Sunday, 21 June 2009

An Excerpt from Vol. 4: A Primer on Bond Mathematics (2 of 2)

In its original form, the equation FV = PV (1 + i) assumes nothing. It merely takes the facts of the transaction – $100 lent at 4% for one year, in our example – and calculates how much money is due to the end of the term. Of course, the lender, like all lenders, assumed that he would be paid back in full, otherwise he would not grant the loan. But that is the lender’s assumption and does not affect the equation. Even if the borrower defaults, the validity of the relation would stand, as it only calculates what should be due to the lender.

Things change when we solve the equation for the present value, PV:

PV = FV/(1 + i)

Mathematically, all we did here was to rearrange the equation, a simple operation familiar to 6th graders. But that technical operation shifted the focus to the present value.

This emphasis and the name “present value” would confuse our borrower and lender. “What do you mean by the ‘present value’ of the loan?,” they would demand to know.

– “The present value is the current value of the loan: how much it is worth today.”

– “What do you mean by the ‘worth’ of the loan”?

–“That is how much the loan is worth! How can we say it? How much it cost the lender to finance the loan”

–“That is $100. It is the loan’s principal. Why do you call it the present value?”

But the present value is not the same as the principal. The new vocabulary is telling us that we are no longer in the private world of borrowing and lending between two individuals. Rather, we have entered the world of securities and markets. The relation PV = FV/(1+ i) expresses relations in the markets and presupposes them. Only then the concept of present value becomes meaningful.

To presuppose markets is to presuppose buyers and sellers. The new form of Eq. (1) assumes that when the creditor takes his IOU to markets, he will find Moneybag waiting for him, ready to buy the note at its “fair value”.

What happens if there are no buyers?

To answer that question, we must ask why and under what conditions would there be no buyers?

There could be two reasons; one particular, the other, general.

The particular reason has to do with the perceived “credit risk” of the individual security, credit risk being the risk that the borrower will fail to pay back the loan and interest on the due date. If there are concerns about our borrower’s ability to pay back the loan, Moneybag, like other potential buyers, will stay away. No one comes to market to suffer a loss, and with many securities to choose from, there is no reason to risk one’s capital on a risky bet.

Our creditor would react to this situation the only way sellers all over the world react when the demand for what they are selling softens: by discounting the price. Instead of asking $100, which is the note’s original “fair price”, he marks it down and offers it at say, $98.

In itself, this act of discounting is unremarkable. But something interesting happens on the technical side, when we substitute the new price in the PV equation. With the future value unchanged at $104 – it is the defining characteristic of the bond and cannot be altered – the one variable that must change is the rate i:

PV = FV/(1 +i)

98 = 104/(1+i), or:

i = 6.1%

Technically, this was expected. In equation FV = PV (1 + i), the bond price (PV) and interest rate i are inversely related. If rate increases, the price will decrease. Changing the order, it stands to reason that if price decreases, the rate will increase. This is no different than saying that if the area of the rectangle remains constant and its length decreases, then its width must increase.

Meanwhile, we have said nothing about interest rates in general. That is another way of saying that we assumed they remained unchanged. The increase in rate is therefore something specific to our particular security. That something is the borrower’s potentially deteriorating finances.

What is this rate? That is, what does 6.1% a year correspond to, or represent?

In the nomenclature of modern finance it means that if the borrower were to ask for additional loans, he would not be able to secure it at 4% and would have to pay 6.1%.

This conclusion is counter intuitive. Even primitive societies treat their vulnerable members with extra care. Certainly in the liberal democratic societies we are expected to see senior citizens, for example, on account of their reduced income, receive special discounts for a wide range of social and private services from transportation to movies. “Give me a break” is the cry of the hurt and vulnerable that demands a more lenient treatment. Obama administration’s Helping Families Save Their Homes Act fell squarely into this category before it was gutted out by the lobbyists.

In the case of the financially vulnerable, though, the fundamental relation of the bond mathematics dictates the opposite: if a borrower has trouble meeting his obligation, then interest rates on him must rise.

Such a “remedy” at once reveals the viewpoint of Eq. (1), which is that of finance capital. Far from being an abstract, neutral relation expressing a general truth, Eq. (1) expresses the power relation in a social structure in which finance capital dominates.

