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The Coming Rise in Money Velocity

June 28, 2022 2 comments

As M2 money growth soared throughout the COVID and post-COVID period of direct stimulus check-writing funded by massive quantitative easing (QE), monetarism novices thought that this would not result in inflation because money velocity simultaneously collapsed. Consequently, they argued, M*V was not growing at an outrageous rate.

There was precedence for such optimism. In the Global Financial Crisis of 2008-09, money supply grew rapidly with the onset of QE and money velocity declined, never to recover. The chart below shows in a normalized fashion the rise in M, the decline in V, and the relative quiescence of MV/Q, which is of course P by definition as long as you choose your Ms, Vs, and Qs right.

A similar thing happened in this episode, so why would this be any different?

There are many reasons why these episodes are different. To name a few:

  • The absolute scale of the rise in M2 was 2.5x the rise in 2007-2010, and that’s being generous since that measures the growth in 2007-2010 starting almost 2 years before the first QE in November 2008 compared to only 15 months in the second case.
  • As I’ve written previously, QE in the first case was directed at banks; at the same time that the Federal Reserve was adding reserves it was also paying banks interest on reserves – because the point was to strengthen banks, not consumers.
  • 5y interest rates came into 2008 at 3.44%; they came into 2020 at 1.69%. Since velocity is most highly correlated to interest rates, there was less room for this factor to be a lasting downward influence on velocity (after the crisis began in 2008, 5y Treasury rates never exceeded 3% again except for a few days in 2018).
  • Bank credit growth never stopped in the 2020 crisis, while it contracted at a 5% rate in the 2008 crisis (see chart, source Board of Governors of the Fed).

The monetarist novices (you can tell they’re novices because they say things like “Friedman said velocity was constant,” which is false, or “velocity is just a plug number [true] and has no independent meaning of its own [false]”) insisted that velocity was in a permanently declining state and that there was no reason at all to expect it to ever “bounce.” After all, it bounced only slightly after the GFC; why should it do so now?

But after 2008, as I noted, interest rates bounced only briefly before declining again…with the added phenomenon that some global debt came to bear negative yields, calling into fair question whether there was in fact any natural “bottom” to velocity if interest rates are the main driver! And velocity, obediently, dripped lower as well.

There is at least one other big driver to money velocity, although it is rarely important and almost never for very long. And that is economic uncertainty, which creates a demand to carry excess cash balances (implying lower money velocity). A model driven (mainly) by rates and a measure of uncertainty has done a pretty good job at explaining velocity over time (see chart, source Enduring Investments), including explaining the collapse in velocity during the COVID crisis out-of-sample.

Now, explaining velocity is a helluva lot easier than predicting it, because it isn’t easy to predict interest rates. Nor is it easy to predict the precautionary demand for money – but at least we can count on that being somewhat mean-reverting. The latest point from the model shown above uses current data, and suggests (largely because of the rise in interest rates, but also because precautionary balances are declining) that money velocity should bounce. Not that the model predicts it will happen this week, but it should not be surprising when it does.

A rise in velocity would be a really bad thing, because the money supply is very unlikely to decline very far especially while bank credit growth continues to grow. The only reason we have been able to sustain 6% or 8% money growth for a very long time has been because we could count on velocity to keep declining with interest rates. If money growth ticks up at, say, a mere 6% while money velocity rises 5%, then nominal GDP is going to rise 11%…and most of that will be in prices.

Now, this is a very slow-moving story. I mention it now for one specific reason, and that is that we are almost certain to see a rise in velocity in Q2 when the GDP figures come out in late July. That’s because money growth for the quarter has been very slow so far. So far, the Q2 average M2 is 0.06% higher than the Q1 average. My best wild guess is that we will end up with an 0.5% annualized q/q growth rate. The Atlanta Fed GDPNow model estimates 0.25% GDP growth in Q2 (the Blue Chip Consensus is still at 3%). And if the inflation market is right, Q/Q inflation in Q2 will be about 11.7%. That’s CPI, so let’s be generous and say 9%. We don’t know all of these numbers, but we know 2/3 of all of them. Let’s use the Blue Chip consensus for GDP and assume M2 doesn’t spike next month and the price level doesn’t collapse. Then:

If that happened, the increase would be the largest quarterly jump in money velocity – absent the reactionary bounce in 2020Q3 after the 20% plunge in 2020Q2 – since 1981. And here’s the rub: because of the mathematics of declines and recoveries, that would still leave us with velocity that prior to 2020 would have been an all-time record low.

