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The Economic Consequences of Mr. Greenspan

The World Could Be Sucked into the Blackhole of Zero Interest

December 7, 2001


Economists and the financial press have failed to sound the alarm as a - so far unprecedented - curse hit the world: the rate of interest in Japan started plunging to zero. While the public is kept in the dark, authorities are trying desperate measures, including the encouragement of and subsidy to the yen-carry trade, in the hope to relieve the downward pressure on the rate of interest in Japan through the sale of Japanese bonds - to no avail. The yen carry-trade is the very mechanism whereby the deflationary tumor metastasises across the Pacific. What it does is merely to shift the downward pressure on the rate of interest from Japan to the United States. From this vantage point, the gold-carry trade is also highly deflationary as it also contributes to the downward pressure. The world has been hit by the greatest deflationary iceberg in economic history, and the captains of the international monetary system are busy rearranging the deck-chairs, telling passengers that the boat is unsinkable.

A reliable indicator of deflation is the rate of interest falling towards zero. It can be compared to a blackhole the attraction of which is hard to escape and from where (just as from Hades) no one has ever returned. Why is a zero-bound rate of interest such an unmitigated disaster? Because, as we shall see, it makes the (present value of) debt go to infinity - just like gravitation becomes infinitely large inside of a blackhole of the physical universe.

There are, in fact, two blackholes in the economic universe: blackhole #1 is the infinite-interest blackhole (runaway inflation), and blackhole #2 is the zero-interest blackhole (runaway deflation). When gold was put beyond the pale just 25 years ago in 1976, little did the world realize that it was firing the policeman in charge of cordoning off blackholes. By 1980 the world had a close brush with runaway inflation as the dollar was tottering at the brink of one of the blackholes. Many ad hocexplanations were concocted, from the machinations of the gnomes of Zürich to the malice of Arab sheiks. Nobody raised the question whether the firing of the policeman may have had something to do with the disaster. The scare passed when the Soviet Union showed signs of disintegration and the successor states of the Evil Empire, like a dry sponge, started absorbing dollars with abandon. The people of these countries were lapping up dollars at the trough as if they were imbibing the elixir of life which had for so many years been denied to them. This meant a stay of execution for the dollar which appeared doomed only a few short years before. But neither the economists' profession, nor the top brass at the Fed was interested in taking advantage of the remission to initiate an inquiry into the wisdom of having put into abeyance the monetary clauses of the United States Constitution half a century earlier. Instead, they joined the enthusiastic crowd at the Currency Circus watching with fascination Clown #1, the dollar doing fancy footwork dancing away from blackhole #1, while neglecting to pay attention to Clown #2, the yen waltzing around blackhole #2.

Of course, the rate of interest can never be exactly zero. Likewise, it can never be infinity either. We are in the habit of rounding figures. But just as we never round to infinity, we should never round to zero either. For example, if the rate of interest is 0.01%, one must not round it to zero. It could get halved a dozen times or even a hundred times, and will still not be exactly zero. Yet each halving would mean that the debt burden got doubled, causing ever more bankruptcies and punching ever greater holes in the balance sheets of banks.

The question arises why it is that we never hear about blackhole #2, even though the other blackhole is familiar to students of inflations. In fact, the phrase 'runaway deflation' is not even in the dictionary despite great formal similarities between the two blackholes. The answer is that John Maynard Keynes, the godfather of contra-cyclical policy, a seasoned speculator himself, made a serious blunder in ignoring the consequences of bond speculation when he designed his Brave New World of irredeemable debt and irredeemable currencies. Alan Greenspan's greatest ambition appears to be that he be remembered as the most worthy henchman of the godfather. He copies the original blueprint, warts, blunders and all. As far as we know, he has never ordered a detached, critical analysis of the principles underlying contracyclical policy. After all, the policy worked in the 1930's, didn't it? Blackhole #2 didn't devour the world, did it? So the Keynesian nostrum worked, didn't it? Well, the truth is that we shall never know. The nostrum certainly did not work up until 1940. Thereafter the interference of World War II confused the issue. It seems to be a reasonable assumption that, without the war, the rate of interest in America would have continued its plunge to zero. This is an indication that a lot more research ought to be done on this question, but nobody is doing it. The frightening possibility cannot be dismissed that history will repeat itself and it will take another World War to escape from the clutches of the blackhole once again.

