Toxic Assets: What Went Wrong with ABS CDOs?

Although there is no exact data available about the ex-post loss rate by products at any moment in time, the International Monetary Fund (IMF) estimates suggest that, among the many structured and property-related assets, ABS CDOs exhibited the highest loss ratio, amounting to more than 70% of their par value (Table 1 [ PDF 78.7KB | 1 page ]).⁵ This was an average number for the outstanding total; the number for lower rated tranches (e.g., those rated below BBB) would probably be much higher. Usually, the lower rated tranches of these CDOs are regarded as “toxic”; however, since these products were so vulnerable to a change in the default rate in the underlying assets and other related conditions, even the most senior tranches were not really immune to systematic risks and should thus also be regarded as “toxic.” Table 1 indicates that ABS CDOs are “toxic”, even with higher ratings, under the stressed situations in housing markets.

The typical rating process for structured products involves two stages: In the first stage, an expected loss distribution for the underlying collateral pool is estimated; in the second stage, cash flow simulations are used to determine whether a tranche can withstand the necessary level of defaults to earn a given rating. In the calculation of cash flows of RMBS, many items indicating the quality of the underlying loans are incorporated. However, in estimating an expected loss distribution for ABS CDOs, the model basically depends on five key parameters: current ratings, maturity, location, industry, and type of the underlying structured products. Using this information, important data such as default rate, recovery, and asset correlation was worked out. Some simplified assumptions were also made about default correlation, and the Monte Carlo simulation was used to generate the distribution of portfolio cash flow losses.

To illustrate the causes that led to the collapse of subprime-related RMBS CDOs, I conduct a simulation exercise of cash flows and show the sensitivity of these flows to the various parameter values.

3.1 Analytical Framework and Simplified Assumptions: A Simulation Exercise

I construct a simple model of RMBSs and CDOs, both comprising three tiers: senior, mezzanine, and equity tranches. For simplicity, it is assumed that all tranches have a maturity period of five years. In the first stage, I collect 1,000 loans to create an RMBS. Underlying mortgages are assumed to be homogeneous with a prespecified default rate and recovery (loss given default, or LGD) in the event of default. Specifically, it is assumed that the annual default rate is 3% and the LGD is 50%; both are set to be constant over the period. Default correlation is given as a parameter, and in our base case scenario, 0.1 is assumed as the model value of asset correlation. In the second stage, 10 mezzanine tranches of RMBSs are pooled to create a new ABS CDO, which is also sliced into three tiers.

To obtain the loss distribution of the cash flows of the loan pool and tranches, a standard one-factor Gaussian copula model is used. The details are explained in the Appendix [ PDF 105.9KB | 3 pages ]. In this specification, the loss distribution depends on the following parameters: default probability of underlying mortgages, asset correlation, and LGD. It should be noted that this exercise only shows the loss in terms of cash flows; the interactions between loan defaults and interest rate movements are abstracted because of a simplifying assumption on cash flows.

Tranching in RMBS is carried out so that the senior tranche has 1% of the expected chance of default and 10% of the principal is rated as equity. Thus, the remaining part is rated as the mezzanine tranche, which consists of approximately 10% of the total amount of the principal in the case of the first-stage RMBS, since approximately 80% of the principal is rated as a senior tranche according to the criteria described above. For our second-stage hypothetical CDO, 30% is rated as senior and 60% as mezzanine in our example.

3.2 Asset Correlation and Loss Distribution of the Pool

Given the above assumptions, Figure 3 [ PDF 105.9KB | 1 page ] illustrates the relationship between the loss distribution of our hypothetical loan pool and the correlation parameter of the underlying mortgages. If there is zero correlation, the expected rate of loss approaches the mean, which is 7% in the 5-year maturity in this model. However, if the pool assets have a higher positive correlation, the loss distributions tend to be skewed to the left with a heavier tail. It should be noted that in the CDO-like multi-tier structure, a rise in correlation implies more adverse effects on senior tranches rather than on subordinated tranches.

