WASHINGTON, Aug. 23 (UPI) -- Earnings restatements by both Fannie Mae and Freddie Mac, and last week a "Wells notice" from the Securities and Exchange Commission to Freddie Mac suggest that all is not well in the world of housing finance. That may be putting it mildly.

To deal with the technical term first, the "Wells notice" advised Freddie Mac that the SEC is considering initiating a civil action against Freddie Mac in relation to its accounting, which has for the last year been the subject of scandal and has already resulted in several earnings restatements and a $125 million fine.

Fannie Mae and Freddie Mac are the two gigantic stockholder-owned corporations chartered by Congress to engage in home mortgage lending. They borrow money in the capital markets at interest rates only marginally above those paid by the Federal government and then guarantee home loans, allowing such loans to be packaged and sold in the mortgage loan securitization markets at the finest rates. In recent years, their balance sheets have expanded very rapidly, to a level of leverage over twice what would be permitted a commercial bank, as they have themselves invested in home mortgages, using borrowed funds to do so.

There are two risks incurred by Fannie Mae and Freddie Mac. First, there is the risk that the home mortgages in which they have invested or which they have guaranteed will default. Second, there is the prepayment risk. Home mortgages are typically (though not now universally -- about 70 percent currently) made at fixed interest rates, and the homeowner has the right to refinance the mortgage, generally at no penalty -- originally for the simple reason that homeowners need to be able to move. However, if the homeowner prepays, the investor is left with no asset, which is bad news if interest rates have dropped (conversely it's good news for the homeowner -- he can refinance with a cheaper mortgage.)

Fannie Mae and Freddie Mac think, because there are millions of home loans in their portfolio and guaranteed by them, that the laws of probability will keep the default rate fairly constant (albeit fluctuating with the economy) so they can build it into their pricing and then ignore it. They think they can hedge the interest rate risk by using derivatives contracts, expecting that the profits on the contracts will counteract any losses from early refinancing of their mortgage loan portfolio.

The accounting scandal and "Wells notice" suggest that their hedging strategy isn't working, or if it is, that their attempts to account for the derivatives portfolios are hopelessly tangled.

Having spent 5 years managing a derivatives operation, I'm not surprised. I would expect both their insouciance about mortgage defaults and their attempts to hedge the loan refinancing risk eventually to lead them into serious trouble, quite likely, given their excessive leverage, fatal trouble.

The reason is a technical one (no, non-techie readers, please don't glaze over your eyes; this stuff isn't rocket science, it's a misapplication of a high school math theorem that was invented almost 250 years ago. I promise: there are NO formulas and, if you graduated high school, NO math you haven't heard of!)

The Reverend Thomas Bayes (1703-1761) was a British Nonconformist minister who spent his copious spare time researching and writing about probability theory, then fairly recently invented by the Frenchman Blaise Pascal (1623-1662.) He did this by considering experiments whereby you draw balls out of a giant hidden urn full of different colored balls, and see what color they are. His famous Bayes' Theorem (you did this in high school, right?) states that the probability of drawing a blue ball followed by a green ball out of the urn is the probability of drawing a blue ball, multiplied by the probability of drawing a green ball. A big, big step forward in human thought in 1761, when his work was published.

The problem is that Bayes wasn't investing in mortgage portfolios, or valuing options, or thinking about any of the other business problems for which people now use his theorem (sometimes heavily disguised, for example as the Black-Scholes options valuation equation.) None of that stuff had been invented in 1761; if you'd told a 1761 businessman he should be using Bayes' Theorem to make business decisions, working it all out on paper without a computer or even a calculator, he'd have laughed at you.

Bayes' Theorem works only when the events you're looking at have two characteristics: (i) they're truly random and (ii) they're truly completely independent of each other. In real life VERY few events fulfill both these criteria.

Cynics have an intuitive answer to the theoretical beauties of Bayes' Theorem: it's Murphy's Law. Bayes' Theorem says that if each of 4 bits of bad news has a 10 percent probability, the chance of all 4 happening is 1 in 10,000, so unlikely you can ignore it. Murphy says Naah! -- if one thing goes wrong, all the other bad stuff will probably happen too. In real life, Murphy is a more useful mathematician than Bayes.

You have to distinguish between the truly random and the merely unknown. Whether a particular homeowner moves house (and so refinances his mortgage), or loses his job (and so maybe defaults on it) isn't random at all. It depends on lots of circumstances surrounding the homeowner's life that you don't know about, but that are in themselves perfectly deterministic (his wife has a baby, his company gets in financial difficulties, etc.) Even whether he doesn't move, but simply refinances his mortgage, is determined by a whole host of factors that are not random but have nothing to do with interest rates as such (his credit rating has declined, he hates paperwork, he's thinking about moving soon, he needs "takeout" money to buy a car, etc.)

It must be stated and restated: if the event isn't random, you can't use Bayes, indeed you can't use probability theory at all. You can, if you like, use fuzzy logic, but fuzzy logic states that the intersection of four sets of "belief" 10 percent still has "belief" of 10 percent -- a very different result indeed to Bayes' Theorem (the belief of the intersection is the minimum of the beliefs, not their product).

