Thirty-seven years ago, the late founder of Strategic Analysis Corporation, Dr. Verne Atrill, made a remarkable calculation based on a set of mathematical theorems that he had spent his life developing. He discovered that there is a precise point, a mathematical singularity, which we can measure as the Ratio of GDP/ Total Debt, at which an economy stops expanding and begins to contract instead. This point is the equivalent to the event horizon of celestial ‘black holes’ and it acts in a similar manner, the first one drawing energy (light and matter) into its vortex, and the second drawing economic energy – GDP – into its ‘vortex’ due to the dead weight of massive debts. Below that point, if central banks continue to use so-called Quantitative Easing in all its forms, debt will continue to expand (and may do so increasingly rapidly), but more and more GDP will be sucked in, eventually causing a collapse of the economy along with the value of the currency. Today, parts of the Euro Zone, Japan, and Brazil, are already sliding into that vortex, the US is dancing on the rim, and China appears to be doing its level best to move there as well! I can therefore forecast with confidence (and regret) that there is no global recovery lying ahead of us about to ‘kick in’, regardless of what our central bankers and economists expect.Capture

For those who are curious, the complete mathematics are freely available online by simply googling The Limits of Debt. In it, I have shown the full mathematical development and analysis of a theorem of solvency, from first principles, and have included the associated table of values, as well as the graphic relationship which results (as shown in the chart below). In the chart, a GDP/Debt ratio of .289 ($3.50 of debt per $1.00 of GDP) is the financial equivalent of the “event horizon” of a celestial black hole. Like the celestial sort, the table of values shows that the size of economic ‘black holes’ keeps increasing as the mass of debt increases, but in doing so, sucks in more and more GDP to support that debt (that is, reverses the growth of GDP) as the debt vortex increases. Activity, as measured by the total of [GDP plus Total Debt] may increase, but the growth of real GDP itself turns negative while Total Debt keeps expanding at a faster and faster rate. Total economic activity becomes increasingly frenetic as value (GDP) is being destroyed by the very effort used to keep trying to produce it, that is, the issue of more and more debt. The problem is, nothing sticks to the bottom line. It is activity for the sake of activity, which only serves to crush GDP itself and increase the dead weight of debt on the economy.

Money-issuing governments and central banks, faced with this problem in the past century, have typically reacted by trying to issue more and more paper to compensate for the failure of the real economy to catch fire, not realizing that in doing so, it only serves to feed the debt vortex, actually making the problem worse. Since the beginning of the 20thcentury, from a study by the Cato Institute dated August 15, 2012, 55 governments have executed this ‘strategy’, all with devastatingly similar consequences for the value of their respective economies and currencies. Thus far in the 21st Century, we have seen this approach at work in Greece, Spain, and Brazil (among several others), and Japan is valiantly trying to follow suit. Of course, while currency values and real GDP may decline, stock market values often soar, so that “stimulus” policies seem to work. Looking at it another way, as the debt aneurism expands and the money has to go somewhere, so it heads into the “safety” of the ownership of hard assets. However, if history is a reliable guide, sooner or later it then heads into price (and wage) hyper-inflation. The US is currently dancing on the edge of its own “event horizon”, and is only still standing because it is the global key currency. It is drawing money from both Japan and Europe, as both are in worse financial condition and there is a flight of money to the US. It is not a situation in which GDP growth will prove to be self-sustaining, however, although it is ‘self-delusioning’ for a while.

At and below a GDP/Debt ratio of .289, the incremental value generation of additional debt in terms of GDP falls to and then below zero. We term this a scientific(mathematical) bankruptcy because the effects of bankruptcy hold, namely that debt compounds while value (GDP activity) recedes. Parenthetically, such a point must exist, because otherwise, Zimbabwe (for one) would be one of the richest countries in Africa, and Greece and Spain would be sitting atop all of Europe.

Japan is a test in real time of the solvency mathematics in Limits of Debt, and will be our canary in the coalmine for the economy of the US. Unfortunately, the minor economies of Greece and Spain are well through that level and their respective GDPs have already been crushed to the tune of some -25%, so studying them is only an academic exercise in hindsight. However, other European economies bear close attention, notably Italy and France. 

