Monday, October 12, 2009

Denninger Gives an Old but Timely Lesson in Math…

This is a great old parable explaining how exponential math works. Karl is right on in giving this as an example and also is right on with his conclusion. The doubling process of debt has happened for the last time, it will not happen again.

Here’s Karl from his article, "Is The Dollar Doomed?"

…Again, for the mathematically-challenged, consider the following story.

Many years ago there lived a monarch in India who ruled that all of the people must store their 90% of their rice harvests with him for safekeeping, so in the event of famine there would be enough rice to eat.

One year a famine hit but he refused to release the stored rice, fearing that he would run out and starve himself.

After a couple of months a clever girl came to the monarch and asked for one grain of rice, and for the next month to double it each day.

The Raja agreed, and shortly discovered the magic of exponents, much to his chagrin.

On the first day, he gave 1 grain of rice.
On the second, two.
On the third, four.
On the fourth, eight.
On the fifth, sixteen.
On the sixth, thirty-two.
On the seventh, sixty-four.
On the eight, 128.
On the ninth, 256.
On the 10th, 512.
On the 11th, 1024.
On the 12th, 2048.
On the 13th, 4096 (it was now taking a while to count!)
On the 14th, 8192
On the 15th, 16,384 (The Raja now knew he was in trouble)
On the 16th, 32,768
On the 17th, 65,536
On the 18th, 131,072
On the 19th, 262,144
On the 20th, 524,288
On the 21st, 1,048,576
On the 22nd, 2,097,152
On the 23rd, 4,194,304
On the 24th, 8,388,608
On the 25th, 16,777,216
On the 26th, 33,554,432
On the 27th, 67,108,864
On the 28th, 134,217,728
On the 29th, 268,435,456
And on the 30th, 536,870,912

Needless to say before the 30th day the village was quite-well fed and the Raja was the one who went hungry.

But I want you to pay special attention to the above table, which is why I reproduced it all - most renditions of this story do not.

Notice that on the 29th day the girl was due more rice than had been paid to her in all of the previous 28 days. This is also true for each day in the series - a fact that you need to think about for however long it takes to sink in.

This is the fundamental truth of all exponential (or "power") functions. It is a mathematical truth, not a theory or possibility.

Now let's add another fact - if you take the growth rate of anything and divide 70 by it, you get the doubling - or halving - time. (Yes, I know this imprecise - but it's close enough to do with a paper and pencil or in your head, which is what counts here.)

So let's take the so-called "average" 3.5% inflation rate over the last couple of decades. If you're saving money, this is a problem. Why? Well, divide 70 by 3.5 and you get 20, which means that money stuffed in your safe loses half its purchasing power in 20 years. In another 20 it loses another half, and is now worth 25% of what it was in terms of what it will buy.

Now let's look at the debt growth percentage from 1990 onward. On an average annualized basis, it is 7.90% (this is from the Fed's Z1 table, by the way - go argue with them if you disagree. As an aside from 1953 to the present debt has grown at an annualized rate of 8.77%, and since 2000 onward at 8.495%, so I'm being nice here by using the 1990 forward numbers.)

This means that the total debt doubles every 8.86 years (or around 8-1/4 years if you use either of the other rates.)

Now go back to the above table again.

Notice that this table shows the unfortunate reality - every 8.86 years there is more NEW debt taken on than has been taken on in the entire history in The United States up to that point.

This cannot continue forever. The politicians do not want to talk about this, nor do the economists and central bankers, but it is a mathematical fact, and if we continue to ignore it we will suffer the loss of our currency and, in all probability, our form of government.

This, by the way, is why credit-led recessions cannot be "printed" or "eased" out of.
Credit-led recessions occur because debt service cannot be met by the population any longer, and as a consequence they begin to go bankrupt, forcing credit contraction instead of expansion. Yet all modern monetary systems are debt-based, and as a consequence as this contraction occurs it begets more contraction.

Lowering the cost of borrowing money (making money/credit more available) is nothing more than an attempt to allow "one more doubling" to take place in avoidance of reality. But as you can see, had the Raja above not made a "forward promise" of allowing thirty doublings, he could have stopped before he was bankrupted.

Everyone in America wants "a pony" - the magical alchemy that will turn lead into gold, or return their stock market portfolio to its previous purchasing power.

It won't happen so long as our government and citizens spend more than they make.

There is one and only one way to make that happen: You must grow output faster than debt. When there is a credit overhang this means you must get rid of the debt at a faster rate than GDP declines.

There is only one way to achieve the necessary outcome - what is called "creative destruction", where those who made bad bets (both as lenders AND borrowers) go bankrupt, clearing the path for new lenders to spring up and take their place. Attempting to prop up GDP with government spending is exactly backward and in fact insanely destructive since to do so you must expand debt issued by the government dollar-for-dollar and due to inefficiency (which is very high in the government!) the debt taken on for each point in GDP created is ridiculous.

In the last quarter, for example, government handouts and spending added about four points to GDP. That works out to about $130 billion dollars (the math is ~$13 trillion X 4% / 4 quarters = $130 billion). But to generate that $130 billion government took on $435 billion in new debt (Source: Treasury Direct "debt to the penny"), or roughly $3.35 for each dollar of GDP boost.

There is no durable recovery that can come so long as debt expands faster than GDP does. The math simply does not permit it.

In 1930 there was a tremendous stock market bounce, and everyone and their brother thought that The Depression had been avoided as a consequence of looser money and recovery of asset values. Indeed, I am hearing echoes of President Hoover and James Davis in my head these days.....

May 1, 1930

“While the crash only took place six months ago, I am convinced we have now passed the worst and with continued unity of effort we shall rapidly recover. There is one certainty of the future of a people of the resources, intelligence and character of the people of the United States – that is, prosperity.” – President Hoover
June 29, 1930

“The worst is over without a doubt.” – James J. Davis, Secretary of Labor.
June 9, 1931

Uh huh. The government tried to shield borrowers and lenders from having to take their medicine in 1930 too.

The result was a Depression that lasted until we entered WWII in 1941. The Depression was not exited despite more than a decade of attempts from our government as the government never forced those who had gone bust to take their medicine and thus allow creative destruction to run its course - instead they interfered at every turn (even to the point of burning fields and shooting cattle!) and as a consequence until we were faced with a war that killed a large percentage of the workforce and destroyed massive amounts of material, thereby forcing full employment and realignment of industry, our economy languished.

If The Government comes to recognize the sixth-grade math and implements policy that comports with the immutable mathematical facts the dollar would strengthen significantly and, if maintained, such a policy would guarantee the preservation of reserve status.

However, such a set of policy actions would also prohibit the hiding of losses and force their recognition, thereby forcing the oligarchs and thieves out of business on Wall Street who are currently hiding defaulted paper in the hope that devaluation will allow them to abscond with all of their ill-gotten gains.

The choice is quite simply between economic and policy stability and the banksters on Wall Street along with their handmaidens in Congress.

That's the debate folks when it comes to the dollar and indeed the future of our nation, and the sooner we recognize it the sooner we can exit from this mess.