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.



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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124 Comments on "Why $500bn and not $500 quadrillion? I bothered to do the Math."

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4 years 10 months ago

If you want to think like that you can but as long as people do we will deal with problems like this.

Dunce Cap Aficionado
4 years 10 months ago

How do you think of it then?

4 years 11 months ago

It’s not free shit. It is shit that they should have been paid enough to buy in the first place and maybe we wouldn’t be in this situation. All the businesses the top echelon own wouldn’t mean dick if it wasn’t for the 2/3’s labor.

Morgan Warstler
4 years 11 months ago

you do a job, you get paid, that’s it…

there’s no extra good will left over that gives you a piece of somebody else.

Dan Kervick
4 years 11 months ago
4 years 11 months ago

Mike here is a piece Sumner wrote about NGDP futures back in 2010. His modus operandi is clear. He’s just going to keep saying you haven’t read his proposal.


That’s his story and I expect he will stick to it.

Keep doing what you’re doing I look forward to Part III, but don’t necessarily presume he is operating in good faith where the truth is the only objective.

4 years 11 months ago

THey are more like a parasite that wraps itself around it’s host and lives off it’s lifeblood.

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