Implications of Economic Black Holes

Our central bankers may not be all that happy that they have been unable to get the economic growth trajectory back to something like the economic recoveries from recessions in the past, but at least they can say that all that ‘pump priming’ has not led to inflation, and interest rates are low and encouraging. Milton Friedman’s “Monetarism” theory seems to be out the window, for which everyone can say a hearty ‘thank goodness’. Unfortunately, none of that is true.

For one thing, since growth grinds to a halt, then there are no price pressures due to demand-based shortages. Without demand pressure on goods and services, why would anyone expect price inflation? And without demand pressure, wages and prices will either be steady or go into a slow decline – for a while.

For another, without growth, there is no increase in the demand for money. Both households and businesses have been paying down their debt, not increasing it as has happened following recoveries from past cyclical contractions. Growth is not only grinding to a halt; but worse, shows signs of heading into decline as Corporate America is paying out to shareholders through dividends and share buybacks as much as or more than it is taking in. One need go no further than this to grasp why loan growth hasn’t caught fire in this cycle, even with near zero interest rates. As a consequence, in the shorter term, if we then have a marginal negative demand for money, why would we expect anything but a marginal negative return on money?

In the shorter term, the failure of wages and prices to react to massive monetary stimulus as Milton Friedman had suggested has lulled our central bankers into a sense that the real risk lies in a 1930s-style deflation. (Quick: when was the last time that you can remember that anyone talked meaningfully about the US government deficit?) In truth, the exact opposite is the case. Our central bankers argue that deflation, with falling prices, is the risk when in fact, we are facing rampant inflation, the problem being one of measurement.

Dana Skinner, in his book Seven Kinds of Inflation (written in 1937) pointed out that inflation takes many forms. He identified asset price inflation as one form, and we have had that in spades since 2008-9. He failed, however, to identify an 8th kind of inflation, namely the cost of a dollar of GDP. Consider that for most of the 20th century until about 1984-5, in the US it used to take about $1.45-.50 of additional debt to generate $1.00 of additional GDP (the peak of the Atrill Curve). Since then, the marginal “cost” of an additional $1.00 of GDP has escalated to $3.50 (and more in some countries). Yet central banks and main stream economists are completely mute on this critical issue that has reached global epidemic proportions. They certainly do not refer to this as “inflation”! However, the pathology of country insolvency is clear from the 55 examples since 1900. All of them pursued massive monetary easing of some sort, and all of them ended with a collapse of both their economies and associated currencies. The advent of paper currencies has been a double-edged sword, with as much damage wrought as good has been done thanks to the lack of a mathematics of leverage (“solvency”)! 
The Chinese Miracle Explained…and the Myth Exploded

I now draw your attention to the right hand side of the curve. One can plainly see that there is an area in which additional debt adds to the generation of value (GDP), and for some while in an accelerating fashion. From the MPD Curve, it is clear that the emergence of China as a global economic power has not been due to some superior insight into the economic growth process, the so-called “command economy” to which some Chinese leaders like to attribute their success, but simply to the growing use of leverage (debt). Indeed, the serendipitous advantage of debt is that you can get lots of money (capital) for expansion with the wave of the hand and growth will simply follow almost magically! You can even finance entire ghost cities and roads to nowhere and the economy will keep humming along. The surprising disadvantage (for those not used to obeying what I might call the ‘banking discipline’) comes when an economy roars up and over the peak and heads down the slippery slope towards the Black Hole bankruptcy condition. Suddenly, debt has a cost: the economy slows drastically and retrenchment becomes the order of the day.

China has not discovered a ‘new way’ of managing the economy. It has actually simply followed the post-war roadmap left behind by Japan which followed a similar solvency trajectory. Back then, people rushed to “explain” the Japanese ‘miracle’. (Does anyone remember Herman Khan?) Then 20 years ago, Japan crossed the .289 boundary condition and in a trice, it was all over but the shouting. (You can look up the numbers yourself from Japanese records: it’s all there!)

We don’t (and probably can’t) know the precise Debt/GDP ratio of China, but some analysts do measure it as being in excess of 2.5, in which case China is now solidly on the wrong side of the peak of the MPD curve. The very fact that China is now and has been visibly slowing despite all efforts to the contrary does suggest very strongly that this is now very much likely to be the case. This suggests that to really get the country moving, China will need to rein in its lending activities, restructure its debts, and really start to focus on productivity instead.

