Arnold Kling  

The Hold-to-Maturity Nonsense

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This morning, I realized why people think you can make money holding mortgage securities to maturity. They think that these securities are bonds. In reality, they are (or include) short option positions.

A short option position is not something that you can just finance. It may be exercised against you.

The option that is embedded in mortgages is the borrower's option to default. That was the insight of Chet Foster and Bob Van Order that I referred to in my chapter. The default option tends to be "in the money" when the house price falls by more than the amount of the down payment. A lot of mortgages out there have default options that are in the money or close to it.

Anyway, you cannot talk about holding to maturity a portfolio of short positions in options. Sure, if nobody defaults you get to hold to maturity. But depending on circumstances, some people will default, at great cost to you as the security-holder.

If Bernanke and Paulson really believe the hold-to-maturity argument, then they know even less about mortgage crecit risk than I thought. Let me offer a variation on the explanation in the update to my previous post.

Suppose we play a dice game, where you roll one six-sided die. If it comes up 1, 2, 3, 4, or 5, I give you one dollar. If it comes up 6, you give me everything in all your bank accounts. Will you probably win playing this game?

An old AP statistics exam had a question quite like this (I teach AP stats in high school). The correct response was to contrast the most likely outcome (winning) with the average outcome (losing). That is the sort of game that the government is playing in buying mortgage securities.

But win or lose, the government is not necessarily buying undervalued securities. It is buying securities whose value has been marked down because they are like short positions in options that are not far out of the money, if at all. That markdown may be quite large, but that does not necessarily mean that it is inappropriate.


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COMMENTS (6 to date)
Shivering Timbers writes:

By this logic, doesn't every non-government bond have a put option embedded in it?

GM (to take a random example) always has the option of defaulting on its corporate bonds if the bond is "out of the money" (i.e. the company's cash position is insufficient to cover the payments due). The likelihood of that happening has to be priced into the bond.

I don't think B and P are claiming that the "hold to maturity" price is the same as par value on these mortgage-backed securities; that would clearly be absurd. Rather, they are claiming that the current market price is less than what a rational investor would expect to get back even after all defaults are factored in (or, if you prefer, after the implicit put option is properly priced).

You can argue about whether the "hold to maturity" value of these securities would be 30 cents on the dollar or 60, but nobody is claiming it's 0 or 100.

Bob Knaus writes:

Thus arguing for a quick attempt by the Fed to ratchet up inflation expectations by a percentage point or two. That should raise home prices by enough to put your "default option" back out of the money.

If the current Fed target of 2% inflation serves as sufficient "social lubricant" to eliminate most wage cuts for unproductive workers, might not a target of 4% eliminate most defaults by unprofitable home borrowers?

So sorry for all you bondholders and fixed-income folks out there :-(

aaron writes:

How do you expect them to direct the inflation at houses? Right now the price of everything consumable seems to be going up, but houses aren't.

Bob Knaus writes:

Oh, that's precisely my point. You can't direct inflation at houses. Inflation is a monetary thang. It affects the whole system.

Inflation will be the horrible consequence of the bail-out. But, it will rescue home borrowers, by allowing them to pay off their mortgages with less valuable dollars.

dwg writes:

Shivering Timbers makes a point with respect to any non-corporate bond being a "put option."

I believe this highlights the importance of the lender requiring the "put option" holder to have equity in the enterprise to reduce the risk of the option's exercise. And other factors also bear on the analysis. For example, California does not allow a deficiency judgment against a home borrower who walks away from a mortgage, while other jurisdictions do. Consequently, everything else being equal, this attribute of California law should have increased the amount of equity required by lenders in California, or possibly a requirement by first lien holders that a second mortgagee participate to take a portion of the non-equity share.

Since any lending situation carries an aspect of a put option, the analogy helps to put into perspective the importance of equity requirements, or other factors that permit this aspect of the transaction to bear less weight in the analysis.

kingstu writes:
By this logic, doesn't every non-government bond have a put option embedded in it?

GM (to take a random example) always has the option of defaulting on its corporate bonds if the bond is "out of the money" (i.e. the company's cash position is insufficient to cover the payments due). The likelihood of that happening has to be priced into the bond.

I don't think B and P are claiming that the "hold to maturity" price is the same as par value on these mortgage-backed securities; that would clearly be absurd. Rather, they are claiming that the current market price is less than what a rational investor would expect to get back even after all defaults are factored in (or, if you prefer, after the implicit put option is properly priced).

You can argue about whether the "hold to maturity" value of these securities would be 30 cents on the dollar or 60, but nobody is claiming it's 0 or 100.

This is exactly right! There is no question there are going to be defaults but how many defaults must occur to justify a price of 50. In addition, if a default rate of 50 is reached...what would the recovery value have to be for the foreclosed properties?

If you hold a portfolio of 10 mortgages at a value of $1,000,000 and the price of those mortgages falls by 20% and 50% of borrowers default...you still recover near 80% on the defaults and 100% on the ones who don't default.

Pay on time - 100% recovered
Defaults - 50% recovered at 80%

It seems to me...you would only lose 10% in this scenario...

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