The see-saw of interest rates and bond prices

The fact that the yield and the price of a bond are in inverse relation is well-known to security analysts, although it is often puzzling to laymen. Even professionals may occasionally think that it is merely a statistical law. Well, it is not: it is a mathematical law that does not bear exceptions. A related common mistake is to think that the see-saw of the rate of interest and the bond price is limited by the face value of the bond, which cannot be exceeded by market value no matter how far the rate of interest falls. The fact is that the face value of a bond does by no means or manner limit its market value. Any given value, however high, is theoretically possible, provided that the rate of interest is low and maturity is far enough. The mathematical apparatus to prove this is given in the Excursus. The mathematics becomes quite simple for perpetual bonds (consols in British parlance). A perpetual bond with face value A has no maturity, but it pays interest in perpetuity at a fixed rate a. If the market rate of interest is b, and the market value of the perpetual bond is B, then the mathematical relationship between the variables b and B is given by the attractive formula:

Aa = Bb = constant

For example, if the rate of interest b gets halved, then the market value of the bond B must double (and conversely). Moreover, if b plunges to zero, then B tends to infinity. While there are no perpetual bonds around any more, the formula is still relevant, because it provides a reasonable approximation for the relation between the market value of long-term bonds and the rate of interest. Furthermore, the longer the term the better the approximation (for a 30-year bond the error in percentage terms would still be single-digit).

Wrong way to report debt

Another reason why the formula Aa = Bb is relevant is the fact that it can be used to calculate the present value B of the total debt A in a country as a function of the rate of interest b (a > 0 is immaterial.) In this case it has the force of an exact formula rather than an approximation, because the existing debt of virtually every country today may be assumed to be perpetual debt. By no rational calculus can it be expected that it will be retired through the normal process of repayment (that is to say, without wiping it out either through default of through currency depreciation). We may verbalize our formula as follows: Every time the rate of interest in a country is cut into half, the (present value of the) total debt in that country doubles. In particular, as the rate of interest is plunging to zero, the (present value of the) total debt is galloping to infinity.

It follows that our way of reporting total debt is flawed. It reports only the principal sum due, overlooking the stream of interest payments thereon that is also due. Under a gold standard, where the rate of interest does not go up-and-down and cannot fall to the ground like a Yo-Yo, the omission is not significant. When you discount an infinite stream of payments by a stable rate of interest, the present value is finite. By contrast, if we discount a stream of payments as small as one dollar per year by zero, we shall find that the present value is infinite. This epitomizes the plight of the world in view of the rate of interest plunging to zero. The total debt in Japan (or in any other country) could double without approving a single new loan, or without selling a single new bond, if the rate of interest is halved.

The zero-bound rate of interest brought the United States to its knees in the 20th century when it was the greatest creditor nation on earth. It may do it again in the 21st for the stronger reason that the U.S. is now the greatest debtor nation on earth.

Siren song from the blackhole

The blackhole threatening Japan is particularly treacherous. From it comes the sweetest siren sound, drawing unsuspecting seafarers to their destruction. But Odysseus had been warned of the dangers. He was shrewd enough to have himself tied to the mast and to order the ears of his crew members to be plugged, so that the siren song could not deflect their journey. No such shrewdness is apparent in the conduct of skipper Greenspan. The boat under his command is happily sailing ever closer to the source of the inviting siren song, promising budgetary surpluses as far as the eye can see, and abolishing inflation for good, quite unaware of the dangers awaiting the people aboard.