Does this matter? Not if you believe the monetarism dabblers, who will say this is a mechanical adjustment that will soon be reversed as velocity continues its long slide to oblivion. Nor will it matter to the Fed, who at best will take executive notice of the fact before ignoring it since they aren’t monetarists any longer. But for those who think that inflation comes from too much money chasing too few goods? It’s scary.

Why Roughly 2.25% is an Equilibrium Real Rate

Recently, Fed officials have taken to discussing “long-term equilibrium” interest rates as a way of indicating to the market where interest rates might ultimately be heading. It is not exactly a terrifying prospect. The Fed seems to collectively believe that the “neutral” short-term nominal interest rate is in the 2.50%-2.75% range; some fear that the Fed funds target right may have to be lifted “modestly” above this level for a time. This seems hard to believe, with inflation running with an 8% handle – such an overnight rate would equate to an annual 5-6% incineration of purchasing power. The only way this could be considered “neutral” is if one begs the question by asserting contrary to evidence that the long-run equilibrium inflation rate is around 2%-2.25%.

I have noted repeatedly over the last year or so why it is unlikely in my opinion that the current equilibrium for inflation is in the 2% range; I feel it is closer to 4%-5% in the medium-term. But if an observer has a model which has been ‘trained’ on data from the last thirty years, the model will assuredly tell you that any time inflation deviates from 2%, it comes back to 2%. In fact, any model which did not produce that prediction would not have been considered a good model: it would have made predictions which, for 30 years, would have been noticeably incorrect from time to time. Ergo, all surviving models will view something like 2% as an attracting level for inflation, and we know the Fed continues to believe this. So, evidently, do many other economists. I keep showing this following chart because I think it’s delicious. Take today’s level; take the level your model says is a self-enforcing equilibrium, and draw a straight line. That’s your forecast. You too can be a million-dollar Wall Street economist.

Faced with awful predictions from this cadre of models, one solution is to consider why they had bad predictions, and attempt to develop models that would perform on data from the 1970s and 1980s as well. A more attractive solution, from an institutional perspective, is to blame model-exogenous events. That is, “the model is fine; who could have foreseen that supply chain issues would have triggered such a large inflation?” And so, we preserve the FOMCs ability to continue making terrible forecasts.

Similarly, Minneapolis Fed President Neel Kashkari stated not too long ago that the Fed may have to “push long-term real rates into restrictive territory.”[1] This continues the Fed’s error of obsessing on the price of liquidity rather than its quantity, but that isn’t the point I am making here. Kashkari made a different error, in an essay posted on the Minneapolis Fed website on May 6th.[2] He claimed that the neutral long-term real interest rate is around 0.25%, which conveniently is where long-term real rates are now.

However, we can demonstrate that logic, reinforced by history, indicates that long-term real rates ought to be in the neighborhood of the economy’s long-term real growth rate potential.

I will use the classic economist’s expedient of a desert-island economy. Consider such an island, which has two coconut-milk producers and for mathematical convenience no inflation, so that real and nominal quantities are the same. These producers are able to expand production and profits by about 2% per year by deploying new machinery to extract the milk from the coconuts. Now, let’s suppose that one of the producers offers to sell his company to the other, and to finance the purchase by lending money at 5%. The proposal will fall on deaf ears, since paying 5% to expand production and profits by 2% makes no sense. At that interest rate, either producer would rather be a banker. Conversely, suppose one producer offers to sell his company to the other and to finance the purchase at a 0% rate of interest – the buyer can pay off the loan over time with no interest charged. Now the buyer will jump at the chance, because he can pay off the loan with the increased production and keep more money in the bargain. The leverage granted him by this loan is very attractive. In this circumstance, the only way the deal is struck is if the lender is not good at math. Clearly, the lender could increase his wealth by 2% per year by producing coconut milk, but is choosing instead to maintain his current level of wealth. Perhaps he likes playing golf more than cracking coconuts.

In this economy, a lender cannot charge more than the natural growth in production since a borrower will not intentionally reduce his real wealth by borrowing to buy an asset that returns less than the loan costs. And a lender will not intentionally reduce his real wealth by lending at a rate lower than he could expand his wealth by producing. Thus, the natural real rate of interest will tend to be in equilibrium at the natural real rate of economic growth. Lower real interest rates will induce leveraging of productive activities; higher real interest rates will result in deleveraging.