With at least three of the key economies of the world, the US, Japan and much of Europe in a deeply insolvent, near bankrupt condition (as I defined it above please!), it is no surprise that global GDP is grinding to a halt. And, of course, if, as seems clear, China has joined the rest on the wrong side of the curve, then China will become less and less of the stimulus than they have been for the last 2½ decades. Add a few other major countries including Brazil (and goodness knows who else), as we all have fallen under the spell of modern central bank solutions for slow- or no-growth, and the grim outlook that lies before us is (at least) easy to grasp.

Six consequences that flow from the Atrill MPD Curve

  1. The Lifeboat Economy

When growth ends and an economy stops expanding and starts to contract, we are left with two possible outcomes, share what there is or grab everything that we can. I call this the Lifeboat Economy because growth can no longer skate our overall desire for more onside. In the US, it is quite clear to what I am referring, as the expansion of budgetary entitlement rights has grown from a modest percentage of government revenues to more than 100% (before deficit financing). Cooperation between political parties has fallen below zero because to share what we already have with someone else is to take away from what we now have. The US political scene has bifurcated into two parts, those who are at least trying to expand the sharing process, although they have nothing to share that doesn’t belong to someone else in the absence of real growth, and the One Percent Party which is determined to keep even more of what they have at the expense of the rest of the populace. Internationally, Greece represents a caricature of the lifeboat phenomenon. Having eaten themselves out of house and home and watched their economy collapse, they have come demanding that others support them. I am sorry to have to say to them: Germany is on the right track about fixing, not pandering to, their debt problem.


  1. Austerity Cannot Work

It’s difficult to cover every detail in a short summary of Black Hole Economics but at this point, I need to point out that .289 is what we refer to as a second-order insolvency. There are two additional orders, a first-order insolvency being one that is most relevant to the current discussion. This occurs at a solvency ratio of .499… and marks the point of chronic deficit. This was the precise condition of the US in 1992 when Bill Clinton took the reins of office and set out to clean up the US government balance sheet by raising taxes and cutting costs (i.e., austerity!) – which he did with such devastating effectiveness that there was a fear that government bonds would disappear, as some may recall! When he left office in 2000, the US was on top of the world, its currency was at an all-time high, consumer confidence was at an all-time high, the stock market was booming, and the economy was on fire. Small wonder that he is still revered today on both sides of the political spectrum. Austerity “worked” in 1992-2000 because the impact of an increasingly solvent government balance sheet spilled directly and immediately over into the real economy. The resulting decline in leverage pushed the US economy up the MPD Curve! (It might be impertinent for a Canadian to say, but there is another Clinton running for the presidency this year in the US. Who knows if her mate can work his “fiscal magic” once again!?)

The point of all of this is to say that the reason that austerity cannot and does not work for scientifically bankrupt economies is due to the reality that those economies are so deep in the chronic deficit phase that they will find that austerity cuts do not actually improve living standards. They can only cut into the deficit (debt expansion), but with no gain in GDP, at least for a much longer time than the body politic in democratic countries has any patience for.


  • Economic Collapse versus Currency Collapse: Greece and Spain versus Japan

In Greece and Spain, the economy massively declined, while in Japan (so far) only the currency has tumbled but the economy in nominal terms has not. Yet both are scientific bankrupts. Why the difference? I think that the answer is fairly self-evident. Greece is lumbered with a currency, the Euro, that is more or less fixed and immutable (to Greek tampering, at any rate). And so the downwards insolvency pressures fall directly on the economy. In Japan, the same pressures are in evidence, but the currency value has taken the heat in the shorter term and it has fallen instead. The Japanese may be a lot poorer in international terms than a few years ago, but relative to each other in Japan, not much has changed. People aren’t happy but they are not rioting in the streets – yet. If I were Japanese, I would not count on this situation to hold up much longer, and already we are seeing evidence that the Japanese economy is now also starting to implode.