The optical illusion that halving a small number is inconsequential has desensitized the public to the danger. The rate of interest declining from 0.2% to 0.1% is no big deal, people say. Not so! It is doubling the debt burden, same as a decline from 16% to 8%. The role of Cassandra is a thankless one. To begin with, there is euphoria that we have "licked inflation". The doubling of the present value of the public debt is a piece of intelligence that is easily hidden under the bushel by treasury officials, for example, by phasing out the 30-year T-bond. All we are told is that "the budget deficit will also be licked" as the rate of interest keeps falling; but we are not told what is happening at the other end of the see-saw. So when the public debt gets doubled, and doubled again, nobody will care a hoot. On the contrary, people will be jubilant that more public money can be raised at ever lower rates of interest.

At first there is little sympathy for firms going bankrupt. People say: "serves them right, they have taken all the money from the banks while the taking was good". The realization will come later that even the most conservatively managed firms are in deep trouble on account of the plunging rate of interest. While the low rate may appear as a palliative, it will turn out to be a trap. Furthermore, those who take the money on these spectacularly easy terms will be sorry later when the rate of interest gets halved again and again. Prices decline together with the rate of interest. Businesses scramble to liquidate inventory and debt. As they do, a vicious circle sets in. Liquidation of debt becomes the cause of another round of interest-rate cuts; and liquidation of inventory of another round of price cuts. Lower prices squeeze profits. Receivables may become illusory or may disappear altogether, and so may profits. Servicing debt contracted at higher rates of interest earlier becomes excruciatingly painful. Those businessmen are the lucky ones who have sold out their businesses at the start of deflationary spiral and put the proceeds in bonds. They have no payroll to meet, no risks or labor trouble to face, no receivables or profits to worry about while they are enjoying not just a steady fixed income from the coupons, but also a nice capital gain on the principal. And, when the deflationary storm blows over, they could repurchase their businesses at a fraction of the price.

What makes people walk away from their dream-home?

Most of us have never had the opportunity to serve as the CEO of an enterprise and have little appreciation of business problems connected with falling interest rates. For those who had to face the problems connected with the financing of the family home the following example may be more meaningful in showing how deflation can make innocent people suffer.

You bought the house of your dreams, putting down 50% of the purchase price, your entire life-savings, which is now your equity, financing the other 50% with a conventional mortgage at 6% interest. Now deflation comes and the same mortgage is offered at 3%, half of what you have to pay. The bank refuses to renegotiate the mortgage as it is flooded with similar requests. You shrug and say: "So what? I like my home and stay put. I don't care that my equity has been wiped out. Those are just numbers."

Brave talk! But now you see "house for sale" signs cropping up around you and hear talk that houses don't move even at half of the appraised value. The situation is now this: you carry twice the debt on a house the market says is worth only half of what you have paid for it. For a moment you think that you want to walk away from your dream home, because it makes no economic sense to pay that much per month for shelter when you could rent a nice apartment for a fraction of debt servicing. But throwing away your life-savings is just too painful to contemplate.

However, you are a confirmed optimist and say: "Let's just tough it out and wait for the turnaround that the President says is just around the corner". Your house is now your coffin, and you are lying in it. They threaten to drive in the nails when your salary is unexpectedly reduced by half. Then you climb out of your coffin and, broken-hearted, walk away from your dream-home, because you prefer life to death.

Enter the bad guy

The script so far has followed that of Keynes. The gold standard was blamed for everything. The "barbarous relic", as he preferred to call it, was deflation-prone. Man has a pathological craving for gold, making it responsible for the contractionist tendencies of the capitalist economy. Gold must be taken away from "man's greedy palms" and put beyond his reach so that he can start spending his income rather than saving it. He likened craving for gold to craving for the moon. Man must be told that he cannot have the moon but that green cheese (sic) is just as good, and the Central Bank is tooling up to produce lots of green cheese for his delight. Since the capitalist mode of production is structurally flawed, Keynes went on saying, therefore the government ought to step in and prime the pump by public work spending. He had a pet project for public works in mind: the government should put greenbacks in coke bottles, bury them underground, and then hire the unemployed to dig them up again. That, he was fond of saying, would make more sense than prospecting for gold. Finally, he suggested that the central bank buy the bonds that finance public works in order to lubricate the economy, so that the capitalist system of production will not come to a screeching halt - as in his opinion otherwise it obviously must.

