Why $500bn and not $500 quadrillion? I bothered to do the Math.

Scott Sumner responded to my first post about NGDP futures. He seems to think I pulled the $500bn number out of thin air. He is wrong.

Before I get started, I’d once again like to express my support for NGDP level targets. NGDP level targets are superior to our current dual mandate.

Also, I’d also point out the critique I am making has absolutely nothing to do the quality or usefulness of information which might be given to Central Bankers if NGDP futures existed and traded. Bernanke and Woodford do not address the problems I am raising here.  I say there is no possible futures market. I am not saying that if a futures market for NGDP levels existed, the information the CB would get from that futures market would be useless.There is no can opener.

Here’s Scott:

“The traders might be so smart that they steal $500 billion from the Fed.  I wonder why he didn’t pick $500 quadrillion? Seriously, I’d argue the market need be no larger that $100 million, maybe $10 million.  And I’ve published proposals where the Fed would not take a net long or short position. “

Here is commenter dwb with a version of the same concern:

“err, 500 BN or 3% of nominal GDP? some faulty analysis there. there are a whole lot of flawed assumptions in your analysis, i don’t have time to go through them all, but 3% of gdp does not even pass the smell test. “

There are a few different ideas in Scott’s response worthy of further discussion, but in this post I am only going to address the $500bn number.

And dwb, you should find the time to let me know those flawed assumptions, because otherwise NGDP level futures will be a smoldering heap of ash in 2 weeks.

But back to the $500bn question, “How did I get $500bn?”

I did the math.

First, I’ll give an explanation of the thinking behind the math. Then I’ll show the math. You’ll see $500bn is a decent estimate for how large of a payment the fed would have made to Goldman Sachs and hedge funds on January 30th, 2009.

First, here is some background information about NGDP levels. David Beckworth’s chart shows the Bank of England (BoE) was extremely successful in targeting 5.3% NGDP for decades – until The Event. The BoE missed by about 10% during The Event. It’s pretty clear a central bank can be extremely successful in targeting NGDP.

 

The U.S. federal reserve isn’t targeting NGDP, but here is a similar chart for the U.S. Not too shabby for a CB not even trying to hit a nominal NGDP target.

But something to notice about both of these charts is the difference between success and failure. There are very few “slight misses”. The series is binary – either extremely close to the NGDP target, or huge misses of 10%.

The success of the Central Bank in hitting the NGDP target during normal times is the source of the $500bn.

We want to create an NGDP level futures contract with specifications economically useful to end users during non-recessionary periods. If the Central Bank is to get useful information from this the NGDP level futures, somebody must trade the contract.

To do this, we need to create a contract hedgers can use in a capital efficient manner to hedge fluctuations in NGDP levels during normal times. We need a contract hedgers can use during the times when NGDP is close to the target line.

Economically Useful Futures Contracts

Economically useful contracts apply to every possible futures contract design. If the contracts aren’t economically useful, nobody trades them. This means the Central Bank does not get private sector forecasts from NGDP level futures.

Scott Sumner says in his response:

“I would add that the “futures” market being proposed is unlike any real world futures market.”

I think he’s implying I wouldn’t understand a futures market with an unusual design. Hmmm. He’s also implying he’s discovered some special new futures market which the real world futures markets didn’t feel worthy of launching over the last 175 years. Hmmm.

But every futures market, of any structure, must be economically useful to the participants. There are no special designs, no magic tricks, and no special “designed by an economist, not that dumbass Mike Sankowski” exemptions to being economically useful to the participants. The contract must make economic sense for the participants, or they don’t use it, and the fed doesn’t get information.

This means the leverage on the contract is above 50 to 1, most likely above 80:1, and perhaps as high as 100:1.

Why must leverage be this high?

  1. NGDP doesn’t move around that much during good economic times.
  2. Firms do not and cannot tie up large amounts of capital on hedging operations

David Beckworth’s famous chart shows us how this works for the UK. NGDP has minor fluctuations around the NGDP target level. NGDP growth doesn’t vary enough to justify high margins/low leverage.

