Author Topic: The Global Debt Trap  (Read 6741 times)

bh2115

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The Global Debt Trap
« on: May 29, 2017, 08:37:39 PM »
I picked this one up at the library last weekend as I still struggle to understand if we're in this "new normal" type of world with extremely low interest rates but yet minimal inflation or if we're just kicking the can down the road to something even worse.

Needless to say, this book didn't erase any concerns that I had. In summary, the key points were:
1) If we had let the markets self correct in 2000, we likely would have minimized the 2007 event, and subsequently if we had let markets work themselves out in 2007 (tougher scenario for me to buy), we'd have avoided the next, worst crisis that will hit us
2) Once currency is decoupled from a finite asset (e.g., gold) you have governments that will push ever larger budget deficits knowing that payment of these bills will fall on someone else's shoulders and that it can boost output in the short term
3) We should have underwent deflation but since central banks were so poised to avoid any type of deflation the massive stimulus packages around the globe have offset those effects leading to tepid inflation. However, the authors believe that the money supply growth (that has far outpaced real economic growth) will push inflation.

Once inflation hits, they believe it will hit rather quickly and the Fed will be forced to raise interest rates leading to further issues since all countries have accumulated so much debt and will therefore pay a larger share of their budget to servicing interest costs vs. investing in growth.

What I find ironic is that the book was written at the end of 2010, and their suggestions were to allocate money to both commodities and gold (both of which would have been terrible investments over the past 7 years). In their defense, they did not claim to know a time period (which would have been impossible), but they generally believed that at some point in the 5-10 year time frame, debts will become so burdensome that a massive correction will be forced on the entire global economy.

I'm not a contrarian (and started working full-time in 2009 so I've never witnessed a bear market as an investor), but I'm tempted to allocate up to 10-15% of my portfolio in GLD given those statements above coupled with the CAPE currently hovering around 30. I know that no one can predict the next market correction but it sure feels like it could be upon us.

Anyone else care to share their thoughts on idea of the "Global Debt Trap"?


« Last Edit: May 29, 2017, 08:39:32 PM by bh2115 »

aceyou

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Re: The Global Debt Trap
« Reply #1 on: May 29, 2017, 09:37:24 PM »
I have no idea what the economy and market will do.

Reading your post made me think of Jim Collin's quotes. 

#1: The market always goes up long term

#2:  If you are going to time the market (which you essentially doing if you do a GLD play), then you actually have to time it twice.  Suppose you really ARE able to predict the peak of a market get out of stocks and into GLD.  Well, then you also have to be smart enough to know when to get back in.  That's would be just as hard as predicting the peak, which we already can't do. 

And that makes me think of a Buffet comment about how anyone could have possibly lost money in the stock market in the 1900's when it began the century at a few hundred points and finished it at over 10,000. 

I'll give you a hint...it was because of really smart people trying to get in and out at the "right" time. 

The 20th century survived far gloomier times than the "global debt trap" of 2017 and the markets kicked ass. 

More VTSAX please:)

PDXTabs

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Re: The Global Debt Trap
« Reply #2 on: May 29, 2017, 09:58:06 PM »
3) We should have underwent deflation but since central banks were so poised to avoid any type of deflation the massive stimulus packages around the globe have offset those effects leading to tepid inflation. However, the authors believe that the money supply growth (that has far outpaced real economic growth) will push inflation.

Once inflation hits, they believe it will hit rather quickly and the Fed will be forced to raise interest rates leading to further issues since all countries have accumulated so much debt and will therefore pay a larger share of their budget to servicing interest costs vs. investing in growth.

I'm not a trained economist, but the best feature of a fiat currency is that you never end up in a deflationary spiral. That's how you end up with the great depression.

As far as inflation, I consider that a solved problem. You need political will, but not much sophistication. See: Fed under Paul Volcker.

ChpBstrd

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Re: The Global Debt Trap
« Reply #3 on: May 29, 2017, 10:25:54 PM »
Haven't read The Global Debt Trap, but from the synopsis you provided, it is not unique. It was probably written in 2009 at the bottom of the market to investors looking for a paradigm to understand what happened and what would happen next. However, it was a wrong / debunked approach.

