By Glen McDermott, head of global structured bond research, Terry Benzschawel, and Adrian Lui, of Salomon Smith Barney

Because the multi-tranched investment structure of a CDO may not be flexible enough to address the objectives of some investors, the market has developed a class of structures called combination securities, whose return is derived from the cash flows of two or more underlying instruments, at least one of which is a CDO security.

The simplest example, the principal protected unit (PPU), is created by bundling a piece of CDO equity with a zero coupon Treasury STRIP. These units are designed to protect investors from the loss of their initial investment while still providing the potential for attractive returns. For example, a buyer might invest $45 million for a PPU, $23 million of which is used to purchase the 12-year STRIP (with a face value of $45mm) and the remainder of which is used to purchase CDO equity. Even if the equity fails to return any cash flow, the STRIP will accrete to a face of $45 mm at maturity and the investor will recoup its initial capital outlay. Moody's Investors Service can rate this PPU triple-A for return of principal.

In recent years, combination securities have evolved from the simple PPU to more sophisticated combinations, such as a Baa2-rated combination security backed by a Baa2-rated tranche issued from the same CDO (30%) and equity (70%). As our [Figure 1] illustrates, this combination can garner a Moody's Baa2 rating reflecting return of principal only but its return profile differs meaningfully from a similarly-rated "plain vanilla" tranche issued from the same deal. The return profile for the "plain vanilla" CDO tranche remains unchanged under all but the most stressful default scenarios the 8% return deteriorates only slightly (7.3%) when defaults hit 2.25% per annum. By contrast, our simulations show that the return on the Baa2 combination security can range from 16.4% with zero defaults to -0.4% with 2.25% annual defaults.

In our opinion, the ratings-based, constant default rate (CDR) investment framework outlined in Figure 1 has serious limitations. First, as our analysis illustrates, two securities can have the same rating but radically different return profiles. Second, the CDR method assumes that default rates are uniformly distributed in the investment-grade and high yield rating categories. They are not (see Figure 2). Third, combination security returns are critically path dependent (i.e. defaults occurring earlier in the life of a transaction will impair an investment more than defaults occurring at the tail end). Finally, while the traditional methodology produces average returns for a given annual default rate, it gives no guidance to an investor regarding the dispersion or variability of returns around that mean.

Combination return analysis

As we have mentioned, there are certain weaknesses in analyzing CDO combination securities based on a constant default rate methodology. First, annual default rates are not uniformly distributed in either investment-grade or high-yield rating categories. To illustrate this point, Figure Two shows frequency distributions of annual default rates for bonds rated Baa3 and B2. For Baa3 bonds (left panel), the mean is 0.31%, close to the 0.25% constant default rate assumption commonly used to price investment-grade CDOs. The frequency distribution of Baa3 default rates is highly skewed, however, with the closest approximation being either a Poisson or negative exponential distribution. Also, notice that the standard deviation of Baa3 credits is 0.9%, but that at -1 standard deviation Baa3 credits have an annual default rate of negative 0.59%. Similarly, for B2 credits (right panel), the distribution is highly skewed, such that the distribution is more Poisson than normal, and the standard deviation is inadequate as a measure of dispersion.

Finally, with respect to the timing of defaults, both investment-grade and high yield CDO combination security returns are critically path dependent. That is, large defaults that occur early in the life of the CDO have a much greater negative effect on returns than later defaults. Timing is key. Thus, even one early year with a 10% default rate for the high yield CDO or an early 5% annual default rate for an investment-grade CDO can impair the return on CDO combination securities.

Monte Carlo solution

Given the limitations of the current analytical approach, we believe that a refinement based on Monte Carlo simulations and actual historical default rates would represent an improvement on current methodologies. The fact that the distribution of annual default rates is not normal presents difficulties in generating meaningful annual default paths for the simulation. Our approach is to make no parametric assumptions about the underlying distribution, but rather to generate annual default rates for each pricing vector by sampling (with replacement) from the historical default rates published by Moody's since 1970. Accordingly, we randomly sampled from these annual default rates and constructed 2,000 default vectors that are a mix of front, middle, and back-loaded curves.

We then took the capital structure and initial portfolio of a recent investment-grade average CDO and computed the cash flows along the 2000 simulated default vectors. For the purposes of calculating ex-ante Sharpe ratios, cash flows for a given tranche were discounted back to the pricing date, using values obtained from the yield curve on that date. We then calculated the mean, standard deviation, and Sharpe ratio on the combination security cash flows.

In summary

Although both CDR and the Monte Carlo methods predict similar returns for the various combinations, only the Monte Carlo method allows us to calculate the relative risk/reward characteristics of each instrument.

Results confirm our earlier analysis (see SSB's Investment-Grade CDOs) that securities (equity and otherwise) backed by a pool of investment-grade bonds produce high expected returns and high Sharpe ratios under historical default scenarios. For example, in our simulations CDO equity had an expected IRR of 18% with a Sharpe ratio of 1.7, whereas a Aa2 rated combination security with 8% equity and a minimum rated coupon of 4%, yielded 8% with a Sharpe ratio of 5.0. Onerous simulations based on 2x historical default rates decreased the yield on the CDO equity to 15% and its Sharpe ratio to 0.6, whereas the combination security's yield decreased to 7.4% with a Sharpe ratio of 2.3.

In general, we find a direct relationship between expected IRR and the proportion of CDO equity in each security, but an inverse relationship between CDO equity and Sharpe ratio. In addition, not all similarly rated combination securities produce equal expected returns and in particular may differ greatly in Sharpe ratios.

CDO combination securities can be tailored for each investor based on their desired rating, minimum coupon, yield target and capital guidelines. Using both traditional and simulation-based analytics, we examined how varying combinations along those dimensions affect IRRs and Sharpe ratios. We found that securities backed by investment grade bonds produce high expected returns and Sharpe ratios under historical default conditions and multiples of historical default conditions. Also, we found not all similarly rated combination securities produce equal expected returns and may differ greatly in Sharpe ratios. Our analytical method can be used by investors to customize the mix of CDO senior, mezzanine and equity tranches to achieve their investment objective.

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