Japan is indeed a story about the failure of Quantitative Easing. If you check the records, you will find that it has been almost 20 years since Japan became a second-order insolvent (bankrupt) with a GDP/Debt ratio of .289. Curiously enough, for a long time after, Japan hung right there and did not get any worse (or any better) although Government Debt as a percentage of GDP rose from 100% in 1995 to about 200% today. GDP essentially flat-lined: it is quite remarkable to look at a chart of their GDP for that entire period. At the same time, household and corporate debt fell to keep the ratio constant. This was not a happy time for Japan, and that country has enjoyed/suffered a succession of 11 prime ministers in that period, each promising an escape from their no-growth economy. Ben Bernanke is the one widely considered to be the cause of current militant QE in Japan by chiding Prime Minister Abe that the problem with Japanese stimulus to that date was that it was not enough and that Japan should try harder. Well, Japan has done so. The results? Since then, the currency has collapsed by some 50%, with more to come I would forecast, and now we are seeing Japanese real GDP start to head into decline. (Consumer spending in 9 of the past 12 months has declined, the other three months being flat.) I would guess that every Japanese citizen should join together in saying, “Thank you, Ben”.


  1. Money On Strike

One truly striking characteristic of Japan, the US, and Europe is that the velocity of money in all of those places is not only declining but has been in a steady decline for a long time, in some cases going back nearly three decades (MZM in the US). This is one key characteristic of increasingly insolvent economies: money does less and less “work’ as time goes on, in essence ‘trying’ to offset the overall financial inefficiencies brought on by excess debt. The problem and the challenge to monetary authorities is that of trying to overcome what is effectively a decline in money availability caused by falling velocity. This they have done historically by issuing more and more money through programmes equivalent to very aggressive ‘quantitative easing’. Unfortunately, the solvency mathematics of Dr. Atrill demonstrate all too clearly that this makes the problem worse. This last point is mathematically unimpeachable and as well, there is an abundance of hard evidence.

As 55 countries have already shown, there is a tipping point when price and wage inflation suddenly start to accelerate, and currency values implode. I do not have debt/GDP numbers from those 55, so I cannot be pedantic about where it occurs. I could make an informed guess based on the mathematics, which I would anticipate would be at Atrill’s Third-Order Insolvency level or 0.135 (e2), which he referred to as the “break-up condition”, but that would be a speculation only. Not only does price and wage inflation then reverse their moribund courses but velocity must re-accelerate massively as well (as Weimar Germany, for one, shows. By the way, Germany has left an excellent record of that period for anyone to see, and I recommend the proceedings of the Bundesbank to all students of national insolvencies.). As holders of the currency in question try to get rid of it in exchange for things – anything – which can hold its value, the value of those currencies must and do collapse. Seen in this light, we should all hope that the quest by central banks to stimulate an uptick in inflation (as measured by wages and prices) fails, as they are most likely to waken a sleeping tiger. Germany alone, among advanced Western economies, has already been there but cannot seem to convince the unfortunate Greeks that far worse things may lie ahead.


  1. The Miller/Modigliani Hypothesis Can be Retired

I do not know anyone who has initially encountered the Miller/Modigliani Hypothesis (frequently mistakenly labeled as a ‘Theorem’ which it is not, save in the weakest definition of the word) and did not think that it was complete nonsense. Anyone with an ounce of common sense “knows” instinctively and intuitively that debt does count in the valuation process that the market carries out, and in the generation of activity that must fall if there is too much debt. However, having proved that debt does not seem to particularly matter in the valuation process – by using the wrong measure of leverage, the debt/equity ratio – Messrs. Miller and Modigliani did inspire at least one ‘client’, government, to cheerfully ignore the impact of too much debt. [Note that a number of companies also tried to ignore the impact of over-indebtedness during the great LBO craze a couple of decades ago, but the resulting bankruptcies brought the corporate world back to the “banking discipline” again.]

Leverage – as measured by the Atrill Solvency Ratio (see Limits) – does count. As the MPD Curve shows, at .289 economic activity starts to go into reverse. Indeed, I should note that one of SAC’s board members did his Ph.D. thesis on forecasting currency and interest rate movements using the Atrill Solvency mathematics, with excellent success. SAC has been using this measure to forecast currency movements ever since. In our common stock valuation work, it is a truism that price follows solvency (leverage). In short, it is time to expunge the M/M ‘Theorem’ from the books of both government and academia.