Keynes assumed that no bad guy could wreck his plans to save the world. But, as it turned out, there was a bad guy waiting in the wings: the bond speculator. Keynes, of course, knew him well. They were buddies in Germany in 1923, speculating in Reichmarks. However, Keynes thought he was as harmless in the bond as in the foreign exchange market. For every bull there must be a bear. The speculators' activities cancelled out in the long run and could be safely ignored. Bond speculation is a zero-sum game, he insisted, and that's that. With this assumption Keynes made the greatest scientific blunder of the century, if not in the entire history of science. Nowhere in his voluminous work did he examine the consequences of bond speculation as related to his proposed schemes of pump-priming, make-believe work, and debt-monetization in spite of the fact that he treated speculation at length. It is our task here to show that Keynes' assumption of a zero-sum game in the bond market does not hold water.

Speculation versus gambling

The speculators' long- and short legs entering the bond market do not alternate randomly. Bond speculators march in lockstep. Their activities give rise to enormously destructive forces, threatening the international financial system with a collapse. Bond speculation, just as foreign exchange speculation, is a form of gambling. It has no social value any more than shooting craps has. The risks in the bond and foreign exchange markets are entirely artificial: they were created when governments first sabotaged and then destroyed the gold standard. Neither form of speculation had existed in countries adhering to the international gold standard. Foreign exchange and interest rates were stable by nature, leaving no room for speculative profits. This conclusively proves that foreign exchange and bond speculation is the consequence of artificial risk-creation and it offers no benefits to the public. On the contrary, it is a rip-off. The same is of course not true for commodity speculation where the risks are nature-given and the speculator's activity has great social value and public benefit in alleviating gluts and shortages whenever they occur.

The bond market is huge. Initially it was about ten times the size of the stock market but, by now, it has grown by leaps and bounds thanks to the proliferation of derivatives such as bond futures, options on bond futures, interest-rate swaps, repos, knockout puts, and so on ad libitum. Not only does this activity require a large pool of currency (tens of trillions of dollars in America, which is a high multiple of the amount required to support productive activity) that otherwise would have no reason for being in existence. It also draws capital and talent away from productive enterprise. All this is bad enough, but the worst part is that bond speculation exposes society to the gravest dangers of economic collapse. It is drawing the economy into the blackhole as speculation drives up bond prices, that is to say, pushes the rate of interest to zero. This is the evil Keynes didn't see. Generations of economists following him didn't see it either. They simply pretended that bond speculation was irrelevant because it was a zero-sum game. They believed that the government and the central bank can do as they please in the bond market with impunity. Now it turns out that their actions, too, have consequences.

It is still a sacrilege to criticize Keynes. The postwar generation of economists put Keynes on a pedestal and worshiped him as savior. Greenspan is no exception, his pretensions of being a free-market man notwithstanding. "We are all Keynesians now", declared the President who defaulted on America's foreign gold obligations. Keynes' recipes are followed blindly and slavishly by Greenspan. Unlike Odysseus, he doesn't pay attention to the warning that he should steer away from the blackhole. It is not too soon to question Keynes' theories which have apparently led the world into temptation - and to disaster.

Why bond speculation is not a zero-sum game

Speculators don't buy the bond because they want to earn the interest income. They buy it because they want to ride the uptrend in bond prices. In view of the see-saw we can also express this by saying that they want to ride the downtrend in the rate of interest. They don't sell the bond because they want to invest the proceeds in the real economy. They sell it because they want to ride the yield curve (selling the short bond and buying the long), or they want to hitch a ride on the bandwagon of the carry-trade (selling the bonds of a country with a lower, and buying the bonds of a country with a higher interest rate). It is clear that bond speculators act in concert, and not at random as Keynes thought. They put themselves in position so that they can enjoy the tail-wind provided by the contracyclical policy of the central bank. They all want to buy the bond just before the central bank enters the open market with its own shopping list, and take profits after. Collectively, they represent a formidable financial force. It does not matter whether they act as part of a conspiracy, or they are acting on their own. The effect is the same: theirs is not a zero-sum game. They are on the winning side virtually all the time. It is simply not true that one speculator's gain is another's loss. The bond speculators profit together, at the expense of the productive segment of society. The public is losing whenever there is a protracted fall in interest rates, but it is also losing when there is a protracted rise. To understand this, we have to remember the see-saw. In the first instance, when interest rates fall, there is a prolonged rise in the present value of debt and productive enterprise is forced into bankruptcy. In the second, when interest rates rise, the value of bonds falls and with it falls the value of productive capital.

