Wednesday, April 02, 2008

On the negative concavity of sentences with improperly nested prepositional phrases of jargon and discussing complex issues.

National treasure Mark Kleiman directs me to national treasure William K Black (of whose existence I was unaware). Black appears to be a stunningly brilliant accountant ?!?!?!? who saw the S&L crisis coming. Kleiman flags Black largely because Black has the goods on McCain.

William Black (not to be confused with Fisher Black) explains the foolishness of relying on models to price financial assets (I'm being unfair. actually Fisher was well aware of the folly of people who justified their recklessness by appealing to his academic research).

The basic point is that regulators must not allow investment banks to use proprietary models to value their assets, because the properties of proprietary models belong to the proprieters which perpetuates perilous improprieties. It's like having the fox count how many chickes are left in the chicken coop.

Now I am going to complain that Black's English is unclear with persnickity picayune pignoloria. Consider

Consider, particularly given federal pay caps and the extraordinary salaries on the Street for those with advanced skills in constructing models, how impossible it becomes for regulators to try to prevent this abuse (even if they had meaningful regulatory authority over investment banks). Consider the practicalities of trying to explain, and prove, to a judge that the properietary model understates risk by assuming a normal distribution when in fact the tails are unusually fat and truncating the distribution at 95% (which is still common with Value at Risk (VAR) models).


After much effort, I realize that this sentence makes sense if prepositional phrases are clearly indicated say [with square brackets] nested, if necessary ((in double parentheses [with the risk of confusion])). My keyboard doesn't support curly braces.

"Consider the practicalities of trying to explain, and prove, [to a judge] that the properietary model understates risk ((by assuming a normal distribution [when in fact the tails are unusually fat] and truncating the distribution at 95%)) (which is still common with Value at Risk (VAR) models)."

The problem is that there is nothing in English which corresponds to the second ], so the sentence, as written, must be read

"Consider the practicalities of trying to explain, and prove, [to a judge] that the properietary model understates risk [by assuming a normal distribution when in fact the tails are unusually fat] and truncating the distribution at 95%] (which is still common with Value at Risk (VAR) models)."

That is as asserting that the fat tails are truncating the distribution (fat they may be but they are also sharp). English does not support nested prepositional phrases. The sentence can be made comprehensible using standard English by adding the word "by" -- just two letters as in

Consider the practicalities of trying to explain, and prove, to a judge that the properietary model understates risk by assuming a normal distribution when in fact the tails are unusually fat and by truncating the distribution at 95%] (which is still common with Value at Risk (VAR) models).

Which is unambiguously

Consider the practicalities of trying to explain, and prove, [to a judge] that the properietary model understates risk ((by assuming a normal distribution [when in fact the tails are unusually fat])) and ]by truncating the distribution at 95%] (which is still common with Value at Risk (VAR) models).

So then I say WHHHHHAAATTTTTT they truncate the tails in Value at Risk models !?!!?!?!! You have got to be kidding me !!?!!?!?!! The whole point of assessing risk is to avoid going bankrupt when one of the fat but sharp tails slashes your equity. This has to be a joke right ????

Back to English

"Then add in trying to explain why the negative convexity of the implied prepayment option in (U.S.) mortgage instruments"

In English "negative convexity" is called "concavity" just as "negative up" is called "down". Now I think I understand what Black means. The value of the implied prepayment option is a convex function of an underlying variable (an interest rate -- I want to repay if I can refinance at a lower rate). This convexity is negative for the owner of the mortgage bond, because the bank have written the options. The value of the mortgage bond is therefore concave in the interest rate. This means really low interest rates hurt bondholders as the value of the option they have given to homeowners increases. Also really high interest rates are, as always, bad for bondholders because the bonds are long term nominal assets.

Look, if you even think of trying to explain these things to a judge, you have to learn how to avoid nested prepositional phrases and newly invented phrases like "negative convexity" which cause negative clarification.

This is important, because Black does indeed have the goods on McCain and he better learn how to explain himself to voters who are less attentive than judges and maybe even to journalists (a negative probability event ?).

4 comments:

Felix said...

Robert, convexity is the second derivative of the price-yield curve, or the first derivative of duration. There's no such thing as concavity.

http://en.wikipedia.org/wiki/Bond_convexity

Robert said...