This isn’t only true of the coconut economy, although I would strongly caution that this isn’t exactly a trading model and only a natural tendency with a long history. The chart below shows (1) a naïve real 10-year yield created by taking the 10-year nominal Treasury yield and subtracting trailing 1-year inflation, in purple; (2) a real yield series derived from a research paper by Shanken & Kothari, in red; (3) the Enduring Investments real yield series, in green, and (4) 10y TIPS, in black.

The long-term averages for these four series are as follows:

  • Naïve real: 2.34%
  • Shanken/Kothari: 3.13%
  • Enduring Investments: 2.34%
  • 10y TIPS: 1.39%
  • Shanken/Kothari thru 2007; 10y TIPS from 2007-present: 2.50%

It isn’t just a coincidence that calculating a long-term average of long-term real interest rates, no matter how you do it, ends up being about 2.3%-2.5%. That is also close to the long-term real growth rate of the economy. Using Commerce Department data, the compounded annual US growth rate from 1954-2021 was 2.95%.

It is generally conceded that the economy’s sustainable growth rate has fallen over the last 50 years, although some people place great stock (no pun intended) on the productivity enhancements which power the fantasies of tech sector investors. I believe that something like 2.25%-2.50% is the long-term growth rate that the US economy can sustain, although global demographic trends may be dampening that further. Which in turn implies that something like 2.00%-2.25% is where long-term real interest rates should be, in equilibrium.[3] Kashkari says “We do know that neutral rates have been falling in advanced economies around the world due to factors outside the influence of monetary policy, such as demographics, technology developments and trade.” Except that we don’t know anything of the sort, since there is a strong argument against each of these totems. Abbreviating, those counterarguments are (a) aging demographics is a supply shock which should decrease output and raise prices with the singular counterargument of Japan also happening to be the country with the lowest growth rate in money in the last three decades; (b) productivity has been improving since the Middle Ages, and there is no evidence that it is improving noticeably faster today – and if it did, that would raise the expected real growth rate and the demand for money; and (c) while trade certainly was a following wind for the last quarter century, every indication is that it is going to be the opposite sign for the next decade. It is time to retire these shibboleths. Real interest rates have been kept artificially too low for far too long, inducing excessive financial leverage. They will eventually return to equilibrium…but it will be a long and painful process.


[1] https://www.reuters.com/business/finance/feds-kashkari-we-may-have-push-long-term-real-rates-into-restrictive-territory-2022-05-06/

[2] https://www.minneapolisfed.org/article/2022/policy-has-tightened-a-lot-is-it-enough

[3] The reason that real interest rates will be slightly lower than real growth rates is that real interest rates are typically computed using the Consumer Price Index, which is generally slightly higher than the GDP Deflator.

Categories: Economics, Economy, Theory Tags:

High Prices Don’t Cure High Prices

April 23, 2022 10 comments

This was an interesting week, in which it seemed that equity investors finally and abruptly got the message that high inflation is bad for the market; increasing interest rates are bad for the market; declining bid/offer liquidity is bad for the market; high energy prices are bad for the market; global geopolitical unrest is bad for the market; and a strong dollar is (eventually) bad for the market. The last two days in the stock market was a remarkably steady and orderly melting. Will it continue? Well, none of those trends I just mentioned look as if they are about to change significantly, so the only question is whether the extraordinary popular delusion returns.

The proximate cause for the selloff seems to have been the hawkish talk from Fed speakers, including the floating of the trial balloon early in the week about the possibility of a 75bp tightening. By the end of Friday, Cleveland Fed President Mester was actively pouring cold water on the notion that anything so aggressive was out of the question, while still talking in terms of 50bps increments.

I admit that as of only a few months ago, I didn’t think the Fed would hike rates more than about 75bps in total before they lost their nerve. On the other hand, they’re about 500bps behind the curve, so color me surprised…but not impressed.

To be sure, I also thought the stock market would have reacted before this point. And I do think that it is easier to talk about how much you’re going to work out this summer until it gets hot. So we will see.

But, on to my real topic today: the annoying canard that “high prices are the cure for high prices,” which is a phrase so absurd on its face that the discussion really shouldn’t go much further than that. The phrase implies that we can’t have inflation because if we have inflation, then prices will come down. It’s one reason that people are expecting used car prices to drop by as much as they previously rose – because “no one can afford a car at those prices!”