Any possible futures contract needs to be capital efficient for end users. Futures contracts don’t have high leverage by accident. Futures have high amounts of leverage in order to be capital efficient for the target audience of the futures markets, hedgers and speculators.

Consider what degree of leverage Walmart would require to even consider using NGDP futures to hedge either top line sales or corporate profits. If Walmart is hedging top line sales, they need to hedge $440 billion of sales. If the hedge ratio is 1:1, they will need to sell $440bn of NGDP futures.

How much money is Walmart willing to use to hedge their sales? Are they willing to put up the entire $440bn in margin? Of course not. They may be willing to tie up $4bn in cash every year to hedge their exposure to NGDP. But anything more than $4bn starts to be not worth the cost. That’s a ton of money to be sitting on a hedge, doing nothing for a company)

If Walmart is hedging profits, the issue facing Walmart is still the same. Margins in the futures markets are extremely low – and leverage extremely high – because participants have cash efficiency concerns.

I’d argue with the minor fluctuations around the NGDP target level, the Walmarts of the world will push for even higher levels of leverage than 100:1

(Now, there are HUGE PROBLEMS with the uncertainty of the NGDP index. The uncertainty of measuring NGDP will cause constant tension between the margin/leverage of the contract and the economic requirements of hedgers. This is a problem with the underlying index – another issue not addressed by economists, but extremely important to end users. I am ignoring these problems for right now, but these problems are yet another problem for NGDP futures which will be difficult to overcome.)

So, we are puttering along with economic good times, and people are using this contract with 100 to 1 leverage.
Then, something like 2008 happens. If the fed is the market maker at the target NGDP level (so the fed can judge hpw much OMO the need to do to push NGDP to target), when the fed makes its 2008 mistake, somebody makes $500bn.

The most common formulation for NGDP level futures was “fed as market maker at a static price” – at least up until a few days ago. Scott used the “fed as market maker at a static price” design to push back against Noah Smith’s critique of volatility.

Here is Scott Sumner responding in an email to Noah Smith on NGDP level futures contract design:

“In an email exchange, Scott Sumner has clarified the nature of his NGDP futures market proposal. In a nutshell, he proposes that the Fed act as a market maker, buying and selling infinite quantities of NGDP futures at the target price. Demand for NGDP futures would then be used to determine Fed policy; if NGDP futures demand increased, the Fed would commence open-market operations to bring down expected NGDP. The price of NGDP futures would not move, but demand would swing from positive to negative, moving Fed policy as it swung.” [Bold Mine]

Well, if the fed is the target price market maker for infinite quantities at target NGDP, and leverage is 100:1, somebody makes $500bn on January 30th, 2009.

How do we know this?

NGDP fell 4.1% in Q4 of 2009:

“Current-dollar GDP — the market value of the nation’s output of goods and services — decreased 4.1 percent, or $148.2 billion, in the fourth quarter to a level of $14,264.6 billion. In the third quarter, current-dollar GDP increased 3.4 percent, or $118.3 billion.”

5% growth per year means each quarter needs to grow at 1.22% per quarter.

I think 5% is a low NGDP level target. A reasonable NGDP target really needs to be a “NGDP per capita target” and should include population growth. The U.S. population is growing at .98% per year.

This means NGDP levels should grow at 6.0% annually to hit 2% inflation and 3% per capita real GDP growth. 6% annual NGDP growth translates to 1.47% growth per quarter.

So how much notional contract value would it take for the Fed to give away $500bn? If the NGDP level growth target is 5% – which I believe is low – then we missed the growth rate target by 5.012% for Q4 2008.

How much notional value of contracts are necessary to generate $500bn in profits? Math tells us

$500,000,000,000/.0532 = $9,398 bn of notional contract value. At 100:1 leverage, we only require 1% of this amount to be put up in margin. This is $93.9bn of margin required to fund this position.

If the target level is 6% – which makes more sense – then the margin required is only $89bn.

That sounds like a lot of money. It is not. The hedge fund industry has $2.3 Trillion under management.

