribution of possible cash flows and losses for each tranche is generated. This allows analysts to calculate key risk metrics like the expected loss, Value at Risk (VaR), and the probability of a specific tranche suffering a principal loss.

• Factors to Consider:

  • Probability of Default (PD): For each loan in the collateral pool, a random number is drawn to determine if it defaults in a given period. This is based on the loan's individual PD, but also considers the impact of...

  • Default Correlation: This is a critical input in any structured credit simulation. Default correlation, or the tendency of defaults to happen together, is modeled using a copula function. A higher correlation means that when one loan defaults, others are more likely to default as well. This leads to fatter tails in the loss distribution, which is especially detrimental to the senior tranches. The simulation allows analysts to explicitly model this relationship and see its direct impact on the performance of each tranche.

Topic 2. Impact of Probability of Default and Default Correlation

• Impact of Probability of Default (PD): The probability of default is a fundamental driver of credit risk. In a securitization, an increase in the PD of the underlying loans leads to fewer total cash flows into the trust, as more loans fail to make their scheduled payments. The effect of this reduction is felt unevenly across the tranches.

  • Senior Tranche: This tranche is designed to be highly resilient to increases in PD. Since it is first in the waterfall, it is protected by the more junior tranches. Only a very large increase in PD that completely exhausts the equity and mezzanine tranches will begin to impact the senior tranche's value. Its value is relatively stable with small changes in PD.

  • Mezzanine Tranche: This tranche is highly sensitive to changes in PD. As the first-loss equity tranche is depleted by defaults, the mezzanine tranche is next in line to absorb losses. Therefore, a moderate increase in the PD can cause a disproportionately large decrease in the value of the mezzanine tranche.

  • Equity Tranche: The equity tranche is the most sensitive to PD changes. Since it is the first to absorb losses, even a small increase in the overall PD of the collateral pool can significantly reduce its residual cash flow and, consequently, its value.

• Impact of Default Correlation: Default correlation measures the tendency of loans to default at the same time. The impact of correlation is particularly important for the risk of the senior tranches.

  • Senior Tranche: A higher default correlation is detrimental. When defaults are highly correlated, it increases the likelihood of a "perfect storm" scenario where a large number of loans default simultaneously. This type of event can quickly overwhelm the credit enhancements (the equity and mezzanine tranches) and cause significant losses for the senior tranche. Therefore, the risk of the senior tranche is highly sensitive to default correlation, and its value decreases as correlation increases.

  • Mezzanine Tranche: A higher default correlation is also detrimental to the mezzanine tranche. A large, correlated wave of defaults can exhaust the equity tranche more quickly, causing the losses to "spill up" to the mezzanine tranche. As correlation increases, the probability of a mezzanine investor suffering a loss also increases.

  • Equity Tranche: The equity tranche is less sensitive to default correlation. Since it is designed to absorb the first losses, it is expected to suffer a loss in most scenarios regardless of whether the defaults happen at the same time or are spread out. The equity tranche's value is primarily driven by the overall default rate, not so much by the clustering of defaults.

Practice Questions: Q1

Q1. Which of the following statements about portfolio losses and default correlation are most likely correct?

I. Increasing default correlation decreases senior tranche values but increases equity tranche values.
II. At high default rates, increasing default correlation decreases mezzanine bond prices.
A. I only.
B. II only.
C. Both I and II.
D. Neither I nor II.

Practice Questions: Q1 Answer

Explanation: A is correct.

Statement I is true. Increasing default correlation increases the likelihood of more extreme portfolio returns (very high or very low number of defaults). The increased likelihood of high defaults negatively impacts the senior tranche. On the other hand, the increased likelihood of few defaults benefits the equity tranche as it bears first loss.

Statement II is false. At high default rates, increasing the correlation increases the likelihood of more extreme portfolio returns which benefits equity investors and mezzanine investors.

Topic 3. Measuring Default Sensitivities

• Default Sensitivity: This is a measure that quantifies how a tranche's value changes with a change in a specific risk driver, such as the probability of default or the default correlation. It is a concept analogous to DV01 in interest rate risk, which measures the change in a bond's price for a one-basis-point change in interest rates. Similarly, default sensitivity provides a way to express the exposure of each tranche to changes in the key credit risk factors.

• Risk Measurement: The simulation approach described in the previous section is used to analyze the impact of changing default probability and default correlation on both the mean and risk of each tranche.

  • Mean (Average): This refers to the expected or average value of the cash flows and returns for a given tranche across all simulated scenarios. It is used to analyze the impact of changes on the expected performance of a tranche.

  • Risk (Credit VaR): The risk is measured using a metric like Credit Value at Risk (VaR). Credit VaR is a measure of the maximum expected loss over a given time horizon at a specific confidence level (e.g., 99%). The simulation allows us to build a full distribution of potential losses, from which we can extract the Credit VaR to understand the downside risk for each tranche.

Topic 4. Risks for Structured Products

• Prepayment Risk: The risk that homeowners will pay off their loans early, reducing the cash flows to investors. This risk is particularly relevant for mortgage-backed securities (MBS). If interest rates fall, homeowners are more likely to refinance their mortgages, leading to a faster-than-expected return of principal to the MBS investors. This can be detrimental as investors receive their principal back at a time when reinvestment opportunities are at lower interest rates.