Bond speculation is a parasitic activity on the body economic. Of course, this is not meant as a smear on the character of any individual. Speculators acting on their own can be, and we may assume that they mostly are, upright people. Like everybody else, they are trying to eke out a living. They are certainly not responsible for the establishment of this vicious system which, by staying the "invisible hand", victimizes the majority. The blame is entirely on the government which is responsible for the institution of this iniquitous system which, rather than promoting social cooperation, pits one citizen against the other. It is another matter if bond speculators act in collusion with one another which would make the majority the victim of vampirism by a small minority. In that case we are facing a conspiracy which is purposely trying to milk society dry of its substance. It is not suggested here that there is evidence of such a conspiracy, only that the existing system is conducive to such conspiratorial activity on the part of bond speculators, hiding behind the façade of a hedge fund, or a gold mining concern with a hedge book, for example. Be that as it may, bond speculation represents an enormous financial force which one can ignore only at one's peril. It controls financial resources that in all likelihood eclipse those of the government. And, above all, bond speculators have a superb strategy which makes the central bank, slave to Keynes's mindless contracyclical policy, a sitting duck.


In my talk Kondratieff Revisited given at Sf. Gheorghe, Romania, I discussed at length the phenomenon of linkage which causes the price level and the rate of interest to move, apart from leads and lags, in the same direction. Just as when a man is walking his dog on a leash: while it is possible for either one to get ahead of the other by a few steps from time to time, it is not possible for the two of them to move in opposite directions for any great length of time. Linkage has been recognized and treated by several distinguished economists such as Knut Wicksell, Wilhelm Röpke, Gottfried Haberler, Irving Fisher and many others (internet authors, following Keynes, refer to this phenomenon as the "Gibson-paradox"). In terms of blackholes, linkage means that the zero-bound rate of interest is followed by a weakening or collapsing price structure and profit-squeeze. The financial system may snap as receivables become uncollectible, and the domino-effect sets in wiping out all but a handful of well-heeled enterprises.

Contra-cyclical or counter-productive?

The contracyclical policy mandate of the central bank calls for open market intervention in the bond market. Every time the price structure is weakening (or the stock-market is in danger of collapsing) the central bank enters the open market as a buyer of bonds, in order to replenish bank reserves. By the see-saw effect, the central bank drives down the rate of interest. This is just fine, as far as bond speculators are concerned. They welcome the tail-wind making their sails bulge. Central bank intervention is a virtual guarantee that they will be able to dump their bonds at a hefty profit. At the same time the linkage guarantees that lower interest rates are translated into weaker prices, so that the contra-cyclical policy should more appropriately be called the counter-productive policy of central banking.

In case of a serious decline in commodity prices which by the linkage may indeed be brought about by a zero-bound rate of interest, the central bank is desperately trying to reflate the economy. But pumping more money into the economy is just pouring oil on the fire. The new money is not flowing to the commodity market (nor to the stock market) as intended. Why should it? The fun is elsewhere. The central bank can put all the money in the world into circulation, but cannot make it flow uphill. The new money is going to flow to the bond market, where the fun is.

Avalanche alert!

Deflation is a term loosely applied to the phenomenon of general money scarcity in the economy. Hardly ever is the question asked just what it is that makes money scarce. Here is the answer to that crucial question. Money is made scarce by bond speculation. The bond market acts like a gigantic vacuum cleaner running amok. It siphons money away from every nook and cranny of the economy. The money is channeled into bonds serving as chips in the hands of the speculator with which they make their bets.

A vicious circle is hereby set into motion. The scarcity of money calls for central bank intervention. The open market purchases of bonds by the central bank drive up bond prices making the profits of bond speculators soar. Thereupon bond speculators get bolder and start pyramiding, using easy money made available by the banking system, thanks to the intervention of the central bank. Money becomes scarce again, and the central bank is called upon to act once more. And so on it goes.