The idea is that as prices rise, the amount of money in your pocket can’t buy as many things. Therefore, real demand must suffer because higher prices mean that people can buy less stuff. Ergo, inflation causes recessions (which is weird, because we are always told how expansions cause inflation – which means that expansions must cause recessions. Are you feeling a ‘down the rabbit hole’ sensation yet?).

This is another example of a stock-flow fallacy. Or maybe it’s a fallacy of composition. It’s a micro/macro mistake. The point is that it doesn’t work that way.

The system can’t run out of money. If prices go up 25%, it doesn’t mean that you can buy 20% less stuff. Well, perhaps you can buy 20% less stuff, today, until you run out of money. But the person who sold you the car now has 25% more money than he would have previously, had he sold the same car before. Maybe you are out of money, but he has 25% more money. The money doesn’t leave the system when you buy something. It only leaves your wallet. (The stock market works exactly the same way, and no one ever questions why stock prices can’t keep going up because investors are using up all of their money, right?).

Now, if the total amount of money in the system is the same today as it was before the 25% increase in prices, and the velocity of exchange doesn’t change, then yes – that 25% price increase won’t stick because in aggregate we will be spending the same amount of money at higher prices, which means we take home fewer goods and services. If on the other hand the amount of money in the system went up by 25%, then total expenditures (if velocity is roughly constant) will be the same in unit terms as before. The system doesn’t grind to a halt and force prices lower. The system reaches equilibrium at prices that are 25% higher. By the same token, if there is 40% more money in the system, then those 25% price increases won’t be enough, there will be shortages, and prices will keep rising.

This seems like a good point to recall that M2 money since the end of 2019 has risen 42%. Tell me again why Used Car prices need to retrace so much?

The real question, to me, is why more prices haven’t gone up 42%. My answer is that we are still in the adjustment period. It takes time for that money to wash around the system, and it’s still on the rinse cycle.

Financial Buyers Aren’t to Blame For High Commodities Prices

February 23, 2022 Leave a comment

Today’s does of non-Ukraine content concerns a misunderstanding about commodities that seems to require regular correction. I’ve seen it resurface recently, most recently in a daily digest from Bloomberg this morning:

“There seems to be something of a vicious circle developing in the commodities space, where investors are increasing their exposure as an inflation hedge, thereby possibly driving up prices further. “

This is not something you should worry about.

I suspect this sort of thinking derives from observations about financial futures, in particular cash-settled sorts. But in contracts for physical delivery, it doesn’t work this way. A purely financial investor cannot drive up prices in the spot market, because such an investor never gets to the spot market. No one, outside of a few sophisticated hedge funds, holds physical commodities as an inflation hedge (with the possible exception of precious metals, which isn’t what they’re discussing here). No one keeps a silo of corn or beans for investment, taking that supply off the market in the process. (Almost) no one keeps a tanker truck of gasoline as an inflation hedge or a pile of aluminum.[1] A financial investor must cover their (long) positions by finding an offset before delivery. Only buyers who actually want the commodity delivered, or sellers who actually have the commodity to deliver, go all the way to final settlement. Ergo, the spot price is determined by actual buyers and sellers of the spot commodity and not financial players.

So, if financial investors in commodities do anything at all, they might push up deferred contract prices relative to spot prices, putting the market further in contango. If anything, this actually would cause the opposite effect from the one noted above since a producer who owns future commodities (in other words, they make production decisions about how much to grow or mine) can lock in a higher selling price than the current spot price – which obviously would make them want to supply more to the market.

But if this was the dynamic, then commodities curves would be in contango (deferred contracts higher than spot contracts); instead we find that commodities curves are in backwardation at levels we haven’t seen in a long time.

[N.b.: if you have the Inflation Guy mobile app, you can look for the Daily Chart Pack under “tools” and on page 17 you will find this chart, updated every day.]

Commodities curves being in backwardation is actually one strong piece of evidence that financial buyers are not driving volatility or activity in commodities markets. Curves are in backwardation because there are shortages in the spot market but producers are still willing to sell future production lower than the current level.

In short – don’t blame the financial players for the rise in commodities prices. Blame years of underinvestment followed by massive money-stoked demand. It’s not hard to see why commodities have risen so much. It’s only hard to guess how much farther they will go. But they answer in any event will not depend on how heavily invested institutions or the general public are.