• Default Risk: This is the primary risk addressed by the securitization structure. It is the risk that the underlying loans will default, leading to losses for the investors. The impact of default risk is allocated across the tranches according to the waterfall structure, with the junior tranches bearing the brunt of the losses.

• Spread Risk: Also known as market risk, this is the risk that the spread on the underlying loans will change. Structured products are often valued based on the spread of their cash flows over a benchmark rate (e.g., LIBOR). If the market's required spread for a similar risk profile widens, the value of the structured product will fall. This is an important consideration for CDOs, as the value of the underlying debt can fluctuate.

• Model Risk: The valuation of complex structured products, especially those with multiple tranches and non-linear dependencies like CDOs, relies heavily on mathematical models. Model risk is the risk that these models are inaccurate, incomplete, or based on flawed assumptions. For example, a model that underestimates default correlation could significantly misprice the senior tranches, as was the case during the 2008 financial crisis.

• Liquidity Risk: This is the risk that a security cannot be sold quickly at a fair price in the market. Structured products, especially the more complex or bespoke ones, can have very low trading volumes. This makes it difficult for investors to exit their positions, and in times of market stress, the lack of liquidity can cause significant price drops, even if the underlying assets are performing adequately.

• Correlation Risk: This is the risk that the actual default correlation among the underlying assets is different from what was assumed in the valuation or modeling of the structured product. As discussed in previous sections, a higher-than-expected default correlation can lead to unexpectedly high losses for the senior tranches, while a lower-than-expected correlation might leave the junior tranches with lower returns than anticipated.

Topic 5. Implied Correlation

• Implied Correlation: Implied correlation is a forward-looking measure of default correlation. Unlike historical correlation, which is based on past data, implied correlation is extracted from the current market prices of structured products, particularly collateralized debt obligations (CDOs). It represents the market's collective consensus on the expected joint default behavior of the underlying assets.

• Process: The process of deriving implied correlation is a form of reverse engineering. An analyst uses a standard pricing model, such as a one-factor Gaussian copula model, and inputs all the known variables—tranche thickness, coupon, maturity, and the market price of the tranche. The model is then solved for the one unknown variable: the default correlation. The correlation value that makes the model's output price match the observed market price is the implied correlation.

• Market vs. Historical Correlation: Implied correlation can diverge significantly from historical correlation, especially in periods of market stress. For example, during the lead-up to the 2008 financial crisis, the implied correlation for senior CDO tranches was very low, suggesting the market believed defaults would be uncorrelated. When the housing market collapsed, actual correlation soared, leading to massive losses for investors. In a crisis, the implied correlation for senior tranches will typically spike as the market prices in the higher risk of a systemic wave of defaults.

• Arbitrage and Risk Management: Implied correlation is a key factor in structured credit trading. Traders at "correlation desks" actively trade on the difference between implied and historical correlations. If a trader believes the market's implied correlation is too high (i.e., too pessimistic about future defaults), they can buy the junior tranches and sell the senior tranches of a CDO, betting that actual defaults will be less correlated than the market is currently pricing in.

Topic 6. Motivations for Using Structured Products

• Risk Transfer: One of the most significant motivations for securitization is to transfer credit risk from the originator's balance sheet to the broader investor market. By selling the assets, the originator offloads the risk of default associated with those loans. This is particularly attractive for banks with large, concentrated loan portfolios, as it allows them to diversify and reduce their exposure.

• Regulatory Capital Relief: For banks, holding loans on their balance sheet requires them to set aside a certain amount of capital as a buffer against potential losses, in line with regulations like Basel III. By securitizing these loans and removing them from their balance sheet, the bank frees up this regulatory capital, which can then be used for other purposes, such as new lending or investment.

• Increased Liquidity: Securitization transforms illiquid assets, such as a portfolio of thousands of individual car loans or mortgages, into highly liquid securities. These securities can be easily bought and sold in the capital markets, providing a new and efficient source of funding for the originator. This allows them to originate more loans without having to rely on deposits or other traditional funding sources.

• Arbitrage: This motivation is based on the idea that the cost of funding obtained by selling the securitized tranches is lower than the interest income generated by the underlying assets. The difference, or "excess spread," is captured by the equity investors. If the sum of the coupon rates paid to the senior and mezzanine tranches is less than the weighted average interest rate of the collateral, an arbitrage profit can be realized.

• Customized Risk and Return Profiles: Structured products allow for the creation of securities that are tailored to the specific risk and return objectives of different types of investors. For example, a pension fund that is risk-averse can invest in the highly-rated, low-risk senior tranche, while a hedge fund seeking high returns and willing to take on significant risk can invest in the unrated equity tranche. This customization would not be possible with the original, undifferentiated loan pool.

Practice Questions: Q2

Q2. Which of the following statements best describes the calculation of implied correlation?
A. The implied correlation for the mezzanine tranche assumes non-constant pairwise correlation.
B. Observable market prices of credit default swaps are used to infer the tranche values.
C. The tranche pricing function is calibrated to match the model price with the market price.
D. The risk-adjusted default probabilities are used in model calibration.

Practice Questions: Q2 Answer

Explanation: C is correct.

Starting with observed market prices and a pricing function for the tranches, it is possible to back out the implied correlation to calibrate the model price with the market price. The computation of implied correlation assumes constant pairwise correlation. Both credit default swap and tranche values are observed. Observed tranche values are used in conjunction with risk-neutral default probabilities to compute implied correlation.