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Tuesday, July 28, 2009

Interconnectedness and the Distribution of Default Risk

I was asked what went wrong that caused economists to miss the financial crisis. For me, a key part of it was the belief in the risk distribution model. Let me give a simple example of how risk distribution works:

There are 100 people, each has $1,000 saved, and those balances are sitting idle, they have not been loaned out.

There are 100 different people who have loan projects that promise to pay more than simply putting the money in the bank (for simplicity, assume bank deposits earn no interest, but if they do, that won't change any of the conclusions drawn below). However, the default rate on these loans is 10%.

Suppose that the individuals with the accumulated savings are very risk averse. In particular, suppose that they only have this money temporarily, they will have their own bills to pay in the future (e.g. they will need to repay other types of loans), and they are just looking to put the money to work safely in the interim. If they lose any principal, they will go into default on the loans they need to repay in the future, and that's not a risk they are willing to take.

But this means no loans will be made. With a default rate of 10%, 10 of the 100 people will, in fact, lose everything, and that would mean going into default. Thus, without some means of sharing risk, none of them are not willing to risk losing all of their savings, at least not at an interest rate anyone would be willing to pay, and the market will not exist.

Now suppose that there are financial market intermediaries who come up with the following innovation to distribute risk. They will accept the deposits and pay 3.5% on them, and they will make loans at 15% (I'm assuming that the demand for these loans exists to avoid complicating things unnecessarily).

Let's see what happens if the savers take them up on their 3.5% offer, and then the deposits are lent at 15%. First, let's look at the original principal. There are 100 loans of $1,000 for a total value of (100)*($1,000) = $100,000. But not all of it is paid back. Subtract off the 10% of loans that default, i.e. subtract $10,000 leaving a payback of $90,000. So the original principal falls from $100,000 to $90,000 due to defaults (assuming a zero scrap value).

But the 15% interest rate is more than sufficient to cover the $10,000 loss so that nobody actually loses anything. To see this, the next step is to add interest to the $90,000 in good loans. Since 90 people pay back $150 in interest each, the interest return is $13,500, more than the $10,000 loss. Thus, the total amount paid back, with interest, is $103,500. Now divide this among the lenders, i.e. divide this by 100 to get $1,035 returned to each person who made a loan. Thus, with the risks distributed across all the lenders, instead of 10 people losing everything, everyone makes 3.5% (I didn't build bank profit into the example, but that's easy to do).

So in this example, rather than 10% of the lenders losing everything, a risk they won't take, they all make 3.5% on their investment. So long as the 10% default rate is accurate, this is a fairly certain return and they will be willing to enter the market.

(Note however that if the default rate turns out to be, say, 25% instead of 10%, then the lenders will lose principal, e.g. at 25% they are only repaid $8,625 each leaving an $1,375 shortage. This could cause them to default on their own loan payments, and that could in turn bring about more defaults in a spreading, domino style collapse.)

Before moving on to what I missed - I'm in no hurry to point that out - note one thing about this example. Risk distribution does not reduce risks overall. It does reduce the size of the risk that an individual faces - nobody loses everything unless every single loan defaults (with zero repayment in every case) - but overall the losses are still $10,000 whether individuals or intermediaries make the loans. There are ways in which financial intermediation can reduce overall risk, e.g. the expertise of the intermediaries at assessing risk is supposed to reduce the 10% default rate, and generally it would, I just didn't build this in. But the point is that risk distribution does what it says, it distributes risk, it does not reduce it. Many people misunderstood this.

O.K., here's where I went wrong, or one place anyway. I thought that default in the mortgage market would be like the default of these loans. The defaults would be distributed through complex financial products not just among U.S. lenders, but throughout the world, and that meant nobody would lose very much, certainly not enough to cause big problems. If problems developed, everyone would lose a little bit just like above. This belief was widespread among economists. The financial innovation driven by fancy mathematical models was supposed to assure that risk was widely distributed, and the insiders in these markets repeatedly reassured everyone that if problems did develop, they would be so widely dispersed that there was nothing to worry about.

But that's not what happened. Why? One reason is simple. The default rate was higher than expected, and that brought about unexpected losses. For example, above a 25% default rate means losses of $1,375 on the $10,000 investment leaving a shortage as this money is needed to repay other loans. But those losses still should have been widely dispersed, widely enough to avoid big problems.

But there's something else that explains how these losses spread to create such a big problem. The degree to which the people making the loans and taking out the loans were interconnected was misunderstood (that is, risks were more concentrated than we thought). The people borrowing and lending the money had far more financial interconnections than we noticed or knew about - there was a lot of borrowing and lending among them that was hidden or ignored - and when the higher than expected number of borrowers defaulted, that meant some of the people expecting payments from the lenders were forced into default as well. In the example above, remember that the lenders only had the money short-term, they would need the money later to repay their debts and were just trying to make something on the accumulated balances in the intervening period. But with losses of $1,375 rather than the anticipated gain, they are short on funds and hence must sell assets, call in loans, reduce consumption, etc. to try to accumulate sufficient cash balances to pay what they owe. But not everyone will be able to come up with the money they need, especially as asset prices fall as they are put up for sale, loans dry up, etc., and that will cause more defaults and the problems will spread. Thus, as lenders and everyone else try to rebuild what was lost so they can pay their own bills, that causes even more difficulty, and the result is more defaults on loans, and a process that feeds on itself in a downward spiral of defaults and further problems.

So a key thing I missed was the degree to which these markets are interconnected, and that may explain why I've emphasized finding better measures of interconnectedness, and then insulating markets against it as part of the reform process (and leverage is a key factor driving the interconnections).


Update: As a follow-up to some of the discussion in comments, here are some past posts on the cause of crisis:

    Posted by on Tuesday, July 28, 2009 at 12:34 AM in Economics, Financial System | Permalink  Comments (36)


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