Assumptions of classical, pre-depression economics:

1) Money has zero value unless the government guarantees to exchange it upon demand for (of all valuable things in the world this one thing) gold.
2) Government should not intervene in recessions/depressions because a "cleansing" process must occur. Metaphorically, this is a religious redemption.
3) Inflation occurs because the number of dollars in existence are like shares in a company, and to expand the number of dollars is to dilute existing shareholders.

Let's pick apart these assumptions one at a time.

1) Money only has value because people agree to use it as a medium of exchange. In that sense, it is the same as gold. Its value is in our heads. It is a token system for exchanging and storing the outputs of work. Many elements are more scarce than gold, yet not exchangeable for as much cash. FWIW, the value of the US dollar became more stable in the decades since the "gold standard" was dropped and the dollar became a fully fiat currency.

2) Read up on Herbert Hoover's response to the Great Depression, and what we learned. The "cleansing" that was expected only got worse, and "liquidating" everyone was a humanitarian catastrophe. Note how Ben Bernanke's response to the Great Recession was different than Andrew Mellon's response to what would become the Great Depression. You'll notice that books in this genre promote the discredited Herbert Hoover / Andrew Mellon set of assumptions. Most modern economists think government inaction exacerbated the Depression. http://potus-geeks.livejournal.com/450718.html 

3) To debunk this idea, compare a chart of M3 (one measure of monetary supply) against inflation. Do you see any relationship? As you can see, the amount of money in existence has exploded since that book was written, going from $8.5T to $13.3T.  Yet instead of experiencing hyperinflation like the theory suggests, the US has struggled to avoid deflation and get inflation consistently above 2% for several years.
M3 chart: https://fred.stlouisfed.org/series/MABMM301USM189S
Inflation table:http://www.usinflationcalculator.com/inflation/current-inflation-rates/
Most modern-day economists think inflation is related to the velocity of money, not the quantity of it in existence.

Bottom line... read up on economics. It can be counterintuitive. Pulp books like the one you read seem commonsense and paint a clear picture of economic villains and a predictable future, which is why they sell well, but if you invest based on those assumptions, prepare to be burned. Never accept a theory that the data does not support.

talltexan

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Re: The Global Debt Trap
« Reply #4 on: May 30, 2017, 01:28:04 PM »
Haven't read The Global Debt Trap, but from the synopsis you provided, it is not unique. It was probably written in 2009 at the bottom of the market to investors looking for a paradigm to understand what happened and what would happen next. However, it was a wrong / debunked approach.

Assumptions of classical, pre-depression economics:

1) Money has zero value unless the government guarantees to exchange it upon demand for (of all valuable things in the world this one thing) gold.
2) Government should not intervene in recessions/depressions because a "cleansing" process must occur. Metaphorically, this is a religious redemption.
3) Inflation occurs because the number of dollars in existence are like shares in a company, and to expand the number of dollars is to dilute existing shareholders.

Let's pick apart these assumptions one at a time.

1) Money only has value because people agree to use it as a medium of exchange. In that sense, it is the same as gold. Its value is in our heads. It is a token system for exchanging and storing the outputs of work. Many elements are more scarce than gold, yet not exchangeable for as much cash. FWIW, the value of the US dollar became more stable in the decades since the "gold standard" was dropped and the dollar became a fully fiat currency.

2) Read up on Herbert Hoover's response to the Great Depression, and what we learned. The "cleansing" that was expected only got worse, and "liquidating" everyone was a humanitarian catastrophe. Note how Ben Bernanke's response to the Great Recession was different than Andrew Mellon's response to what would become the Great Depression. You'll notice that books in this genre promote the discredited Herbert Hoover / Andrew Mellon set of assumptions. Most modern economists think government inaction exacerbated the Depression. http://potus-geeks.livejournal.com/450718.html 

3) To debunk this idea, compare a chart of M3 (one measure of monetary supply) against inflation. Do you see any relationship? As you can see, the amount of money in existence has exploded since that book was written, going from $8.5T to $13.3T.  Yet instead of experiencing hyperinflation like the theory suggests, the US has struggled to avoid deflation and get inflation consistently above 2% for several years.
M3 chart: https://fred.stlouisfed.org/series/MABMM301USM189S
Inflation table:http://www.usinflationcalculator.com/inflation/current-inflation-rates/
Most modern-day economists think inflation is related to the velocity of money, not the quantity of it in existence.

