Many CDO noteholders tend to look at the equity portion of a CDO solely as a part of their subordination, rather than as an independent investment in its own right. However, with spreads on the underlying collateral quite wide (on a historical basis) and new deal activity constrained by lack of an equity bid - timing is good for investors to start thinking about buying equity in CDO tranches.

The most common way to evaluate equity on deals is via the internal rate of return (IRR), under different default and recovery scenarios. For example, in a sample CDO (in this case Duke Funding I, which closed in November 2000) at 0.3% CDR/annum (CDR = constant default rate) and 30% recovery, the equity cash flows have an IRR of 19.01%. At 1.0% defaults they yield 6.24%. In this deal, the equity cash flows have an IRR of 0% only if annual default rates rise to between 1.2% and 1.3%; higher default rates will generate negative IRRs.

Obviously, the equity looks considerably better with higher recovery assumptions, especially if defaults are higher. For example, at 50% recovery and 1% annual defaults, the equity yields 12.72% at inception, versus only 6.24% at 30% recovery.

Cracks in IRR

Although IRR analysis is very useful, it is a difficult tool for making comparisons across deals, for a number of reasons:

* It is not clear how to compare two different IRR profiles with different leverage. Two deals with identical collateral and different amounts of leverage will have different IRRs. The bond with greater leverage will generally have a higher IRR at pricing speed, and a steeper profile. That is, deals with higher leverage have both greater upside and greater downside. How does one measure that tradeoff?

* Constant default scenarios do not consider whipsaws, which would cause different equity tranches to behave very differently. For example, if defaults are front- or back-loaded, what are the implications? That depends, in turn, on how binding are the O/C and I/C tests. The less binding, the better for equity holders, as cash flows to the equity tranches are less likely to be cut off. Realize that only by whipsawing the CDO do these consequences become clear. In fact, if investors ask to see the IRR of the equity under different timing scenarios, dealers can usually run this analysis. However further complicating the analysis is the fact that there is some interaction between leverage and the O/C and I/C tests. If leverage is higher (to achieve a given rating), the rating agencies require that coverage tests be more binding.

* Comparisons across different types of collateral are extremely problematic. As hard as it is to compare equity on two different deals backed by the same type of collateral, it is even tougher to compare deals backed by different types of collateral. For example, if comparing ABS equity to high yield equity, what are reasonable assumptions for defaults and recoveries? With similar collateral, at least similar as-sumptions can be made.

As time goes by

The equity receives the excess interest cashflows on the deal plus any principle remaining at the end of the waterfall. As a result, these cashflows tend to be quite front loaded. In the Duke deal, for example, at 0.3% default and 30% recoveries, the initial investment is recouped in less than 4.5 years. The MacCauley duration of this security is 4.1 years.

One implication of the front-loading of cash flows is that the equity tranche, like an IO, pays down over time. Thus, even absent any credit deterioration in the deal, the price of the equity tranche drops as time passes. On the Duke Funding CDO, we know that at 0.3% defaults and 30% recovery, the par priced equity cash flows have an IRR just over 19%. Three years later, assuming that same 19% IRR, the price of the cash flows would be $86 per $100 par. That is, the total value of the equity would be $6.9 million rather than $8 million. Thus, an investor attempting to re-sell that equity, even if performing well, should not expect to receive par. Some of the principal cash flows have essentially already been returned as interest in the prior years. Thus, the equity tranche is essentially an amortizing asset, with a net present value that declines with time.

Which collateral wins?

While the choice of a deal is important, UBS Warburg holds that CDO equity is most importantly a portfolio allocation decision. Which is - do you want to take a leveraged position in that collateral at this point in time?

To answer, it is important to know historic equity returns on various types of collateral. We set up sample high yield, ABS, and investment grade corporate deals. Our "straw dog" $500 million high yield deal consists of three tranches: 77% triple-A rated notes, 14% triple-B rated notes, and 9% equity. The ABS deal has 80% triple-A rated notes, 15% triple-B rated notes, and 5% equity. The investment grade corporate holds 84% triple-A rated notes, 12% triple-B rated notes, and 4% equity.

The high yield collateral is assumed to have a fixed rate equaling the UBS Warburg High Yield Index. The investment grade corporate debt is set to a fixed yield equaling the UBS Warburg triple-B Index. Yield on the ABS collateral is assumed to be the yield on triple-B home equity paper. And the liability spreads are provided monthly by the UBS Warburg desk.

As of 4/20/2001, the yield on UBS Warburg's high yield index was 11.28%. We assumed the triple-A rated liabilities had a 7.5 year average life and paid LIBOR+ 50. The triple-B rated liabilities are floating rate, paying LIBOR+225 for 10 years. Both floating rate liabilities were swapped into fixed for the entire period.

Equity yield calculation is then straightforward. First, calculate interest cash flow, then subtract losses. We assumed defaults of 4%, and recoveries at 40%. Thus, losses equal 2.4% (4% defaults x 60% losses). We also need to subtract payments to the noteholders plus payment of trustee and deal manager expenses. The remainder is cash flow directed to equity holders. We divide these cash flows by the size of the equity tranche ($45,000,000), which results in yield on the equity. Thus, the equity yield on our high yield deal is 23.37%. This actually overstates the equity yield that will be quoted to investors. In our analysis we implicitly assume the deal is fully operational at all times - which ignores any ramp-up period, as well as any period during which the deal is paying down. (It also ignores any trading gains, calls and tenders. These are positive events that may influence equity returns, but they are unlikely to offset the upward bias to our return calculation.) Nonetheless it is a useful guide, as we have the same overstatement at all points in time and across all of our sample deals.

The summary of this analysis is shown below. Notice that high yield deals, which looked extremely unattractive early last year, now look quite attractive. And ABS deals, while less attractive than early last year, still look quite attractive on an equity return basis. Equity returns on the investment grade deal typically look unappealing (and, in fact, only looked attractive in late November through early January).

This analysis clearly indicates that the most favorable collateral, relative to historical levels - is the high yield class. Yes, ABS equity still looks good, and investment grade corporate spreads are currently too tight to make investment grade equity yields appealing to equity holders.

Conclusion

This analysis will still, most likely, leave many frustrated. You plod through our research article, expecting concrete, incisive answers, witty repartee, and compelling trades. Instead, you find that the most common method of analysis, IRR, while useful, is far from all encompassing. But don't sweat. It is important to realize that buying equity is really an asset allocation decision - is this the time you want to buy a leveraged position in this particular underlying collateral? For this, our spreadsheet is very useful.

So take heart. In buying equity tranches in CDOs, individual deal selection is less important than the decision of what assets to take a leveraged position in. Yes, there will be differences between deals, but sensitivity analysis allows you to ferret out if one is obviously better than another. So if an investor believes deals are largely equivalent, the behavior of the underlying collateral will prove far more important than whether to buy equity in Deal A or in Deal B backed by the same collateral. CDO equity can represent an attractive asset class for investors who have done their homework. And understandably, investors will want to buy equity when returns are historically attractive (because the asset class is feared), not when everyone is grabbing for it and equity returns are low. So - we believe the timing is right to BUY equity high yield CDO deals.

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