As of 2009, hedge funds represented 1.1% of the total funds and assets held by financial institutions.[3]As of April 2012, the estimated size of the global hedge fund industry is US$2.13 trillion.[4]

$96bn is roughly 5% of the assets of the hedge fund industry. This number does not include what firms like Goldman Sachs and UBS commit to their active trading.

We need to recognize the utter certainty of the NGDP number coming in below target on January 30th, 2009. The concern wasn’t if GDP would be close to positive 1%, but rather if we should start stocking up on guns and potable water. It was 100% clear NGDP was coming in below target – it was the most certain outcome I’d ever seen. The U.S. was in a massive recession, and there was no doubt NGDP would come in below target.

People like George Soros and Paul Tudor Jones would have bet the farm on this trade. People like John Paulson would have sold billions, while every family office and hedge fund would have sold NGDP level futures as well.

Of course, they would have done their trading on the last day possible, which is a month after the end of Q4 2008.

Recall, the only way a short position loses money selling NGDP futures at positive 1.012% is if the NGDP number comes in at a number larger than 1.012%. This simply didn’t and probably couldn’t of happened.

It’s easy to see how the $500bn number is probably too low. It is entirely possible we would have seen the Fed hand over several trillion U.S. dollars to financial institutions on January 30th, 2009. It’s easy to imagine the problems for countries smaller than the United States adopting NGDP level futures.

Recall the chart from David Beckworth and how it’s obvious the BoE was targeting NGDP levels at 5.3%. This chart is utterly damning for this contract design. The BoE- a Central Bank actively targeting NGDP levels – missed the NGDP level target by a massive amount!

So to recap, any futures contract needs to be economically efficient for participants to trade. This is entirely independent of the final specifications and market structure for the contract. If the “the Fed act(s) as a market maker, buying and selling infinite quantities of NGDP futures at the target price”, then we will eventually see a situation where the Central Bank hands over a significant percentage of GDP to speculators.

I think this fully disposes with the possible contract design where “the Fed act(s) as a market maker, buying and selling infinite quantities of NGDP futures at the target price.”

In his response to Noah Smith, Scott proposes the market for NGDP level futures does not need to be very large. He also proposes alternative contracts where the Fed is not the market maker at a set NGDP target level. Instead this alternative contract design has a floating price level set by market participants.

Before we go on, I think Scott entirely misses how damaging the correlation issue is for NGDP level futures.

In another post, I’ll show allowing the level of NGDP level futures to vary means the market size of the NGDP level futures will be tiny. Then, I’ll demonstrate why an tiny NGDP level futures market is the equivalent of an online survey and prone to massive manipulation. Having an online survey dictate U.S. Federal  policy is a bad idea in another post.

 

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Expert in business development, product development, and direct marketing. Developed strategic sales plans, product innovations, and business plans for multiple companies. Conceived the patent pending Spot Equivalent Futures (SEF) mechanism, which allows true replication of spot and swap like products in the futures space.

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Ross Thomas
4 years 8 months ago

Maybe I’m missing something, but I don’t see how NGDP-targeting is even supposed to work. What is the transmission mechanism from the Fed to spending in the real economy, other than interest rates?

Is there a primer anywhere on NGDP targeting from an MMR perspective?

Admin
4 years 8 months ago

I’ve done a lot of thinking about this. I don’t buy the Sumner notion that the Fed can just say things and the private sector will respond. 95% of the people in the USA don’t even know what the Federal Reserve is and could care less what they’re doing so I don’t see how communicating inflation levels is going to change how mom and pop shop. It won’t. I also did a survey of my readers at Pragcap who are basically older, rich and in the know. And they basically all said the Fed has minimal impact on their every day dos and don’ts. Ie, again, no impact even from the more in touch crowd.

So what’s the real transmission mechanism? It’s gotta be through either rates or some fiscal impact that changes net financial assets. So my conclusion is basically this; the Fed either has to buy assets directly from the private sector which is in some way similar to fiscal policy (like funding states through muni purchases) or they have to target long rates like they do at the short end. Ie, “the 30 year bond is 1%” or something like that and hope for credit demand to pick-up for varying reasons.

There are probably others transmission mechanisms and I’ve thought about NGDP for countless hours and these are the primary ways I think it would have to work. One is basically fiscal and the other is basically monetary policy on roids. So pick your poison.