[1] That can occasionally include pure arbs doing cash-and-carry metals arb, but that’s not much fun when the curves are backwardated like they are now.

A Guess at the Value of Long Inflation Tails

December 7, 2021 1 comment

In my last post, “You Have Not Missed It,” I promised the following:

“There is one final point that I will explain in more detail in another post. Breakevens also should embed some premium because the tails to inflation are to the upside. When you estimate the value of that tail, it’s actually fairly large.”

So, as promised, here is that explanation.

Viewing the forward inflation curve as a forecast of expected inflation (whether using “breakevens” or, more accurately, inflation swaps) is biased in a particular way. Or, at least, it should be. The “breakeven” inflation rate is the rate at which a long-only investor over the ensuing period would be roughly as well off with a nominal bond (which pays a real rate plus a premium for expected inflation) and an inflation-indexed bond (which pays a real rate, plus actual inflation realized over the period). Obviously the inflation-indexed bond is safer in real space, so arguably nominal bonds should also offer a risk premium to induce a buyer to take inflation risk.[1] Ordinarily, though, we ignore this risk and just consider breakeven inflation to be the difference between real and nominal yields. Inflation swaps are cleaner, in that if inflation is higher than the stated fixed rate, the fixed-rate payer on the swap ‘wins’ and receives a cash flow at the end, whereas if inflation turns out to be lower than the stated fixed rate, it is the fixed-rate receiver who wins. So from here on, I will talk in terms of inflation swaps, which also abstract from various bond-financing issues of the breakeven…but the reader should understand that the concept applies to other measures of expected inflation as well.

Now, suppose that you expect 10-year inflation to come in at 2% per annum. Suppose that in the inflation swap market, the 10-year rate is 2% ‘choice’ – that is, you may either buy inflation at 2% or sell inflation at 2%. Since you expect inflation to be 2%, are you indifferent about whether you should buy or sell?

The answer is no. In this case you should be much more eager to buy 2% than to sell 2%, given that your point estimate is 2%. The reason why is that the distribution of inflation outcomes is not symmetrical: you are much more likely to observe a miss far above your expectation than to observe a miss far below your expectation. Therefore, the expected value of that miss is in your favor if you buy the inflation swap (pay fixed and receive inflation) at 2%. There is, in other words, an embedded option here that means the swap market should trade above where most people expect inflation to be.

We can roughly quantify at least the order of magnitude of this effect. Consider the distribution below. This chart (Source: Enduring Investments) shows the difference, from 1956 until 2011, of 10-year inflation expectations[2] compared with subsequent 10-year actual inflation results. The blue line is at 0% – at that point, actual inflation turned out to be right where a priori expectations had it. The chart obviously only covers until 2011 since that is the last year from which we have a completed 10-year period. Recognize that I am not charting the levels of inflation, but the level of inflation relative to the original expectation.

Notice that the chart has a cluster of outcomes (and in fact, the most-probable outcomes) just to the left of zero, where expectations exceeded the actual outcome by a little bit, but that there are very few long tails to the left. However, misses to the right, where the actual outcome was above the beginning-of-period expectations, were sometimes quite large. The median point (where half of the misses are to the left, and half are to the right) is 0.21%. But this is not a symmetric distribution, so if we randomly sample points from this distribution, we find that the average of that sample is 0.59%.

So, if you buy the inflation swap at 2% when your expectations are at 2%, on average you’ll win by 59bps, at least historically. Of course, past results are no indication of future returns, and a Fed economist would argue that we have much better control of inflation now than we ever have in the past (Ha ha. I crack myself up.). And inflation volatility markets, when they can be found, don’t trade at such high implied volatilities. Noted, although the wild swings in growth and the deficit and the money supply, not to mention recent realized outcomes, might make more cynical observers question whether we should be so confident in that view right at the moment.

Moreover, a counterargument is that at the present time an investor also has the advantage of investing when expectations are fairly low, so the downside tails are not as likely. The worst outcome of that whole 1956-2011 period was an 8.75% undershoot of inflation versus expectations. This happened in the 10 years following September 1981, when expectations were for 10-year inflation of 12.70% and actual inflation was 3.95%. But with expectations at 2.50%, is it really feasible to get a -6.25% compounded inflation rate? That would imply a 50% fall in the price level (and, I should note, it would mean that investors in TIPS would win hugely in real space since they get back no worse than nominal par. But that doesn’t help the swap buyer).

