I gave an example of tranching when looking at the Bear Stearns product a few days ago. Now I want to clear up some possible confusion regarding the practice.

### Quality is Very Expensive

Let us say, just for the sake of an argument, that we have a pile of AA rated securities that we want to securitize. We have two choices:

- We can securitize them in one big bucket, rated AA, or
- We can divide it in two tranches. The first gets priority in distributions and will be rated AAA; the second will be junior and rated A

The second choice will be familiar to preferred share afficionados – it’s the same process that is used in split share corporations. The holders of the senior tranche (the preferred shares) don’t really care a lot about the underlying portfolio, as long as it’s reasonably good quality and there’s a lot of it! The junior tranche holders care a lot, because they’re taking the risk they’ll get paid less than expected in exchange for an expected reward of getting paid more.

It will always be more profitable to the underwriter to split the issue because bond investors pay up for quality. I might get 10 cents less than base price for the junior tranche, but I’ll get 25 cents more for the senior tranche.

This is even more important with the mortgages, because it’s not a 50-50 proposition … there is a better than even chance any particular mortgage in the underlying pool will behave exactly as expected. There is, shall we say, some debate over just what the default probability is, but let’s make up some numbers. The mortgages are all one-year term. I expect 10% of the underlying to disappear completely; interest is received equal to 20% of the original pool; therefore, my return on the overall pool will be 10%.

These numbers are obviously very exaggerated. If anybody wants to make up better numbers – or, even better, wants to dig through ratings reports to get actual numbers – be my guest and let me know what you come up with. Put it in the comments or eMail me and I’ll put it in the post.

OK, so I look at the market and I see that AAA instruments yield 5%, while A instruments yield 20%. So what I do, is I create two tranches. The first tranche is senior and comprises $80 of the original pool of $100. It gets an AAA rating because the pool as a whole can lose 20% of its original value and this tranche won’t even notice. That’s double the loss rate I expect.

On the senior issue, I pay only 5% interest, which comes to $4.

The second tranche, worth $20, takes the first loss, which is expected to be 10% of the original pool, or $10. If the end value of the second tranche is $24 at the end of the year, it will have yielded 20% on invested capital. So on this tranche, I pay $14 from my interest receipts and the expected value of the tranche is $20 (invested) – $10 (loss on pool) + $14 (interest) = $24.

Now I work out my expectations: I’m going to receive $20 interest from the underlying pool. I pay $5 interest to the first tranche and $14 to the second tranche. Hey, looky looky! There’s $1 left over! I’ll invent an IO (Interest Only) tranche to receive that interest and keep that tranche for myself!

Bingo! Financial alchemy!

### Why is Quality Expensive?

The basic reason is segmentation, which will be familiar to readers of my paper on Portfolio Construction. There might be some investors who don’t have a portfolio big enough to diversify. Maybe they can buy only one bond; maybe they’re just a little bigger and are only buying 5 bonds to make a ladder. Five bonds is not a lot. If one goes bad, that’s 20% of the portfolio. Such players, too small to diversify away specific risk, should stick to higher quality instruments so that their portfolios have a greater chance of behaving as expected. So these players are logically restricted to higher quality instruments and shouldn’t invest in our junior tranche. They have to buy the senior tranche virtually irrespective of how much extra they could expect from the junior, because they are highly risk-averse.

Another reason for quality segmentation is fiduciary policies. Maybe the East Podunk Widows’ and Orphans’ Fund has a set policy: AAA only. They’ll go to jail if they buy our junior tranche.

There’s liquidity as well. The senior tranche is worth $80, the junior tranche $20. It’s not unreasonable to expect four times as much trading of the senior tranche in the secondary market. Market timers, for instance, will have a prediliction for the senior tranche because they’ll be able to trade out of it more cheaply if the market moves their way and they want to realize a capital gain.

All these factors conspire to ensure that interest rates on the lower grades of paper will (normally) be higher than they would need to be if default risk was the sole consideration. Therefore, an investor who (i) has no arbitrary limits, and (ii) can purchase a well diversified portfolio and (iii) has no intention of trading a lot can (normally!) achieve excess returns by moving down the quality scale.

This was exploited in the late ’80’s, when the junk bond market was invented.

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