## Tuesday, September 23, 2008

### Hold-to-Maturity Pricing

by Calculated Risk on 9/23/2008 06:11:00 PM

An interesting question is why do Bernanke and Paulson believe the Hold-to-Maturity price is higher than the current market price for MBS?

One possible explanation is market failure based on information asymmetry. Mark Thoma explores this question: "Hold to Maturity" versus "Fire Sale" Prices

Let me try to give a defense of paying above current market prices (in a devil's advocate sense). For markets to function according to competitive ideals, full information must be available to all market participants. When information is lacking, or when it is asymmetric, the outcome is inefficient relative to the full information outcome.

The nature of these assets - their opacity as it has come to be called - makes full information unavailable. I'm not sure how asymmetric information is, people holding the assets don't know themselves whether a particular asset might blow up and lose it's value or not, but there is some degree of asymmetric information in these markets (a standard lemons problem).

This is market failure due to lack of full information, and asymmetric information to the extent it does exist, is depressing prices.
In this case, I don't think the information is asymmetric because both buyer and seller are aware of the characteristics of the MBS. There is uncertainty regarding future house prices (and MBS performance is related to house prices), but that isn't a market failure.

Professor Thoma also links to Professor Kling: Hold-to-Maturity Pricing
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.

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.
First, this analysis assumes 100% loss severity in the event of default. If there is a 50% chance of default, half the time the mortgage will be worth \$110K discounted back to the present. But if the borrower defaults, the value will not be zero since there is a recovery value on most mortgages. Kling apparently assumes a loss severity of 100% in the event of default (perhaps he was thinking of a 2nd mortgage), but a more normal severity would be around 50% or \$55K discounted back to the present. So in this example, and using a 10% discount rate, the mortgage would be worth \$100K * 0.5 + \$50K * 0.5 or \$75K at present.

But I think this might provide a clue to the pricing disparity: because of the uncertainty in future house prices (and MBS performance) potential buyers are probably using a higher discount rate than Bernanke / Paulson. Typically the higher the standard deviation of the potential outcomes (higher risk), the higher the discount rate. So even if investors view the future price the same as Bernanke/Paulson, they might view the NPV as much lower. In addition, the cost of capital is higher for private investors - also impacting their discount rate.

Perhaps Bernanke / Paulson believe that aggregating assets will lower the risk. Usually when you aggregate assets, the overall volatility decreases. This is almost always true for holding a group of stock (the beta on the S&P 500 is lower than the beta on most stocks in the S&P 500). But if the assets are all impacted by one parameter - in this case future house prices - aggregating assets does not lower the risk.

This would make a great question for Bernanke tomorrow. Why does he believe the Hold-to-Maturity price is higher than the current market price? Is this because of some market failure? Or because of different discount rates? Or some other reason?