Posted tagged ‘yield’

In The Year 2010: C.D.O. Edition

October 21, 2008

In another installment of the series called “In The Year 2010″ I will sit here and guess what will be going on by the end of 2010 with respect to various products. (Inspired by the Conan O’Brian skit “In The Year 2000″). This is a thought experiment, nothing more.

This edition, as the title would seem to suggest, is about C.D.O.’s. Please sit down, because I’m about to argue something very counter-intuitive. C.D.O.’s will be alive and well in the year 2010. Now, I’m willing to claim this victory on a technicality–corporate C.D.O.’s are still being issued. Now, safe in my assured technical victory, I’ll go farther out on the limb

It’s somewhat instructive to understand what have been the various motivations behind the C.D.O. market, historically (some of these obviously no longer exist)…

  1. There was the reach for yield. If one could get AAA C.D.O.’s for a higher yield than other AAA bonds, it was a no brainer. Both were AAA, obviously! No extra risk.
  2. A highly customized risk profile. If I looked at a pool and thought 6% of the balance was going to written off, but no more, I could buy the 7%-10% tranche and get a higher return. Obviously this higher return would need to match whatever threshhold I established, but that was most likely related to the market anyway. Some people referred to this as taking a position in the collateral with leverage. C.D.O.’s are, in essence, leverage on leverage, but this is a complicated, technical, and largely semantic argument. The surface intuition is that taking a levered position increases your return if nothing defaults, but less has to default for the buyer to lose money.
  3. C.D.O.’s were used to finance bonds or other debt positions. “How?” is what I heard you say, in the back? Well, think about it this way: an investment bank requires 50% of the purchase price of a set of bonds and charges LIBOR+100bps on the other 50%. We say that you’ve financed the purchase of the bonds two to one at a rate of one hundred basis points over LIBOR. Now, using our example, let’s say one could issue a C.D.O. and sell enough bonds to get 50% of the purchase price of the underlying bonds up front. Let’s also assume that the liabilities have a weighted average interest rate of LIBOR+10bps. Using the C.D.O. instead of a traditional loan, especially since the C.D.O. can’t be cancelled like a loan can and, most likely, contains much more lax terms than a loan, is much more cost effective. Taking this a step further, it was even possible for C.D.O.’s to be issued that allowed more bonds to be put into the C.D.O. or allow bonds that were sold to be replaced. This effecive made the C.D.O. a credit line with an extremely cheap interest rate. Keep in mind the “equity” or “most levered tranche” or “bottom” of the C.D.O. generally was structured to have a very high return, somewhere in the 15-25% range.

Also, the backdrop of the boom in C.D.O.’s, don’t forget, was a very low rate environment. If one could get LIBOR+10-15bps on AAA bonds when rates were, in 2004 for example, 1% (for USD LIBOR and the Fed Funds), that was a major out performance for a AAA security (AAA, how much risk could there be?!).

Now that the historical context is out of the way, it seems pretty clear that some of these reasons for isssuing C.D.O.’s will not diminish in importance. Funds and money managers will always need more yield. Investors that are smart about credit analysis will always want to take the risks they understand and get paid for taking said risks. Funds and other “levered players” will always need financing. So, let’s examine how the landscape changes rather than disappears.

  1. Complexity will die. There are a number of reasons for this. Part of the reason is that buyers of C.D.O.’s will begin to realize that structure adds a layer of complexity that no one really can grasp fully. Why have dozens of triggers and tests at every stage of the waterfall (the way cash is distributed in order of seniority)? In some deals, I’m sure, this complexity helped some tranches of the C.D.O. In some other deals, I’m sure, this complexity hurt some tranches of the C.D.O. The one  constant is that it’s nearly impossible to tell the right levels and specific mechanics beforehand. Hence the complexity will die and structures will simplify. Likely this also means less tranches. Why have a $4 million tranche size in a $400+ million deal when you can’t even predict losses within an order of magnitude (1%, 9%. or 20%? Who knows?!)? This is hardly a new concept, I introduced it already when discussing residential mortgages.
  2. Arbitrage C.D.O.’s will reign supreme. This one is controversial, and the term “Arbitrage C.D.O.” almost takes on a different meaning each time it’s defined. The intuition, though, is that a hedge fund taking advantage of a market dislocation by issuing a C.D.O. is an “Arbitrage C.D.O.” Why will these be popular? Well, C.D.O. shops, or firms that are serial issuers of C.D.O.’s, have mostly blown up and are done. Traditional money managers will be shying away from C.D.O.’s for a long time. So, in order to sell the C.D.O. equity, the most levered risky piece, the firm issuing the C.D.O. will need to also be willing to take on the equity–this leaves only hedge funds. Arbitrage C.D.O.’s also come together more quickly and generally are backed by corporate bonds. Funds and other accounts that, as a core competency, already analyze corporate credit won’t have to go “outside the comfort zone” to buy into arbitrage C.D.O.’s.
  3. C.D.O.’s or C.D.O. technology will become part of the M&A world more and more. Aha! Maybe too clever for my own good, but while all these specialty finance companies used to be able to issue a C.D.O. for funding purposes on their own, now they will need an investment bank to connect them with hedge funds or take on the debt, and thus the risk, themselves. These C.D.O.’s will likely be simple too (see #1), but will be an efficient way for these companies to finance assets or move them off the balance sheet. Here’s an example: a diversified finance firm, with a large lending presence, for example (most likely with a R.E.I.T. subsidiary, a popular structure of the past eight years) will be looking to sell itself. However, because the assets on it’s balance sheet look risky the leveraged finance groups will need to arrange some financing against those assets. The structure? Most likely a C.D.O. with hedge funds providing the cash and getting a “juiced” return on their money. This is essentially the covered bond product, but with an extra layer of complexity (tranching) on top.