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wh10
4 years 8 months ago

Cullen, I thought that pole of yours was really cool. I wonder why more econ/finance research aren’t survey-based like that. It’s interesting to see how people actually think.

Admin
4 years 8 months ago

Hi WH10. You don’t hang out at Pragcap any longer. Did you become convinced like many MMTers that I am out to destroy the whole world by trying to piece together what I believe is an accurate understanding of the monetary system? 🙂

Also, I think my “pole” is really cool also and I’d prefer that you not talk about it, thank you very much!

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wh10
4 years 8 months ago

lol!!!! Again- I wish we had an edit function.

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Mike Sax
4 years 8 months ago

“my conclusion is basically this; the Fed either has to buy assets directly from the private sector which is in some way similar to fiscal policy (like funding states through muni purchases) or they have to target long rates like they do at the short end. Ie, “the 30 year bond is 1%” or something like that and hope for credit demand to pick-up for varying reasons. ”

Aren’t even long term rates now very low though? Doesn’t it seem like at this point we have very low rates even on the long end so this is basically not available? I mean Operation Twist was done with this idea of long rates in mind, wasn’t it?

Admin
4 years 8 months ago

Yeah, I guess the Fed could get crazy and pin rates at something that would basically send the 30 year mortgage to 1% or something, but this still relies on credit channels to work so there has to be demand for debt. This might work, but it’s not my preferred choice right now.

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Ross Thomas
4 years 8 months ago

That’s pretty much been my conclusion too. I’m glad I’m not the only one who doesn’t see a whole lot to get excited about.

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jt26
4 years 8 months ago

A related question is whether price discovery mechanisms actually help CBs. E.g. has TIPS implied inflation actually been useful to the Fed? Does the market give meaningful info? (http://newyorkfed.org/research/conference/2010/cb/Longstaff1.pdf)

Guest
4 years 8 months ago

Michael: “Straight lines in economic and financial data are not natural. It’s not an accident 5.3% happened over 20 years. ”

This is off-topic, but I loved that line. Here are my own thoughts on that same theme: http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/03/are-there-any-straight-lines-in-economics.html

Lets all remember we are not arguing about strategy here. I’m not sure we are even arguing about tactics. More like whether to use a GPS or map and compass to find our way to the target. You say the GPS won’t work.

I’m going to have to try to get my head around this question, and understand your argument better.

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PeterP
4 years 8 months ago

Yeah, but why does the straight line prove the potency of monetary policy and not automatic stabilizers of the fiscal policy? This is not a proof of anything.

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Lars
4 years 8 months ago

“The goal of futures is to put the printed money into the hands of regular folks first, and screw Goldman with its pants on.”

Why not just deficit spend it into people’s hands? Something countercyclical and automatic would work just as well as NGDP targeting, right?

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Morgan Warstler
4 years 8 months ago

No, then the money would go to rent seekers and Dem voters… the goal here is to run a major betting system, that puts new money into the hands / destroys the money from the US citizen risk takers.

You still get a accurate prediction on where the market thinks real growth and inflation is going, and you don’t have bigger government, crony capitalism, or Goldman getting out-sized gains.

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Greg
4 years 8 months ago

“No, then the money would go to rent seekers and Dem voters… the goal here is to run a major betting system, that puts new money into the hands / destroys the money from the US citizen risk takers.”

If they redistribute it per capita inverse of the income tax stratifications then it goes to renters and repub voters too.

I dont really see the value of creating a super casino and encouraging lottery fever. We have plenty of lotteries and plenty of markets in commodities and stocks for people to speculate on if they wish. There is no dearth of outlets for gamblers.

Admin
4 years 8 months ago

I see where Morgan is going with this, its a way to harness the gambling instinct in a socially useful way. It’d be just like sports gambling, the public would be willing to pay handicappers for betting advice.