To be a little more fair, then, the following chart considers only the periods where inflation expectations were 5% per annum or less at the beginning of the period. That truncates only 10% of the distribution, but as you might expect the vast majority of the truncation is on the left-hand side. This is fair because it’s naturally harder to miss far below your expectations when your expectations are very low to begin with.[3]

The value of the expected miss in this contingent view is 1.13%. So, in order for the market to be priced fairly if general expectations are for 2.5% average CPI inflation the 10-year inflation swap would have to be around 3.63%. Again, even allowing for the “policymakers are smarter now” argument (an argument quite lacking, I would argue, in empirical evidence) I would feel comfortable saying that 10-year inflation swaps, and breakevens, should embed at least a 50bps or so ‘option premium’ relative to expectations.

I don’t believe that they do. Indeed, consider that the buyer of 10-year TIPS (with breakevens at 2.50%) not only wins if 10-year inflation is above 2.50% but the average win historically (conditioned on breakevens being below 5% to start, and by construction only considering wins) has been about 2.07% per annum – a massive outperformance. Not only that, but any losses are essentially guaranteed to be small because the tails on the left-hand side are truncated: if inflation is negative (that is, if the loss would have been greater than 2.50%) it is limited by the fact that the Treasury guarantees the nominal principal.

As an aside, we do consider this sort of option in other contexts. In the Eurodollar futures market, for example, we recognize that the person who is short the Eurodollar contract (and therefore gets a positive mark-to-market when interest rates rise) is in a better situation than the long (who gets the positive mark-to-market when interest rates fall), because the short gets to invest wins at higher interest rates and borrow losses at lower interest rates, while the long must borrow to cover losses when interest rates are higher, and but gets to invest wins when interest rates are lower. As a result, Eurodollar futures trade lower than the forwards implied from the swap curve, since the buyer needs to be induced by a better-than-expected price. And there are other such examples. But I am pretty sure I have never seen an example of an embedded option like this that is priced so differently relative to history than the embedded options in the inflation market!


[1] However, since this risk is symmetric – the seller of the bond also has risk in real space, but in the opposite direction – it isn’t immediately obvious why one side should get an inducement over the other. So I will leave the ‘risk premium’ aside.

[2] For long-term inflation expectations back before the advent of TIPS, I used the Enduring model relating real yields to nominal yields, about which I’ve written previously. You can find a brief discussion of this and an illustration of the model at this link: https://inflationguy.blog/2016/12/23/a-very-long-history-of-real-interest-rates/

[3] The author’s wife has been known to make something like this observation from time to time.

Categories: Options, Theory, TIPS Tags: , ,

Shortages are Unmeasured Inflation

October 24, 2021 5 comments

Recently, I’ve been saying occasionally that “shortages are unmeasured inflation.” In some conversations I have had, it became apparent to me that people were taking this statement as being a throwaway line: “inflation is bad, shortages are bad, therefore they’re kinda the same.” But what I mean is actually more profound than that, and so I figured I would explain and illustrate, and hopefully thereby to convince.

Let’s use some charts.

What has happened since the large increase in federal spending and transfer payments were implemented in several waves since the shutdown began is that demand in many product markets has shifted outward. This implies that output “Q” moves from c to d while the price level “P” moves from a to b. [1]

So a strong increase in demand causes an increase in the quantity exchanged at the new equilibrium, and an increase in the price of the good or service at that equilibrium. This is the nice, smooth, continuous markets, instantaneous-adjustment picture from Econ 101. It’s also not the way the real world works, especially with large shifts in demand.

If price only adjusts partially, maybe if “anchored inflation expectations” or a fear of being accused of gouging restrained vendors from raising prices enough to ration the available supply, then a shortage results. This is the same thing which occurs classically if a price cap is instituted from the outside. Now price moves up from a only to b’, but the quantity demanded at that price is at d’. Thus, the bracket on the chart below shows the size of the shortage at that price, where consumers want d’ but suppliers can’t/won’t provide that much.