Bottom line... read up on economics. It can be counterintuitive. Pulp books like the one you read seem commonsense and paint a clear picture of economic villains and a predictable future, which is why they sell well, but if you invest based on those assumptions, prepare to be burned. Never accept a theory that the data does not support.

Ph.D. in Economics here...CheapBstard pretty much hits a homerun. Nothing to add.

DavidAnnArbor

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Re: The Global Debt Trap
« Reply #5 on: May 30, 2017, 01:47:29 PM »
Everything ChpBstrd wrote is 100% correct.

Moreover, you ought to read a counterpoint to the book you site, such as "The Return of Depression Economics and the Crisis of 2008" by Paul Krugman, Nobel prize winning economist.

Bill Gross, PIMCO's bond manager and hedge fund manager Paul Singer and others kept wrongly predicting hyperinflation "any day now." They paid billions for their wrong understanding of macroeconomics.

There's no actual connection developed in macroeconomics between a country's government debt and it's level of inflation. Japan has a national government debt that is 200% of GDP and Japan is even closer to deflation than other major developed countries.

One person's debt is another person's asset.  Debt in fact was in such high demand as a "safe asset" during the 2008 financial crisis that investors were willing to buy bonds that were yielding less than the inflation rate, and this happened even as federal government debt grew as a result of less revenues coming in and paying out more to cover unemployment insurance, and other social stabilizers during a recession.
« Last Edit: May 30, 2017, 01:56:18 PM by DavidAnnArbor »

Mac_MacGyver

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Re: The Global Debt Trap
« Reply #6 on: June 01, 2017, 08:23:09 PM »
It's all fiat

talltexan

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Re: The Global Debt Trap
« Reply #7 on: June 02, 2017, 11:36:35 AM »
Correct me if I'm wrong, but any commodity would do well in a period of high inflation.

ChpBstrd

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Re: The Global Debt Trap
« Reply #8 on: June 02, 2017, 01:17:15 PM »
Correct me if I'm wrong, but any commodity would do well in a period of high inflation.
Not if demand is falling, or supply is rising. For example, oil could drop even as inflation increases if current trends in fuel economy, average miles driven, and fracking continue. If Venezuela and/or Libya get their shit together in the next few years, oil supply could skyrocket just as your neighbor gets his first Tesla.

Demand for copper, tin, iron, etc. is largely driven by the construction and automotive industries, which could flop if interest rates rise in response to inflation or a number of other reasons.

Agri commodities could sink if tariffs are reinstated to make America great, regardless of inflation.

aspiringnomad

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Re: The Global Debt Trap
« Reply #9 on: June 03, 2017, 01:13:43 PM »
The book you read sounds like garbage. You received much more sage advice here and I agree that ChpBstrd summed things up extremely well. I hope the authors of that book followed their own investment advice so that they suffered some financial consequences for peddling such drivel.

I linked this in another thread that was scaremongering about hyperinflation, but if you want to know markets participants' best guess about inflation 5-10 years from today, look here:

https://fred.stlouisfed.org/series/T5YIFR

After "spiking" to 2.2% in the months after the US election, inflation expectations are back below the Fed's long-run target of 2%.

Indexer

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Re: The Global Debt Trap
« Reply #10 on: June 04, 2017, 01:00:11 PM »
ChpBstrd hit the nail on the head.

I want to add to points 2 and 3.

2. Ben Bernanke got a lot of crap for how he handled the crisis. I for one think he should get a medal! We had the right person in the right place at the right time. He has extensively studied the great depression and our failures of that time. He learned from those mistakes and set out to do the opposite. There are a lot of eerie similarities between 1929 and 2008. If we responded to 2008/2009 like the Hoover administration responded to 1929 the '08 Great Recession would likely have turned into the new (worse) Great Depression and the world would be a far more terrifying place today.

3. The Fed took some extreme measures during the recession, and in a healthy economy those measures would likely have created a lot of inflation. The recession was not a health economy, and without Fed intervention we would have had a lot of deflation. The Fed's extreme measures did create inflationary pressure, but since we were going to experience deflation their measures just got us back to even.

Deflation is a nasty beast and it can easily become a self sustaining feedback loop. A little bit of deflation can quickly turn into a lot of deflation. Prices will be 1% cheaper in the future, so wait to buy something.... companies have to compete so they lower prices more... then they have layoffs to compensate for the lower prices... unemployed people spend less... wait for prices to come down some more...