Morgan’s ideas (this and the ebay hiring hall) seem to be about, in Andy Kessler’s terms, the government using technology to distribute decision making to the edge of the network as opposed to using it to put more decision making at the center of the network. In other words, the opposite of Project Cybersyn (though the console chairs were cool).
http://en.wikipedia.org/wiki/Project_Cybersyn

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Dunce Cap Aficionado
4 years 8 months ago

Completely unrelated to almost anything: I would just love it if you would tell the ‘not shower curtain rods’ story again sometime soon. I love that story.

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Morgan Warstler
4 years 8 months ago

huh?

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Morgan Warstler
4 years 8 months ago

ALL OF LIFE is gambling. Don’t be daft.

This is certainly a smarter bet than FOREX.

You didn’t get my point. Repubs PAY the huge bulk of the taxes, so stuff they get from the govt. isn’t free. (not kidding)

The goal is to reward the folks that place smart bets, the reality is you will see all kinds of smart strategy spun up – for people with real jobs in some ways it is a unemployment hedge.

First do no harm! That means: First, do not make the govt. bigger. First, do not make banks bigger.

My plan accomplishes that AND has all the upside of NGDPLT signalling.

Don’t be hater, I’m the guy who figures this shit out.

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Morgan Warstler
4 years 8 months ago

Michael, you’re beat – my plan works…

Noble losers knock over their king, otherwise you can make me chase you around the board, but you lose.

My plan stands.

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Tom Hickey
4 years 8 months ago

Mike, you really think that Congress would permit the Fed to send out checks to people? Really? And you really think that Congress would rather do that than institute a BIG or JG? I am not arguing for either a BIG or a JG here. Jus’ sayin’

Congress is smart enough to know that it controls fiscal disbursements and that fiscal is the most powerful tool that politicians have in their toolbox to reward their constituents. You don’t really think that the politicians are going to cede this the Fed chair, do you?

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Morgan Warstler
4 years 8 months ago

You are an idiot.

MY PLAN: requires no political fighting. It does require a change in law. But it has no tax / spend component. folks are free to choose to hedge on financial instrument – get money , lose money – it is THEIR MONEY.

Your plan pretends all people are equal. You are wrong. money WILL NEVER be handed out monthly to the non tax payers to spur the economy along under any Fed plan.

You are DREAMING that the bottom 2/3 matter. Asserting it doesn’t make it so.

They have no money, they barely vote – they ride along, thats it.

Michael i think the issue is you like to dream big with OTHER PEOPLES MONEY.

If it isn’t done for and by the top 1/3 it doesn’t happen.

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Tom Hickey
4 years 8 months ago

That was appropriated through Congress and the checks came from Treasury, not the Fed as in NGDP schemes in which the Fed bypasses Congress, obviating the need for a messy political fight.

So if you mean another round like GWB, I agree that it is possible but less probable now. It would not be easy if of per capita “redistribution” is not offset and “adds to the deficit.” IIRC, GWB was just sending back “your money.”