We use the term "bond market" and "bond speculation" in the broadest sense, as a generic term embracing not just bond trading and speculating in the narrow sense of the word, but also trading and speculating in derivatives based on bond and interest rate futures, options and swaps. Even gold leasing comes under this heading, as the short position in the gold market is offset with a long position in the bond market. It is an extremely dangerous development that the bond market in the broadest sense is snowballing exponentially, as new players jump on the bandwagon and the old ones pyramid. Even the blind can see the explosion of derivatives. It is an avalanche that will ultimately kill the innocent and unsuspecting people who live down there in the valley.

The central bank is helpless

It is impossible to isolate a single economic force that is capable of resisting the coming avalanche. Would foreigners blow the whistle and withdraw their funds from the casino gone mad ? Far from it: they will send in more to partake in the fun, so irresistible is the attraction of the short road to riches. Would the central bank step in, raise and hold up the rate of interest long enough to put an end to the mad party, and bring speculators to their senses? Not likely. The central bank is helpless. A higher rate of interest would be lethal to the banking system. It would punch enormous holes in the balance sheets of the banks as the volume of non-performing loans exploded. This is the medicine that was tried in Japan. Predictably the patient, the Japanese banking system, went into a coma where it still lies. Nobody dares to shut off the patient's life-support system in fear of the consequences that are incalculable.

Murdering savers in their sleep

It is difficult to put ourselves in the long-forgotten land of the gold standard where interest and foreign exchange rates just do not Yo-Yo, blackholes are off limits, and the rate of interest could not fall to zero. Long before that happened bondholders - who, incidentally, were all genuine savers in that strange land - would step in and sell their overpriced bonds at a profit. They would wait until sanity prevailed once again and bond prices returned from outer space; only then did they buy back their bonds. Keynes was totally insensitive to the evil consequences of abolishing the gold standard. He was content to see bondholders of old, among them widows and orphans, be murdered in their sleep. The new bondholders, the speculators, trampling through the dead bodies of the old, are no longer inclined to sell the bond after the rate of interest fell. They want to go the whole hog. They rather see the rate of interest go to zero, so firmly are they in the saddle at the other end of the see-saw.

But let's give credit where credit is due. Keynes was a great trickster. He bequeathed to Greenspan the magic word how to increase green-cheese production, but took with him the secret of the othermagic word, how to decrease it, to the grave. Greenspan in charge of green-cheese production is now hostage to the speculators who have cleaned up in Japan, and are now after the United States. This year Greenspan is cutting interest rates for the seventh time in a row, each time announcing his intention in advance, causing great rational exuberance among bond speculators.


I am not predicting that the world will plunge into the black hole of zero interest. I am trying to sound the alarm that it might. There is no scientifically credible way to predict the future when it comes to imponderables. Another possible scenario is that speculators make a complete volte-face and, instead of accumulating, they start dumping the bonds. This, however, would bring other dangers in its train. When all the people aboard congregate on the port side and then all of a sudden switch to the starboard side, the boat is in danger of capsizing. A third possible scenario is that countries without a bond market - which makes them immune to the attraction of blackhole #2 - stumble over blackhole #1, pulling other countries along.

Last but not least, let us not forget that we could force a frank public debate on the errors of commission and omission of the economists' profession. Such a debate might lead to a public inquiry into the wisdom of having put into abeyance the monetary clauses of the United States Constitution at the instigation of a foreign upstart. The U.S. House of Representatives could by simple majority vote reinstate and uphold those clauses, the repeal of which neither Greenspan nor his predecessors have had the moral courage to initiate. It is true that such a development would create a Constitutional crisis, but it would focus Greenspan's mind on the danger facing the nation and the world like nothing else could.

And it is possible, if only barely, that the crisis would be resolved by the Senate and the Supreme Court concurring that those clauses must be upheld. This would indeed be a happy ending to a sad saga. Thereafter the global regime of irredeemable currency would be remembered as a brief reactionary episode in the history of mankind.