  1. The Pathology of Insolvency

From our analysis, there are some general characteristics of economies which are heading into mathematical (scientific) bankruptcy, similar to the pathology of a disease. These seem to mark the lull before the storm, and may have been present in all those 55 countries where the currency ended up collapsing under the eventual pressure of hyper-inflation:

  1. Velocity of money falls endemically
  2. Private sector borrowing (and corporate investing) dries up
  3. Interest rates initially fall as there is no demand for money
  4. Inflation, as measured by prices, falls towards zero due the lack of demand growth
  5. The government balance sheet gets steadily worse
  6. Internal political harmony turns to intense dissonance
  7. Central banks are, in effect, left holding the bag in the absence of any political will or agreement to find policy solutions to weakening economies
  8. To central banks, like the proverbial hammer to which every problem looks like a nail, every ‘declining economy’ problem can best be solved by printing more money in one form or another

My suspicion is that when a currency really begins to collapse, that internal prices (i.e.: inflation in that country) start to rise, but their central banks do not react, because to curtail the monetary growth would be to “kill the expansion just as it got underway”. These same fears that stopped Greenspan from acting responsibly (as he openly admitted in his book) were probably there as they were in the US. The difference between the US then and even now and in those 55 countries is that hyperinflation was then underway. The linkage would be fascinating to discover – but now we know where (and why) to look.


VII.     Reducing Debt Will Lead to Strong Growth

If, at the peak of the Atrill Curve, it takes $1.50 of debt to generate $1.00 of GDP in a normal, healthy, and solvent economy, then there is an astonishing amount of excessive debt outstanding today in Europe, Japan, and the US, all of which is weighing down on their economic potential. Note that a few years ago, the economist Ken Rogoff identified the value .289 ($3.50 of debt per $1.00 of GDP) as quite possibly having significance, but without these mathematics to back his findings up, Rogoff could not defend his results as being anything but statistically discursive and he was, essentially, simply ignored. The assertion of possible importance without a rigorous mathematical proof could not and did not stand up to powerful critics with their Keynesian axes to grind.

The resolution of the current debt problem is (axiomatically) simple. When we are in a state of bankruptcy as the curve above (and the associated math) clearly underlines, then dealing with the challenge is straight-forward. How would a bankruptcy lawyer or accountant deal with bankruptcy? He would direct the bankrupt to sell assets and pay down debt, write off any and all debt which the bankrupt is unable to pay down, and then live within one’s means (no credit cards!). From the MPD curve, that outcome would mean a large increase in GDP as a result of the debt burden being lifted, a solution devoutly to be wished. However, governments do not like nor want to abide by what is essentially the banking discipline and Greece is proving to be, perhaps, merely the first example of a 21st Century government to outright reject this suggestion and solution!

As Bill Clinton proved from 1992 to 2000, if that excessive leverage could be lifted, then two things would occur simultaneously. The GDPs of those three bankruptcies would lift to a considerable degree. Elsewhere (in my book), I have calculated that the GDP of the US should be in the order of 18-22% higher than it is today without that excess debt baggage. Indeed, average US household income would rise by something in the order of $10,000 if the US were solvent. If that excessive debt could then be redirected to other parts of the global economy that could use those capital resources efficiently and effectively, then global GDP should also take a mighty step upwards.


So we have at least three major economies, and probably four if we count China as heading that way, in deep trouble thanks to too much debt, and the best that the politicians, central bankers, and all too many economists can say is, “we need more stimulus”. To that, I would have to conclude that if common sense cannot prevail, I would have to end by asking, gold, anyone?



The Divine Right of Kings has been supplanted by the divine right of governments. It is this problem that allows and has allowed government spending and borrowing to run rampantly amok to the massive detriment of employment, resource utilization, and general well-being. This needs to be supplanted by a constitutionalrequirement for the government of every country to be solvent as measured, and as close to peak efficiency as possible.

Let me close by observing that I do not think for a moment that the solvency problems that we are faced with today are the result of political malfeasance, ill will, greed, or even stupidity. In general (in my estimation), politicians and financial leaders in general act in what they consider to be the best interests of the greatest number of people. Their intentions are good. Unfortunately, as Michael Bloomberg has observed, you cannot manage what you cannot measure, to which I have to add, you cannot manage if you don’t know what to measure. Dr. Atrill has shown us what to measure and why: it is now up to us to do something about it.