Okay, okay, I'm sorry; you didn't do THAT theorem in high school. Back to the real world of Fannie Mae and Freddie Mac, which are hedging portfolios of home mortgages, using Bayes' Theorem to look at 2 sets of events: (i) homeowners defaulting, and (ii) homeowners repaying their mortgage early (whether by moving or by refinancing their mortgage at a cheaper rate.)

In the case of default, they accept that the default rate moves up and down with the economy, but since they don't see anything more than a moderate recession on the horizon, they don't worry too much about that -- Fannie and Freddie KNOW what happens to mortgage defaults in moderate recessions, they've lived through at least 3 of them.

Wrong. You see this time around, we've lived through a period of very low interest rates and very high house price rises, which hasn't been the case in any previous recession during Fannie and Freddie's lifetime. This can have a big effect on a homeowners' financial flexibility.

For example, if mortgage rates are 8.5 percent, a homeowner with a $40,000 income after tax and social security payments, whose maximum mortgage payment is (say) 30 percent of net income can service a mortgage debt of $130.053. Assuming he makes a 5 percent down payment, the largest house he can buy then costs $136,898 and his property tax, at 3.5 percent of value, would be $4,791. His house to income ratio is 3.42 times. However, if interest rates drop to 5.5 percent, by paying the same monthly amount he can afford a mortgage of $176,121, and a house of $185,391, on which his property tax payment is $6,489. His house to income ratio is now 4.63 times.

By and large, house prices, at least on the East and West coasts, have risen to reflect the decline in interest rates, so people who have recently bought houses are living in much more expensive houses than they traditionally would have done, since it cost more to buy the house they expected, but they could afford it because of the low interest rates.

This is likely to cause problems, because the homeowner's flexibility to deal with his loan is much less, as it's larger in relation to his income. Further, if interest rates rise back to more normal levels, house prices are more likely to decline in absolute terms, because buyers are priced out of the market at the higher mortgage rates. Further, local government spending has risen to reflect the increased property tax income, so property taxes, which generally rise faster than inflation, are likely to be a larger part of a homeowner's budget than traditionally. For all these reasons, a moderate recession is likely to cause much higher home mortgage default rates than has traditionally been the case.

On the refinancing side the problem is that mortgage refinancing rates are very path dependent, while derivatives prices aren't. If mortgage interest rates drop from 7 percent to 5.5 percent, there is initially a surge in refinancing, which then tails off to zero as everybody who wants to refinance their mortgage and is able to do so has done so. If they then rise back to 7 percent and drop again to 5.5 percent, there is not much refinancing the second time round, because only those who took out new mortgages at the 7 percent rate can now refinance profitably.

Derivatives portfolios are not path dependent, and don't behave like this; thus they are a poor hedge to a mortgage portfolio's refinancing risk. Currently, mortgage interest rates are very low, and likely to rise somewhat if only because of rising inflation caused by the surge in oil prices. Fannie Mae and Freddie Mac's derivatives portfolios, designed during a period of more than 20 years in which interest rates generally declined, are likely to show sharp losses in this event, not offset by corresponding profits from higher rates on new mortgage loans, because loan volume will dry up. In 1994, the last brief period of Fed tightening, there were several unexpected nine figure losses on derivatives portfolios, notably by Orange County and Proctor and Gamble. Fannie Mae and Freddie Mac are in danger of even larger losses (because of their larger derivatives portfolios) today.

It is thus probable that if we get a moderate recession accompanied by some inflation, a housing market slowdown and higher interest rates, that Fannie Mae and Freddie Mac will find themselves in severe difficulties, which given their excessive leverage may well prove terminal.

At that point, there will be two options. One is for Fannie Mae and Freddie Mac to be allowed to go bust. This free market solution would remove all the guarantees in two thirds of the housing market, cause devastation in secondary market mortgage bond prices and make it very difficult indeed to get a home mortgage for several years -- thus it would also hugely deepen the recession.

The other alternative is for Fannie and Freddie to be bailed out by the taxpayer. I give you long odds (Bayesian or fuzzy -- your choice!) that the latter course is chosen by our political masters, whichever party is in power. The savings and loan bailout cost $500 billion, this one may well cost us considerably more, since Fannie Mae and Freddie Mac backed debt is around $4 trillion.

At that point, it is to be hoped that Fannie Mae and Freddie Mac top management's blather about their entrepreneurial skill will quieten, and their pay of around the $10 million per annum mark will diminish.

After all, if the United States wants a dozy state guaranteed home mortgage system, it can follow Germany's system of state savings banks and achieve the same thing at less risk and cost. I bet German savings bank chairmen aren't paid more than a few hundred thousand, and I'm sure they almost never bloviate about entrepreneurship!

(The Bear's Lair is a weekly column that is intended to appear each Monday, an appropriately gloomy day of the week. Its rationale is that, in the long '90s boom, the proportion of "sell" recommendations put out by Wall Street houses declined from 9 percent of all research reports to 1 percent and has only modestly rebounded since. Accordingly, investors have an excess of positive information and very little negative information. The column thus takes the ursine view of life and the market, in the hope that it may be usefully different from what investors see elsewhere.)

Martin Hutchinson is the author of "Great Conservatives" (Academica Press, 2004) -- details can be found on the Web site greatconservatives.com.