The mathematics governing bond values and the present value of debt

Let the price of a bond with face value A and coupon rate a maturing in T years be denoted by BT . There is a mathematical relationship between the variable BT and the prevailing rate of interest b, called the Bond Equation of which we present two equivalent versions (a third version will be added later):

(First Version)       

(Second Version)       

where e denotes the basis of natural logarithm: e = 2.71... We prove it in its First Version. On the right-hand side the first term Ae-bT is the present value of the lump sum A payable T years from now. To this we must add the present value of the income stream derived from the coupons. The coupon payable at time t has value Aa. We have to discount it by the prevailing rate of interest b to get the present value Aae-bt of that coupon. Therefore the present value of the income stream can be calculated as the integral

This completes the proof of the Bond Equation. From the Second Version it follows that

BT  <  A   for   b  >  a,BT =A   for   b = a,      BT  >  A   for   b  <  a

because for all b > 0 and T > 0. In particular, the market price does indeed exceed face value of the bond whenever the rate of interest falls below the coupon rate.

To get the value of consols or perpetual bonds, we have to take the limit B of BT as  . Since in this case  ,  from the First Version it follows that    or

Aa = Bb = constant

where B is the price and Aa is the yearly payout of the consol. It is clear from the Bond Equation that the rate of interest b and the bond price BT are inversely related (for consols, they are inversely proportional).

The British government started selling 3% gold consols in 1751. The rate of interest on consols was lowered in 1889 to 2.75%, and again in 1903 to 2.5%. The issue was discontinued during World War II when the British government defaulted on its domestic and international gold obligations. Even though consols disappeared together with the gold standard, the formula Aa = Bb is still relevant today. First, B can be used as an approximation for BT . The parameters of this approximation may be gleaned from another version of the Bond Equation:

(Third Version)       

where    and BT    A + aAT as b    0. The latter is immediate from the Second Version, since

as b    0. This means that the present value of the bond maturing in T years, when the rate of interest tends to 0, is approaching A + aAT. This is plausible, because aA is the face value of every one of the T coupons so that this sum represents all the payments to the bondholder. The present value is the same since it is discounted by 0. From this we may conclude that the price of the bondBT can be greater than any given value, however large, provided that the rate of interest b is low and the maturity T is large enough. It also follows that the approximation of BT by B gets better as T gets larger.

The formula Aa = Bb can also be used to calculate the present value B of total debt A of a country if the prevailing rate of interest is b. Under the assumption that the total debt is perpetual, this is an exact formula, not an approximation, and it shows that if b is divided by n, then B is multiplied by n. So as the rate of interest starts falling from 5% to 0.5%, 0.05%, 0.005%,... then the total debt increases by a factor of 10, 100, 1000,... For example, if the going rate of interest 5% is cut into half every year for a period of ten years, then by the end of the decade the rate of interest will be about 0.005% and the total debt will increase by a factor of 1000.

July 19, 2001.

Note added December 3, 2001.

Stephen Hawking said in the Foreword to his best-selling book The Brief History of Time that he had been hesitant to include equations because every equation was liable to cut sales of the book into half. When I privately circulated this paper in July, I found that every equation cut the interest of my friends in my thesis into half. Frustrated, I decided to put off publication of my paper awaiting further evidence.

It came on September 11 with the subsequent declaration of an open-ended war, to which the price of oil and the rate of interest responded by falling. Mr. Greenspan's compulsive cutting of interest-rates for the tenth time this year despite the reappearance of irrational exuberance in the stock market, strikes me as measure of utter desperation. Whoever has heard of a central banker deliberately cutting interest rates in the face of a shooting war and calls for unconditional surrender of the enemy? Either Mr. Greenspan does not know what he is doing, or he is being swept off his feet by the dogs of deflation. What we are witnessing is not a war between righteous and terrorist forces. It is something bigger. It is a tug-of-war between inflation and deflation.


Dr. Antal E. Fekete
[email protected]

The Incas thought gold represented the glory of their sun god and referred to the precious metal as “Tears of the Sun.”
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