Dear Felix

I am surprised to learn that "there is no such thing as concavity." IN fact, "concavity" is an english word with a set of definitions. It is, for example, a technical term in math where a function which has a negative second derivative is concave (although a concave function need not have a second or even a first derivative).

On the other hand the convexity of a curve is the fact that the curve lies below the line connecting two points on the curve. In standard mathematical English "non convexity" is used to refer to the case in which this does not occur. "Non-convexity" not "negative convexity."

I think you meant "there is no such thing as 'bond concavity'." I suppose there isn't. I will note that I did not write "bond concavity."

Now I hasten to add that I am not and was not really criticizing Black. Black wrote a deliberately obscure paragraph to illustrate how difficult it is to regulate financial market operators. His points were two. First the issues are genuinely mathematical and therefore difficult for people to understand without study. Second that the people who do not want to be regulated use deliberately obscure language to confuse regulators and as a barrier to entry to their profitable market.

For example, using "convexity" when normal Mathematical English would use "second derivative" and "negative convexity" of a curve for "concavity" of that curve.

I think the solution is for regulators to require the people they regulate to use standard terms with their standard meanings (so a reply to an inquiry including the phrase "negative convexity" would be held to be non-responsive).

No matter how rich people are, they should not feel free to re-defnie standard mathematical terms, at least not when a regulator legitimately demands information.

In fact, there are restrictions on the language which can be used in contracts. Mathematical notation is not allowed, unless it is "explained" by writing it out in English (in which case the English is authoritative). In fact, non one can follow math written out in English without translating it into mathematical notation, but ... don't tell it to me tell it to the judge (you won't convince him or her).

It is entirely possible for regulations to be rewritten to forbid the use of the phrase "negative convexity" in communications with regulators (the first amendment guarantees your right to use it in private conversation).

Of course this would be a silly thing to do. My guess is that financial market regulators are perfectly familiar with the new usage of "convexity" current among financial market operators and have long forgotten that the word is used by more pope with its standard meaning (which is what makes the standard meaning standard). and that it has been used for centuries by mathematicians with that standard meaning .

This comment of mine is utterly silly (I hope and assume that no one will read it). still I have no intention of allowing people to re-define "convexity." In practice, that means that if I were sent a manuscript with the phrase "negative convexity" in it, I would recommend that it not be published unless the phrase was corrected to "negative second derivative of the price yield curve."

In the scholarly literature, at least, changes in the meaning of technical terms should not be allowed.

And don't get me started on how assets may be liquid or illiquid but markets are thick or thin. Or ... well I have long since surpassed self parody and become a bore (I assume no one is reading this).

Anonymous said...

Who should I get in contact with about a states own laws about mortgage broker bonds and as such, how would I get a mortgage bonds form? I life in England and am considering moving to America, don’t know where yet however I was doing some general reading about housing and came across the term mortgage broker bonds and am a little confused, is it a mortgage or a loan to acquire a mortgage?
Also if I want to set up life insurance do I need insurance bonds? Or can I simply open a policy with a company? I’m a little confused by some of the jargon. I am not moving anytime soon but thought I should be aware of things I will need to understand.

Robert said...

Dear anonymous

Don't ask me. I am clueless. I live in Italy, don't own life insurance and have never owned a mortgage bond or borrowed money from a bank.

Mortgage bonds are for investors not home buyers (who get a plain ordinary mortgage). It is very hard to know what a mortgage bond is worth, so they are an investment for super sophisticated investors (who have themselves lost tens of billions on them recently). I wouldn't touch one with a ten foot pole.

Now it is possible in the USA to get a mortgage the old fashioned way -- by going to a bank or savings and loan (I think like a UK building society). One can also go to a mortgage broker who will claim that he or she is looking for the best mortgage for you. Many of them are crooks.

Kevin Drum has a good post on this http://tinyurl.com/3tw5z9. Basically it is a very bad idea to have anything to do with a mortgage broker if you are not rich and especially if you want a "sub prime" loan, that is if you are the sort of borrower who has trouble getting a loan.

If you don't have a very high income and/or don't have a lot of cash in hand for a downpayment, I (who knows nothing really don't listen to me) would advise you to avoid mortgage brokers like the plague.

My general advice is that if it is something US specific that you can't do in the UK, it is probably a bad deal and don't do it.