A common misconception in the analysis of collateralized debt obligations is the assumption that the underlying collateral pool performs just like the market or an index. Such generalizations make historical stress analyses easy, since all one has to do is observe the historical performance of the market or index. However, CDO collateral pools tend to have far fewer securities than any broad measure of the market. As such, there is a significant risk that the collateral pool behaves differently from the market, even if aggregate risk measures, such as ratings, are similar.
The analysis of portfolio sampling risk for CDOs is often in the context of a more general discussion: the choice between managed and static CDOs. Of course, for investors in both managed and static CDOs, portfolio sampling risk is not necessarily a bad thing. In both cases, investors hope that the underlying portfolio performs well relative to the market. In a static deal, investors rely on the initial portfolio selection, while in a managed deal, investors rely on the ability of the collateral manager to navigate through the credit markets over the life of the CDO. This article examines the notion of portfolio sampling risk and the static versus managed portfolio debate.
Tracking Error: Total Return Versus Default Rates
There are many ways to measure the risk of a sample portfolio relative to a broad measure of the market. Index tracking error, perhaps the industry's most popular approach, involves observing the distribution of periodic total return differences between a portfolio, or portfolio strategy, and an index. The standard deviation of this difference is one measure of this tracking error.
For a cash flow CDO, rather than periodic return, it is the default rate that is the most significant variable in determining performance. The risk that a particular tranche of a CDO misses its targeted return is directly related to the probability that the default rate exceeds a certain threshold, the probability of note impairment.
From the CDO mezzanine investor's perspective, it is important to measure the sensitivity of the probability of impairment to the size of the underlying collateral portfolio, number of distinct credits. To measure this sensitivity, the distribution of defaults for a given portfolio strategy needs to be generated. The traditional approach in the CDO market for doing this is to model portfolio default behavior using a binomial distribution. Our model generates a default distribution that we consider to be more realistic, by assuming positive default correlation between credits.
Mezzanine Note Impairment: Sensitivity To Portfolio Size
Graph 1 shows the probability of impairment as a function of the size of the underlying portfolio, for various mean cumulative default rates. The X-axis of the graph is the number of issuers in the portfolio and the Y-axis is the probability that the underlying collateral pool experiences enough defaults to impact the cash flow of the mezzanine notes. This analysis is based on a Baa2 mezzanine tranche of a typical five-year synthetic investment grade CDO whose underlying portfolio has an average rating of Baa1/Baa2.
It is important to note that adding more and more credits to a portfolio does not reduce the probability of mezzanine note impairment to zero. This is true for two reasons. First, because the underlying credits are assumed to have positive default correlation, some of the risk is systematic and cannot be diversified away. Second, there are only a limited number of credits to choose from. We estimate that the global credit investor has access to approximately 1,200 investment-grade credits, based on our analyses of the universe of credits in market indices and credits that trade in the default-swap markets.
In light of the fact that some of the risk of mezzanine impairment cannot be diversified away, it can be useful also to consider the diversifiable risk of impairment, shown in Graph 2. For this calculation, we calculate the probability of impairment, and subtract from that the non-diversifiable risk, as measured by the probability of impairment for a 1,200 credit portfolio.
For a given mean cumulative default rate, two points on this curve can be identified that are important from the perspective of mezzanine note investors. The first is the inflection point, or turning point. The inflection point can be defined as the point at which a sufficient amount of the diversifiable risk has been removed. The second is the sweet spot, which can be defined as the point at which the marginal benefit of additional credit exposure is sufficiently small.
At a 1.5% cumulative default rate--which corresponds to the Moody's Investors Service idealized five-year cumulative probability of default for a Baa2 rated portfolio--the inflection point is approximately 150 credits while the sweet spot is approximately 300 credits. At a 2.5% default rate, the inflection point is approximately 190 credits and the sweet spot is approximately 400 credits. At a 3.5% default rate, the inflection point is approximately 210 credits with a sweet spot of 500 credits.
The Static Versus Managed Debate
Any analysis of portfolio sampling risk within CDOs is usually at the heart of a broader discussion: the debate over investing in static CDOs versus hiring a manager to actively manage the collateral. Managers are generally favored in markets where credit skills and access to assets are limited, such as high-yield bonds, leveraged loans and emerging markets. However, in markets where such skills are broadly available and where access to assets is not as difficult, CDO investors truly have a choice between managed and static transactions. There are clear benefits and drawbacks for each approach.
With a manager, investors hope the portfolio sampling risk is utilized effectively by the manager over the life of the deal to generate outperformance relative to the market. However, there is a cost for management, so any managed strategy has to be credible and should leave the manager with enough room to deviate from the market to earn the alpha.
In contrast, in a static transaction, investors generally hope that initial credit selection will result in portfolio outperformance (with respect to the number of defaults) over the life of the transaction. Alternatively, investors may hope the collateral pool is large enough that the portfolio sampling risk relative to the market or index is sufficiently low. The analysis provided above should aid investors in understanding the potential risks they have as mezzanine note investors, given the wide differences in CDO portfolio sizes.
Portfolio size is an important consideration for mezzanine note investors. If a CDO's underlying portfolio is larger than the inflection point (for a given default rate assumption), the diversifiable default risk can be significantly reduced. sweet spot size, the marginal benefit of adding additional credits is small. It is important to note that portfolio sampling risks may be desirable in cases where investors intend to take name-specific credit risk in either static or managed transactions.
This week's Learning Curve was written by Sivan Mahadevan, head of structured credit research (pictured), and David Schwartz, associate in structured credit research, at Morgan Stanley in New York.