If the Fed had perfect control over inflation they would probably target 0% inflation. Wouldn't that be nice? They target 2% because if they are slightly off you get 1 to 3% inflation, barely noticeable in a given year. If you target 0% inflation you might get 1% deflation... and then that spirals into 5% deflation... or 30% deflation like in the early 1930s.
« Last Edit: June 04, 2017, 01:04:19 PM by Indexer »

talltexan

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Re: The Global Debt Trap
« Reply #11 on: June 05, 2017, 08:44:17 AM »
Indexer and ChpBstard are carrying the thread here...thanks, guys!

sol

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Re: The Global Debt Trap
« Reply #12 on: June 05, 2017, 12:26:33 PM »
Personally, I've started recommending that people like the OP read this kind of book twice through, take careful notes, then do whatever crazy ass stupid shit they think sounds good.

People who come to this forum asking for this kind of advice never seem to listen when it is given.  They can always find a way to rationalize dumb ideas, and the only way for them to really learn is to pay the price.  Make some bad decisions, lose a bunch of money, and come back in a year or two somewhat humbled.

In the meantime, more thoughtful investors will benefit from your mistakes.  Remember that for every losing play, someone else wins.

OP, have you ever heard of Dual Momentum?

AlmstRtrd

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Re: The Global Debt Trap
« Reply #13 on: June 05, 2017, 05:09:21 PM »
Haven't read the book either but surely debt matters at some point, right? Otherwise governments wouldn't even make any kind of attempt to service it. Any money that is spent paying down the debt is money that can't be spent elsewhere. Thoughts?

dividendman

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Re: The Global Debt Trap
« Reply #14 on: June 05, 2017, 05:51:55 PM »
Haven't read the book either but surely debt matters at some point, right? Otherwise governments wouldn't even make any kind of attempt to service it. Any money that is spent paying down the debt is money that can't be spent elsewhere. Thoughts?

Debt does matter, but what matters a lot more is assets and to a lesser extent income.

Typical Joe might own a $380k house, where he put 80K down and has a $300k mortgage. He might also have 20k in the bank. Let's say he earns 60k a year. Most people would say Joe is in decent financial shape.

Joe's debt:asset ratio = 300:100 = 3:1
Joe's debt:income ratio = 300:60 = 5:1

Now the US has about ~128 trillion in net assets (private assets minus private debt and government assets), ~19 trillion in debt (all levels of government), and an income (GDP) ~18T.

US's gov debt:asset ratio = 19:128 = 1:6.7
US's gov debt:income ratio = 19:18 = 1:1

These stats are much better than Joe's!

So... why do you think Joe is in good shape and the US not? The US is in great economic shape as a whole. The US government can theoretically call upon the income and assets in it's purview at any time to service any debt, so, it's not a problem.

P.S. All US stats from: https://en.wikipedia.org/wiki/Financial_position_of_the_United_States

maizeman

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Re: The Global Debt Trap
« Reply #15 on: June 05, 2017, 07:17:39 PM »
Haven't read the book either but surely debt matters at some point, right? Otherwise governments wouldn't even make any kind of attempt to service it. Any money that is spent paying down the debt is money that can't be spent elsewhere. Thoughts?

Debt does matter, but what matters a lot more is assets and to a lesser extent income.

Typical Joe might own a $380k house, where he put 80K down and has a $300k mortgage. He might also have 20k in the bank. Let's say he earns 60k a year. Most people would say Joe is in decent financial shape.

Joe's debt:asset ratio = 300:100 = 3:1
Joe's debt:income ratio = 300:60 = 5:1

Now the US has about ~128 trillion in net assets (private assets minus private debt and government assets), ~19 trillion in debt (all levels of government), and an income (GDP) ~18T.

US's gov debt:asset ratio = 19:128 = 1:6.7
US's gov debt:income ratio = 19:18 = 1:1

These stats are much better than Joe's!

So... why do you think Joe is in good shape and the US not? The US is in great economic shape as a whole. The US government can theoretically call upon the income and assets in it's purview at any time to service any debt, so, it's not a problem.

P.S. All US stats from: https://en.wikipedia.org/wiki/Financial_position_of_the_United_States

I don't think counting all GDP as income of the federal government is the best analogy. If the government tried to harvest the entirety of GDP for debt repayment or other spending, total GDP would decline rapidly. Also a non-trivial fraction of that GDP is going to other levels of government (state, county, local), some of which gets spent servicing their debt load.

