Arnold Kling  

Hold-to-Maturity Pricing

Morning Commentary... I'm Going to See Singapore for...

Mark Thoma writes,

Now I just have to figure out how the "hold to maturity" price is to be determined, and how purchasing at that price minimizes losses.

Suppose that you owe $110,000 on your mortgage, due in one payment a year from now. The "hold to maturity price" is that $110,000, discounted back to the present. At an interest rate of 10 percent, the price is $100,000.....NOT!

The fair price depends on the probability that you will default. If there is a 50 percent chance that you will default, the fair price is more like $50,000.

[UPDATE: To keep the example simple, I did not talk about the mortgage lender recovering some of their loss by selling the property. Including this factor makes the example more realistic, but it also complicates the arithmetic without adding anything to the point. However, since commenters brought it up, let me add this. Historically, about half the loss is is covered by selling the real estate, although in this market my guess would be that the recovery rate is less. If you can sell the property for $50,000 in case of default, then the value of the mortgage asset is approximately $75,000.]

The probability that you will default depends on the distribution of possible paths of future home prices. Along paths of falling home prices, defaults are much more likely than along paths of stable or rising prices.

It's hard to know how home prices will behave, but right now if I were pricing the risk (something I used to do for a living, unlike the key decision-makers in this bailout), I would include a lot of paths where prices go down. That would make the "hold-to-maturity" prices of the mortgage securities, properly calculated, pretty low in many cases.

I sure hope that Bernanke and Paulson know what business they're getting into. Part of me thinks they don't know. Part of me thinks they don't even care. They're so desperate to try to make the mess go away that they don't think little details matter.

Comments and Sharing

COMMENTS (11 to date)
stylized.fact writes:

Perhaps the idea is to provide banks with as much liquidity as possible for commercial paper rollovers. Hold-to-maturity is the only credible sounding benchmark for such an action. It definitely sounds to me like certain details are being withheld in the name of Keynesianism (you can't handle the truth).

spencer writes:

Generally, the probability of default is built into the interest rate spread.

If the probability of default is 1% the rate might be 10%.

But if the probability of default is 50%, the rate might be 60%.

shayne writes:


In your example, a 50% chance of default would make the value of the loan far less than $50,000 due to the fact that the underlying collateral has a lower current market value than what was loaned against it in the first place. The higher default rate is only one component of the toxicity of the 'toxic paper'.

I heard the Bernanke testimony before Congress this morning and he's obviously making the same mistaken assumption. He said this toxic paper has two values: a. the 'fire sale' value (currently 22 to 53 cents on the dollar of face value, based on yesterday's trades), and b. 'hold to maturity' value that is very close to face value. He further asserts there is a 'real' value - much higher than the 'fire sale' value, and closer to 'hold to maturity'. I suspect the 'fire sale' value is more real. To begin with, it is the law. The value of anything is firmly established in law by offering it for sale, and selling it to a willing buyer at a mutually agreed upon price. Secondarily, I suspect the 'fire sale' price quite accurately reflects the risk premium demanded by buyers of this paper, given the known situation of the underlying assets' market price deterioration.

The only way higher than 'fire sale' prices can be justified - or the government can make a 'profit' in this, as some pundits allege will happen - is if the $700 Billion is used to re-inflate home prices to peak-bubble levels. That is evidently the desired outcome of Bernanke, Paulson and everyone else advocating this 'solution'.

GlennW writes:

If there is a 50 percent chance that you will default, the fair price is more like $50,000.

That seems to be assuming an asset value of $0, or no underlying asset at all. Extreme even with "falling prices."

If the asset value is 80% of the mortgage then a 50% default would result in a current fair price of about $90,000 ((100,000 + 80.000)/2). Even at an asset value of only 50% then the current value would be around $75,000 ((100,000 + 50000)/2). Of course, in the case of default there would be some additional costs to consider reducing these figures a bit.

But, I'm not sure that Paulson et al mean to take into account default in their "hold to maturity" pricing.

floccina writes:

GlennW you also need to add in the legal and other costs of foreclosing.

IMO house prices need to fall because not enough buyers can afford the existing homes to fill them all.

Sarcasm follows:

We can solve this and all our education problems by letting 100 million Chinese immigrants into the country. They will need a place to live, will work hard and their children will do well in those standardized test that we use to judge which countries schools are better.

Les writes:

Required rates of return consist of 3 elements:

1) The real riskless rate - currently very low.
2) Anticipated inflation - fairly modest at present.
3) Risk.

Since (1) and (2) are quite low, risk is the key factor. And risk seems to be very opaque at this time. So we seem to have a "Black Swan" on our hands.

Dr. T writes:

GlennW is completely correct, because in his examples some of the losses in home values at foreclosures are due to a combination of poor market for sales, real estate selling fees, and legal fees. Even with all these circumstances, it is unlikely that the value of the foreclosed property would fall below 70% of the original price.

cent21 writes:

I think you're basically correct, but perhaps missed something.

Perhaps there aren't enough other buyers out there with both deep pockets and the ability to both take a loss and hold the paper to maturity. The rest of the normal bidders for this paper already hold similar paper at a loss. They may be facing a credit squeeze of their own. So, while they would savor at the opportunity to do a Warren Buffet over the entrails, they can't afford to. And even Buffet can't afford to take any but the most under-valued assets with a clean risk profile.

I still think it must be a pretty deep pit for the treasury to be essetially asking for an $800 Billion corporate welfare stimulus plan, just to avoid increasing the probabiliby of a recession. And would bet the pit has to do with leverage.

Why, oh why? I guess the answer is that everyone else was doing it, and it became the only game in town. Particularly with low interest rates and $600 Billion a year of loans from unwary foreigners.

Walt French writes:

"That would make the "hold-to-maturity" ... pretty low in many cases."

Well, this is just the problem, isn't it: the Mother of All Bailouts does nothing to actually remedy the uncertainty underlying MBS assets. $0.7Tril. later, we will have done nothing to fix the uncertainty on the OTHER $5Tril. of loans. It will still be impossible to securitize loans.

This is Paulson trying to subsidize Akerlofian ("used car") lemons a few thousand per car sold and presuming that all subsequent defective cars sold are going to be happily taken by buyers. It seems utterly ignorant about the research into markets of the past decade.

TB writes:

DrT and GlennW must be in areas of modest decline in home values. In San Diego the values have dropped 26% in the last year alone...and trust me they were already dropping before that point. The majority of the loans going bad are in the overly inflated real estate market areas so you must expect more a larger drop in real value.

Steve writes:

The key thing here though is that the hold to maturity losses modelled by S&P ($437bn) are pretty close to the mark-to-market writedowns projected.

In other words, the notion of “markups” to come as the markets recover is flawed.

Global Financial Institutions Eye Another Wave Of Write-Downs As U.S. Housing Woes Spread

A Hold-To-Maturity Estimate Assesses Economic Value In an effort to better estimate the loss in underlying economic value of MBS, we apply a hold-to-maturity approach to all nonprime segments of MBS. Our hold-to-maturity estimate of ultimate losses for the wider range of MBS is $437 billion--and $482 billion including leveraged loans (see table 10). Table 10 All Nonprime MBS Segments: Estimated Losses On A Hold-To-Maturity Basis (Bil. $) ABS CDOs 264 Subprime RMBS outside of ABS CDOs 69 CES 37 Alt-A RMBS outside of ABS CDOs 40 CMBS 14 HELOC RMBS 13 Total 437 Leveraged loans 45 Total including leveraged loans 482 Source: Standard & Poor's.
Date: 2008-09-17 | Similar pages

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