Note that this shortage is a direct substitute for the increase in price that would otherwise happen if prices could instantly and fully adjust. Moreover, the picture is somewhat worse in the short-term because the supply curve – in the short-term – is much more inelastic at some point (because, for example, no matter how high the price gets we can’t deliver more used cars in the short run). So, in the picture below the short-run supply curve in blue implies that the large increase in demand pushes prices to b’ with output only at d’, until supply eventually adjusts to the long-run supply curve S(lr), when we end up in the new market-clearing equilibrium.

In this case, the difference between b and b’ is “transitory” inflation, caused by temporary supply constraints. But note that in this picture, there is no perceived shortage. The market clears at b’ and d’. In other words, the conditions leading to the “transitory” increase inflation are not the same ones leading to the shortages.

We can combine these; if in the last picture above vendors also constrain prices to b, then there is a shortage as the quantity demanded stays up at d rather than at the market-clearing level d’. But, again, in that instance the shortage reflects the fact that prices should have adjusted to b’ but did not. Also in that case, it would be inaccurate to claim that the inflation was transitory, since prices should remain at b even when the supply eventually adjusts to the long-run equilibrium. It would be the shortage that was transitory.

In theory, if we knew the shapes of the curves of supply and demand for each product market, we could estimate how much higher prices would be at equilibrium and therefore how much additional inflation the shortage implies. We could directly translate the shortages to an “equilibrium” price level and therefore inflation. It strikes me as plausible that we could develop a rough estimate of such a number, but I leave that to the PhD candidates looking for dissertation topics. In the meantime, just remember that with inflation over 5% presently and shortly headed above 6%…the inflation rate is understated, and we know that because there are lots of shortages.


[1] If the deficits, funded by Fed purchases of Treasuries, had just offset the loss in incomes due to the shutdown – perfectly, across all individual markets – then there would have been no demand shift and no net change in output or prices. And if the deficits had not been accompanied by an increase in the Fed balance sheet, then it would have been individuals buying the bonds and so the only effect would have been because the marginal propensity to consume of the people receiving transfer payments is higher than the marginal propensity to consumer of the people buying the bond issuance. But in this column I’m trying not to muddy the discussion with the argument of whether we need both fiscal and monetary stimulus to cause inflation. I’m just focused on the narrow question of what it means when I say “shortages are unmeasured inflation.”

When Over-Ordering is More Than Hoarding

September 8, 2021 2 comments

It is a lament I have heard recently from the manufacturing/supply side, but also an excuse I’ve heard from some of the economist ranks for why “this supply chain issue will all get sorted out; people are just going crazy.” In this column I want to explain why “overordering” is not only perfectly rational but actually demanded by some typical operational procedures.

The complaint is “our customers are not only ordering what they used to order, but they’re ordering far more than they used to. Basically, they’re hoarding and we have had to ration our product and only partially fill orders/only fill them for our top customers.” Now, hoarding is a real thing, but moreso for consumers than in B2B. There are, though, some serious reasons (by which I mean, ‘reasons that are held by serious people’) why it makes sense to increase orders at a time like this. And it’s not because you are assuming you’ll get 50% fill rates on your orders, so you order double in the hopes that you’ll get the actual amount you want. That’s an “unserious” reason.

One of the reasons I have written about before. Back in January, I wrote an article called “The Optionality of Inventories,” in which I predicted the companies would move away from lean inventory models because inventory serves as an option against bad things happening: if bad things don’t happen, you’ve paid a little more for your inventory; if bad things happen, you have a large gain (loss averted) because you had a cushion. That article is worth a quick read. I also point out that, as inflation increases, there is a financial incentive to hold larger inventories because the inventories themselves are increasing in value. To the extent that more firms are recognizing the option value of inventory, it makes total sense that the demand gets fiercer the closer to raw materials you get. The entire supply chain needs to hold more inventories.

But there’s another “serious” reason that is related to the length of the supply chain itself. “Fred, last year you only ordered 1,000 units. This year you ordered 2,000 units! I know your business hasn’t doubled. Why are you doing that?” Fred might well be doing this because lead times are increasing, and that mathematically increases his reorder point and quantity.

Reorder quantity mathematics, at the simplest level, is just “number of days of lead time” times “average use per day,” and you reorder when inventory declines below that number plus some “safety stock” which is essentially a fudge factor. So, if we are using one ton of flour per day, and it takes us a week to get flour, then we need to reorder whenever we get down to seven tons of flour (call it 8, just in case. That extra one is the ‘safety stock.’) And, when we reorder, we reorder at least seven tons of flour since by the time that order arrives, we’ll be down to one ton of flour. But if the lead time now stretches to two weeks, we are suddenly ordering 14 tons of flour even if our usage didn’t change.