Okay… that’s enough prognosticating for now. Still deciding which product is next. Drop me a line if you have a favorite!

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Assume all Bonds are Spheres: Part I

February 14, 2008

This segment is a regularly occurring feature. It gets its name from a joke that is commonly made about technical people. Usually a very simple problem is presented about horses (or sometimes cows) and a physicist/engineer/mathematician is asked to provide a solution. The solution is made complex because incorporating the nuances of the animals in question is extremely difficult, hence the highly technical person is required. The solution then starts with the technical person saying, “I made two assumptions. The first assumption is gravity. The second assumption I made was that all horses are spheres.” The crux of the joke, which is often found in the markets, is that approximating is both easier and “accurate enough.” Hence the naming of this series on mathematical financial tricks and other interesting tidbits.

Loans are simple enough. I tell you that I would like to originate a loan, which I will securitize, and your interest rate on a loan is going to be 10%. Easy! You just send in 10% of the loan amount every year. Well, not really:

  • If I followed convention, I quoted you an Act/360 rate (it accrues yearly based on the actual days, but assumes a 360 day year)–the interest you pay is really 10.14% (~ 365/360 * 10%). (Note that the lower the interest rate, the lower the impact of converting to Act/360.)
  • If this was a 10 year loan, those 14 basis points (bps, 1/100th of a percent) are worth about 1.11% of the total notional of the loan (don’t forget, that’s 14 bps extra one pays per year, for 10 years–take the present value of all those cashflows).

Now, let’s look at what happens when I securitize the loan.

  • I monetize the 14 bps because the bonds I sell accrue on a 30/360 basis (market convention), so those extra days of interest never get paid to bondholders–I keep it.
  • Another nuance: The bonds are priced to the market convention, which is assuming a semi-annual yield. Investors will demand, say, a 10% coupon on their bonds. The bonds, though, match the loan–they pay monthly. What is the 10% worth on a monthly basis? About 9.80% (see below). What do I earn on arbitraging the difference? Well, about 20 bps per year, which, present valued, is worth about 1.59% of the loan amount.

Let’s review: I quoted you a loan at 10%. The 10% tuned out to be more than 10%. I then sold the loan using a completely different set of assumptions and, doing nothing at all, managed to pocket 2.7% of the loan amount. On $10 million dollars that’s $270,000 I made just for arbitraging various conventions and the difference in how bond investors think and how lenders generally think. Would you have been better off to take the 10.05% loan from the insurance company, quoted on a 30/360 basis? Yep. But the rate was lower … and all bonds are spheres.

————————–

The voodoo behind the 9.80% monthly equivalent coupon is easy. The first insight is to recognize that a yield is essentially a discount rate. To find a monthly equivalent to a semi-annual yield one needs only to find the interest rate that, when compounded twelve times a year, equals the yield that assumes compounding twice a year (the semi-annual yield).

We start by saying that an annualized yield, assuming compounding x times a year is

     (1 + i/x)^(x) – 1 = annualized yield       Formula that codifies the above intuition.

For our example of a 10% semi-annual yield, we get the following:

ann. yield (12 pmts.) = ann. yield (2 pmts)
(1 + (r/12))^12 – 1 = (1 + (10%/2))^2 – 1 
1+ (r/12)) = (1+5%)^(2/12)                      
Algebra… 😦
r/12 = (1.05)^(2/12) – 1
r = 12 * ((1.05)^(2/12) – 1)
r =  9.79781526%   
                                   Our answer!

And that’s how I arrived at that solution. I’m sure I’m missing something minor that excel would do for me, but you get the idea.