The overall risk of the financial system is based not only on the sum of the risks arising from within individual institutions but also on the degree of correlation among the institutions' balance sheets: the higher the correlation, the higher one would expect the systemic risk to be.

3.3 Larger Tail Risk and Higher Sensitivity to Macro Risk in ABS CDOs

In this model, cash flows are subject to two types of risk: idiosyncratic risk and economy-wide systematic risk.⁶ When I simulate the cash flows of these hypothetical RMBS and resultant ABS CDOs, it is clearly shown that the tranches of the ABS CDOs are more vulnerable to systematic risk than those of RMBS. There are two reasons for this. First, the quality of the underlying assets is inferior in CDOs to those in first-stage RMBSs. Note that second-stage CDOs comprise mezzanine tranches of RMBS. Second, the size of each tranche decreases in comparison with the original size of the mortgage pool; securitization is repeated and this causes the losses in that tranche to be highly sensitive to a default of any one of the underlying mortgages. Numerical results show these characteristics more clearly.

Table 2 [ PDF 16.5KB | 1 page ] shows the simulation results represented by several risk measures of each tranche of our hypothetical RMBSs and ABS CDOs. In the case of a CDO comprising mezzanine tranches of RMBSs, even a senior tranche has a higher tail risk—the risk of the event is infrequent but very damaging—as shown in the large values of 99% value at risk (VaR) and 99% expected shortfall (ES).

3.4 Sensitivity Analysis for Changes of Parameter Values

In the simple model employed in this paper, the performance of our hypothetical RMBS and CDOs is highly dependent on the quality of the underlying housing loans, specifically, the probability of default and the correlation among them. The higher probability of default markedly amplifies the tail risk as shown in Table 3 [ PDF 19.2KB | 1 page ], in which the probability of default of the underlying loans is set to be 1.5 times higher than the base case, that is, 4.5% instead of 3%, annually. Similarly, Table 4 [ PDF 19.2KB | 1 page ] shows the simulation results of a higher correlation equal to 0.5, instead of 0.1 of the base case. I can confirm that the performance of senior tranches deteriorates greatly and there is a small positive impact on the equity tranche of RMBS if the assumed correlation increases.

It is also possible to have simulation results against various situations in economy-wide systematic risk which is modeled as a latent macrovariable. In the model, idiosyncratic risk is independent given a particular value of a systematic risk. By changing the size of the systematic risk, the sensitivity of the cash flows of securitized products to the latent macrovariable could be shown as a graph. The result suggests that each tranche of CDOs exhibits higher sensitivity to these changes than each tranche of RMBSs. Figure 4 [ PDF 175.3KB | 1 page ] and Figure 5 [ PDF 173.1KB | 1 page ] illustrate a contrast of these differences in the properties of our hypothetical RMBS and ABS CDOs.

The charts clearly show that resecuritized products such as our hypothetical ABS CDO have higher sensitivity to macro common factors and this is also true for its senior tranches. A high probability of default significantly reduces the level of the risk of macrofactors at which the loss starts to increase sharply. Thus, once the subprime markets deteriorate and some other macroconditions affect them adversely, there should be a sharp rise in the losses in ABS CDOs. The simulation results suggest that this could lead to a collapse of the CDO market.

3.5 Collapse of CDO Markets

In the previous simulation examples, a latent variable representing systematic risk may correspond to the condition of the real estate markets or the level of interest rates that affect all mortgages simultaneously. In addition to this variable, a higher value of the default correlation among loans implies greater vulnerability of senior tranches, especially in ABS CDOs; there is a high probability of this characteristic of resecuritized products contributing to the collapse of the CDO market.

During the boom, several factors contributed to obfuscate the true risk of subprime-related CDOs. First, the housing boom and the Federal Reserve's interest rate policy lowered the default probability by providing opportunities to refinance with better terms, which also lowered the correlation among defaults. Second, the ratings of CDO tranches had been inflated on the basis of these data.

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