Under these conditions, the well being or survival of individual borrowers is not of concern – not because finance capital has “no heart” but because such matters are irrelevant. “So says the bond,” finance capital’s spokesman, Shylock, declares, further demanding that the judge second his view: “Doth it not, noble judge?” And when the judge asks him to bring a surgeon to attend Antonio's wounds lest he bleed to death in consequence of giving a pound of flesh, Shylock inquires: “Is it so nominated in the bond?” Therein lies the basis of the contract law which is the centerpiece of the Anglo-Saxon jurisprudence. All the learned erudition the law scholars at Yale and Harvard and the pompous musings of the U.S. Supreme Court judges on the subject of contract law never go beyond the self-serving utterances of this usurer.

As finance capital tightens its grip on the economy, its viewpoint is presented as a universal truth: the less credit-worthy the borrower, the higher the interest rate he must pay. Michael Milken’s junk bond operation in the 1980s was based on this idea. A straight line connects him to the recent sub-prime mortgage fiasco.

(A reader in the comment section asked whether interest rate is always positive. That, too, is the question that finance capital floats. Setting aside some technical exceptions such as when a security “goes special” in the repo market, the interest rate is always positive in the sense that the lender will always charge the borrower; a negative interest rate means that a lender will pay you interest to borrow his money. This is prima facie absurd. However, if the rate is 4% and inflation is running at 5%, the lender presumably loses 1% when lending. It is in that sense that the interest rate for him is negative. That, needless to say, is also the viewpoint of finance capital.)

The subject of the borrower’s deteriorating finances has been extensively researched in finance. The borrower’s probability of default (PD) and the lender’s exposure at default (EAD) and his loss given default (LGD) are extensively studied. Google these terms to see what I mean.

But then there is the general case of why there might not be any buyers in the market. In the aftermath of the Lehman bankruptcy in September 2008, the commercial paper market completely shut down.

Under this condition, no security, regardless of the financial health of the issuer or borrower, would find a buyer. The creditors holding the IOUs would cry in frustration: “But this security of mine is absolutely guaranteed to pay back $104 at maturity.” To which the market would reply by quoting the oft quoted line from The Godfather: It’s not personal Sonny!

Modern finance has nothing to offer on this topic. You will sooner find Taleban mullahs writing about distilling single malt whiskey than finance scholars of the Western liberal democracies writing about this subject – and for a good reason. The main pillar of modern finance, Equation (1), does not lend itself to even considering the question of the absence of buyers. Why there would be no buyers, i.e., why markets would break down, is something completely outside the realm of its consideration. In fact, the entire theoretical edifice of modern finance and economics is based on the assumption that every seller brings his own buyer to the market, a preposterous assumption that is refuted thousands of times a day every time a commercial is aired, an advertisement is posted, a sales call is made and a price is discounted. So in the aftermath of Lehman bankruptcy, when the CP market shut down, all the best and the brightest of finance in business and academia could offer was that buyers had “gone on strike”!

Why and under what condition buyers would disappear en masse from a market is the subject of Vol. 4 of Speculative Capital. The condition is the prerequisite for the realization of systemic risk, its trigger point.

It is under these conditions that the role and activities of the Federal Reserve call for a brief comment.

For the past several months, the Fed has been trying to reduce the interest rates and particularly, the mortgage rates. To that end, it has been buying Treasuries – that is called “quantitative easing” – and the agencies, the latter being the IOUs of Fannie Mae and Freddie Mac. The logic is that buying the securities would increase the demand for them and thus, their price. (Remember supply and demand! If the price of IOUs increases, “their” interest rates would decrease.) The understanding of the members of the Board of Governors of the Federal Reserve of the nature and role of interest rate in the country – and hundreds of analysts, economists, policy makers, ex-banker, MBAs and quants that they employ – boils down to this embarrassingly crude logic. Therefore, in the face of rates behaving in the most unexpected manner, they have nothing to say. “Learned helplessness” has become de rigeur.


The Fed, at the same time, is being assigned the role of supervising the financial system with the purpose of preventing a systemic collapse. But with its mechanical view of how markets work, it would not know why buyers might suddenly vanish. The subject of finance is not the psychology of buyers and sellers but the laws of movement of finance capital. This subject is not simply within the Fed’s theoretical ken.

The setup reminds me of an Iranian poem on the eve of the Mongolian attack on Iran. The poet wrote:

The king is drunk, the world is in chaos and the enemies are front and back;

It is well too obvious what will come out of this.