Total federal government revenue is on the order of $3.6T while the federal debt is on track to hit $20 trillion in the next couple of months* which gives the federal government an debt to income ratio of 5.5:1.

Now unlike Joe, the Fed can inflate away the debt of the federal government any time it pleases, which is why we don't have to worry about ending up like Greece, even if spending and tax rates remain about where they are today.

*Adding in state and local debt only bumps this up to $23.4T

dividendman

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Re: The Global Debt Trap
« Reply #16 on: June 05, 2017, 07:25:46 PM »

I don't think counting all GDP as income of the federal government is the best analogy. If the government tried to harvest the entirety of GDP for debt repayment or other spending, total GDP would decline rapidly.


Hrm, yeah, but if Joe spent all his 60k on debt repayment he wouldn't eat or be able to get to work, so I think the analogy still works!

EdwardMM

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Re: The Global Debt Trap
« Reply #17 on: June 05, 2017, 07:27:19 PM »
Haven't read The Global Debt Trap, but from the synopsis you provided, it is not unique. It was probably written in 2009 at the bottom of the market to investors looking for a paradigm to understand what happened and what would happen next. However, it was a wrong / debunked approach.

Assumptions of classical, pre-depression economics:

1) Money has zero value unless the government guarantees to exchange it upon demand for (of all valuable things in the world this one thing) gold.
2) Government should not intervene in recessions/depressions because a "cleansing" process must occur. Metaphorically, this is a religious redemption.
3) Inflation occurs because the number of dollars in existence are like shares in a company, and to expand the number of dollars is to dilute existing shareholders.

Let's pick apart these assumptions one at a time.

1) Money only has value because people agree to use it as a medium of exchange. In that sense, it is the same as gold. Its value is in our heads. It is a token system for exchanging and storing the outputs of work. Many elements are more scarce than gold, yet not exchangeable for as much cash. FWIW, the value of the US dollar became more stable in the decades since the "gold standard" was dropped and the dollar became a fully fiat currency.

2) Read up on Herbert Hoover's response to the Great Depression, and what we learned. The "cleansing" that was expected only got worse, and "liquidating" everyone was a humanitarian catastrophe. Note how Ben Bernanke's response to the Great Recession was different than Andrew Mellon's response to what would become the Great Depression. You'll notice that books in this genre promote the discredited Herbert Hoover / Andrew Mellon set of assumptions. Most modern economists think government inaction exacerbated the Depression. http://potus-geeks.livejournal.com/450718.html 

3) To debunk this idea, compare a chart of M3 (one measure of monetary supply) against inflation. Do you see any relationship? As you can see, the amount of money in existence has exploded since that book was written, going from $8.5T to $13.3T.  Yet instead of experiencing hyperinflation like the theory suggests, the US has struggled to avoid deflation and get inflation consistently above 2% for several years.
M3 chart: https://fred.stlouisfed.org/series/MABMM301USM189S
Inflation table:http://www.usinflationcalculator.com/inflation/current-inflation-rates/
Most modern-day economists think inflation is related to the velocity of money, not the quantity of it in existence.

Bottom line... read up on economics. It can be counterintuitive. Pulp books like the one you read seem commonsense and paint a clear picture of economic villains and a predictable future, which is why they sell well, but if you invest based on those assumptions, prepare to be burned. Never accept a theory that the data does not support.

I don't have anything to add to the discussion, but I just wanted to say that this response right here is why I love these forums. Well done, ChpBstrd - excellent response.

AlmstRtrd

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Re: The Global Debt Trap
« Reply #18 on: June 06, 2017, 06:56:13 AM »
Now unlike Joe, the Fed can inflate away the debt of the federal government any time it pleases, which is why we don't have to worry about ending up like Greece, even if spending and tax rates remain about where they are today.

I often hear this notion of "inflating away the debt" but I don't really get what that would look like in practice. I get that the general idea is that the government pays down the debt in devalued dollars but the consequences of such a weakened dollar are surely dire, no?

maizeman

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Re: The Global Debt Trap
« Reply #19 on: June 06, 2017, 07:32:11 AM »
Now unlike Joe, the Fed can inflate away the debt of the federal government any time it pleases, which is why we don't have to worry about ending up like Greece, even if spending and tax rates remain about where they are today.