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Morgan Warstler
4 years 8 months ago
Dear TARD, 1. The A Power doesn’t support sending a check to everyone, they support opwn market risk taking. 2. Granny is not the one betting here, this is FOREX run like a sportsbook without the spread. You deposit cash into your account, and you make you bet on the under. This is NOT FOOTBALL, where everyday people have a team and knowledge base of.. this is where SMB owners (the A POWER) are hedging against economic downturn directly with the Fed – this is cutting out the middleman (Goldman Sachs). The point here is that when the economy heads south, the GUYS WHO SIGN THE PAYCHECKS are the ones getting handed fresh new printed money. Understand what we’re talking about here Michael… this is Distributism as practiced by the Federal Reserve. The top 1/3 of America, now self-insures itself against economic slow-down. No one cares about Granny on a SS check, she’s watching Fox News, she’ll like seeing that Ron Paul and The Factor agree on something. Michael, you need to understand that EVERYONE is not equal. And that the system is not set up to promote economic equality. it isn’t set up for the 1%, it is set up for the top 1/3, and if you are VERY SMART, you’ll learnt o think about how the 1/3 can be used to take down the 1%. if you are very dumb, you’ll keep thinking about the bottom 2/3 – who barely vote, and have no money, they are renters, they are service industry labor, they are not your salvation. They will not rise up and over throw the top 1/3 who have 200M GUNS, and fund the police depts., own their homes, own the SMBs in small towns all over America. They run the PTAs, they run the churches.… Read more »
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Morgan Warstler
4 years 8 months ago
We don’t give FREE SHIT to the bottom 2/3. get this through your head. the top 1/3 pay ALL the taxes that actually fund the government… (SS doesn’t count form the 2/3 they get it back), so they aren’t being given anything. Look dude, my Guaranteed Income plan works BECAUSE it lets the 1/3 put the unemployed (who the 1/3 subsidizes with the GI) to work doing menial tasks / time saving tasks – so they’ll support it. Giving the GI recipients a private sector bossy boss who wants ROI on the auction win gets the social benefits of hard work and makes society more cohesive. It gets you ghetto renewal and advantages entrepreneurs in poor areas, sot here’s lots there for real progressives. You NEED to let go of the idea that the top 1/3 will let the civil SERVANTS (the teachers, the bureaucrats be more important – they are going to be replaced by computers – govt. is going to be replaced by the Internet. There is no future power base of the public sector which is about to undergo a MASSIVE FORCED PRODUCTIVITY BINGE that will reduce its labor size by more than half. Postal workers, teachers, local office clerks, all of them are going bye-bye. Imagine a new govt. is being built in the modern age of the smart phone. Citizen A takes picture or pot hole, low bidder by end of day fils up pot hole – there is NO govt. in there, just computer and end users. This is whats coming, the baby boomers need the $$$ for medicine and food and that means $1.2T in public sector employment is going to go down to less than $600B, which is where we’d be IF the public sector just stayed on the same productivity gains… Read more »
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Morgan Warstler
4 years 8 months ago

Once again, I think I have figured this out:

1. Wal-Mart, Goldman, etc. aren’t allowed to trade it. Price setters are out.

2. Instead it runs and feels like a national lottery or sports book where only US Citizens are able to bet and they are limited in how much they can drop into their account. They can’t lose more than this in any given month.

3. You can only bet the under… but you predict like Price is Right how much under.

4. If the Fed comes in above target, they destroy everyone’s money (or some percentage of it). Gone. Removed from system.

5. If they come in below target, they print cash and hand the newly printed money to the winners, the closer you come to the number without going under the more outsized your gains.

But if you bet under the under #, you get nothing.

The idea here that when the Fed misses low, there may be BILLIONS being handed to the daring folks who placed the accurate bets, and the whole country will get lottery fever… increasing the players.

And Goldman and WalMart will suck it.

The goal of futures is to put the printed money into the hands of regular folks first, and screw Goldman with its pants on. If you don’t start with a plan like that, then WHY do it?

——

Run the lottery monthly, the first time a bunch of folks get a sick payday, the Fed will have plenty of money to destroy.

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Tom Hickey
4 years 8 months ago

What is the quality of the information to be derived from that though, if a bunch of small, naive and inconsequential players dominate the action, treating it as a lottery?

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Morgan Warstler
4 years 8 months ago

There are BILLIONS of dollars to be won… the fewer the players the more they make!

Greed and professional betting takes over…. oversubscription can’t happen, when there is money destroying going on, everyone just loses less than their full bet.

Have you EVER seen a Vegas book making operation?

It’s OK to just adopt my plan. it won’t bite.

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Tom Hickey
4 years 8 months ago

But point of the futures is the generation of information, money changing hands is the means, not the end. I don’t see how excluding the market makers and shapers is going to generate much useful information.

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Morgan Warstler
4 years 8 months ago

This is wrong.

Let’s say that we need a bump in NGDP after August 2013, so the Fed prints $15B and hands it to 15K people…

What do you think the effect is going to be from minting 1M new millionaires overnight?

How many new home sales will occur?

——

The information is SECOND BEST, if you can get NEW MONEY into regular lottery folks / gamblers hands.

I’m not demeaning the information bit, I’m just saying don’t leave the real benefit on the table.

FUCK GOLDMAN SACHS. Make them work for their money.

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Morgan Warstler
4 years 8 months ago

15K new milionaires

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