Why Tranche

Robert Waldmann

Still almost fishing from archives, but this time I think the version after the jump is maybe even less incoherant than the old version.

Quite a lot of pooling and tranching has been done in the past decade. I think explanations of this fact offered by the tranchers can’t be accurate or at least sure aren’t complete.

So the idea is to set up a special purpose entity which purchases a portfolio of similar assets and issues claims on the income from those assets in tranches. The top tranche has a stated fixed payment. Owners get all the income of the SPE up to that level. A second tranche has a stated fixed payment and gets the income, if any, left after the first tranche has been paid up to that level. Maybe a third tranche is sold. Finally there is a last or equity tranche which gets what’s left over. Typically, the sum of the prices of the trances is greater than the price of the underlying portfolio, so huge amounts of money have been made by pooling and tranching. why ?

A standard argument is that tranching is useful to investors with different attitudes towards risk. The more risk averse like more senior tranches. It is very very hard to make sense of this argument using standard simple finance models.

First the simplest. Assume that assets and agents last 1 period and that agents have constant absolute risk aversion. Assume that there are no non traded assets so investor’s portfolio of traded financial assets is their only wealth and source of income. Agent’s have different coefficients of absolute risk aversion.

In this case agent’s demand for each risky asset will be inversely proportional to their coefficent of risk aversion. All agents will divide their wealth between the safe asset and the whole pool of risky assets. This means, in particular, that all agents will buy tranches in the same proportions so they will reverse the tranching process.

Ok how about constant relative risk aversion. In this case all agents will buy risky assets proportional to their wealth divided by their coefficient or relative risk aversion. Again they detranche.

How about infininitely lived agents in continuous time. same as above.

The existence of agents with different risk tolerance simply does not explain tranching.

OK how about non traded assets. This would typically include ones human wealth or labor earnings (including future labor earnings). 13th amendment says it can’t be bought and sold. On average this is larger than financial wealth (roughly twice financial wealth). It matters a lot.

Agents will not like assets whose returns are positively correlated with the returns on their human wealth (their labor income). So for 2 agents A and B, the junior tranches of some pool might be worth much more to B than to A, because the returns on the pool are more correlated with the labor income of A. Typically, the most senior tranche will be worth more to B than to A. Since it has low variance, it has low correlation with the labor income of A, but stil it is better for B than for A.
I don’t see any plausible way how untraded assets can explain tranching.

OK transactions costs. Maybe the amount of a pool that a risk averse agent would buy is so low that it is not worth paying transactions costs. Well first, the idea that huge numbers of people in finance are employed reducing transactions costs is very odd. Their salaries are transactions costs. The idea sounds totally crazy. Also I don’t see any link with tranching as opposed to pooling.

It really seems to me that it is very hard to explain why tranching is profitable using standard models in finance. I have assumed that agents care only about the distribution of returns on their portfolio and that they are rational. I think one or both assumption must be relaxed.

First irrationality. It would be irrational to assume that all AAA rated instruments are absolutely safe. It would also be irrational to assume that they are equally safe. The ratings aren’t supposed to be comparable across asset classes. AAA rated corporate debt may be less safe than AA rated sovereign debt. The rating agencies don’t claim or even suggest otherwise. Only a very irrational investor would think he was getting something for nothing by buying a high yielding AAA rated CDO and assuming that it is as safe as an AAA rated treasury security. Somewhat less irrationality would be required to think one was getting something for almost nothing. I’m pretty sure that this is a large part of the explanation.

Second many investors have interests other than risk and return. Banks have capital requirements based on the rated risk of their portfolio. Under Basel I rules, that means based on the credit rating of instruments in the portfolio with no consideration of portfolio theory. Thus tranching is useful to agents who want to bear more risk, but don’t want to set aside more capital. Obviously a source of profits from tranching was such regulatory arbitrage.

Finally, I suspect, that many privatre rules explicitly referenced credit ratings and just added up over assets without any consideration of diversification. I would guess than many endowments and pension funds and such had explicit rules about how a share of the money had to be invested in AAA securities. Oh and rules rewarding the managers for return.

Basically, I think tranching was profitable for two reasons. It enabled the tranchers to separate fools from their money and it enabled people investing other people’s money to achieve the appearance of lower risk for the same actual risk.

At the moment, I can’t think of any sound argument against a law banning pooling and tranching.