I often hear this notion of "inflating away the debt" but I don't really get what that would look like in practice. I get that the general idea is that the government pays down the debt in devalued dollars but the consequences of such a weakened dollar are surely dire, no?

A devaluing dollar causes lots of problems in the short to medium term, and the risk is always that you kick off a self reinforcing pattern of hyper inflation you cannot pull out of. A devalued dollar, if you've gotten there and if you are able to return to more regular levels of interest/inflation doesn't actually cause many problems at all, although one side effect would be a significant redistribution of wealth, since the poor tend to owe debts (credit cards, mortgages, unpaid medical bills) and the wealthy tend to own debt (bonds/CDs/etc), and a lot of inflation would drastically reduce the value of both the money the poor owe and the money owed to the wealthy.

So what would inflating the debt away look like? Well there are essentially two tools the Fed has to increase inflation. One is cut interest rates (but these are already almost at zero). The other is to increase the supply of money in the economy by purchasing assets with brand new money (this is the "quantitative easing" that was talked about a lot right after the 2007/2008 crash). It turns out one of the big assets the fed purchases to put new money into the economy is government bonds, right now close to 15% of the total federal government debt of $20T is owned by the federal reserve. Purchasing treasury bonds also decreases the supply, so if demand for treasury bonds from everyone else in the economy stays the same, the interest rate the federal government pays decreases.

Anyway, one way that inflating away the debt could look like is the federal reserve purchasing more and more government bonds on the open market.

1. This increases the money supply since the federal reserve is creating new money to pay for the bonds, which should eventually lead to inflation,* making the whole of government debt worth less and easier to pay off.

2. It puts downward pressure on the interest rates the US treasury has to pay on its debt which makes the debt easier to service and/or even pay off.

3. And, because the federal reserve pays the interest income on the debt it purchases back to the US treasury, the purchased bonds themselves effectively no longer contribute to the national debt, since the treasury is just paying interest to itself.

There are more extreme models where the US Treasury creates new money to pay off the debt themselves, which again increases the money supply, producing higher inflation, but these tend to require either changes to existing laws, or weird end-runs around the intent of existing laws which would certainly produce court challenges and just be a big mess (see "platinum coin seigniorage" and the idea of the trillion dollar coin, which periodically comes up during government shutdowns and debt ceiling crises**).

*It should be mentioned that since the housing crisis the federal reserve has drastically increased the money supply through this very process, yet have inflation has not occurred. One argument is that there is something wrong with the standard economic models in which case point #1 wouldn't have the effect I describe. Another is that we were really in for a lot of deflation (like the great depression), so that and the inflationary pressure of the new money just canceled each other out.

**https://en.wikipedia.org/wiki/Trillion_dollar_coin

ChpBstrd

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Re: The Global Debt Trap
« Reply #20 on: June 06, 2017, 07:46:27 AM »
Personally, I've started recommending that people like the OP read this kind of book twice through, take careful notes, then do whatever crazy ass stupid shit they think sounds good.

People who come to this forum asking for this kind of advice never seem to listen when it is given.  They can always find a way to rationalize dumb ideas, and the only way for them to really learn is to pay the price.  Make some bad decisions, lose a bunch of money, and come back in a year or two somewhat humbled.

In the meantime, more thoughtful investors will benefit from your mistakes.  Remember that for every losing play, someone else wins.

OP, have you ever heard of Dual Momentum?

I didn't get the impression the OP had bought into the theories suggested by the book. I think s/he was just asking for an evaluation of its ideas, which is always a smart thing to do.

DavidAnnArbor

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Re: The Global Debt Trap
« Reply #21 on: June 06, 2017, 10:23:59 AM »
Debt to GDP ratio is the metric economists use to determine whether the debt is sustainable or not.

The national debt can increase by the same percentage that the nominal gdp raises in a year, and the ratio would not change.

If national debt is 14 trillion, and the nominal GDP increases by 4%, then you can have a budget deficit of 560 billion and the debt to gdp ratio wouldn't change.

matchewed

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Re: The Global Debt Trap
« Reply #22 on: June 06, 2017, 01:15:16 PM »
Why do I think that most of these sorts of scaremongery things are just a result of fear of large numbers.