That simple model works for very regular inventory usage patterns, but in many applications the quantity used (or demanded, if we are talking about holding finished goods inventories) is variable. In that case, the reorder point and quantity also depends on the variance in the order flow. Again, inventories are like options, and so the sophisticated way to think about the safety stock is the option value where the stock-out (you run out of inventory) is the strike price. If you want to never lose on that bet, you have to have a high option price (safety stock); moreover, the higher is volatility, the higher is the level of inventory required to maintain a given ‘acceptable’ level of stock outs.[1]

How does 2021 compare to 2019, the last time manufacturers faced “normal” order patterns that they are now seeing customers exceed? Well, there have been substantial increase in lead times, and substantial increases in every kind of volatility you can imagine. Lead times across the globe have increased probably 30-50% at least, and that means that required inventory needs to increase 30-50% at a minimum, plus more because volatility has increased.

So that customer who is ordering a lot more right now than they historically have is not doing it to “hoard.” They’re probably doing it just to manage inventory properly. Of course, that puts more pressure on the supply chain, and increases lead times further. It represents a one-time increase in GDP, as intended inventory accumulation adds to output in the period it is accumulated, and that pressure also boosts price pressure. And ‘round and ‘round we go.

And all of this, we should take pains to remember, started when governments decided to use cardiac paddles to resuscitate a patient they’d actively tried to kill, and central banks made sure they were hooked up to a strong current to do so. The fact that the body economic is convulsing should not be a surprise to anyone. The question is whether we can sue for malpractice.


[1] The only way to guarantee that you’ll never run out of inventory, if there’s any variance in the demand for the inventory, is to hold massive amounts of inventory. So in practice you have to pick an acceptable stock-out frequency, which enters into the calculation.

Are Home Prices Too High?

September 2, 2021 2 comments

There is an advantage to squatting in the same niche of the market for years, even decades. And that is that your brain will sometimes make connections on its own – connections that would not have occurred to your conscious mind, even if you were studying a particular question in what you thought was depth.

A case in point: yesterday I was re-writing an old piece I had on the value of real estate as a hedge, to make it a permanent page on my blog and a “How-To” on the Inflation Guy app. At one point, I’m illustrating how a homeowner might look at the “breakeven inflation” of homeownership, and my brain asked “I wonder how this has changed over time?”

So, I went back in the Shiller dataset and I calculated it. To save you time reading the other article, the basic notion is that a homeowner breaks even when the value of the home rises enough to cover the after-tax cost of interest, property taxes, and insurance. In what follows, I ignore taxes and insurance because those vary tremendously by locality, while interest does not. But you can assume that the “breakeven inflation” line for housing ought to be at least a little higher. In the chart below, I calculate the breakeven inflation assuming that mortgage rates are roughly equal to the long Treasury rate (which isn’t an awful assumption if there’s some upward slope to the yield curve, since the duration of a 30-year mortgage is a lot less than the duration of a 30-year Treasury), that a homeowner finances 80% of the purchase, pays taxes at the top marginal rate, and can fully deduct the amount of mortgage interest. I have a time series of the top marginal rate, but don’t have a good series for “normal down payment,” so this illustration could be more accurate if someone had those data. The series for inflation-linked bonds is the Enduring Investments imputed real yield series prior to 1997 (discussed in more detail here, but better and more realistic than other real yield research series). Here then are the breakeven inflation rates for bonds and homes.

It makes perfect sense that these should look similar. In both cases, the long bond rate plays an important role, because in both cases you are “borrowing” at the fixed rate to invest in something inflation-sensitive.

The intuition behind the relationship between the two lines makes sense as well. Prior to the administration of Ronald Wilson Reagan, the top income tax rate was 70% or above. Consequently, the value of the tax sheltering aspect of the mortgage interest made it much easier to break even on the housing investment than to invest in inflation bonds (had they existed). That’s why the red line is so much lower than the blue line, prior to 1982 (when the top marginal rate was cut to 50%) and why the lines converged further in 1986 or so (the top marginal rate dropped to 39% in 1987). The red line even moves above the blue line, indicating that it was becoming harder to break even owning a home, when the top rate dropped to 28%-31% for 1988-1992. Pretty cool, huh?

Now, this just looks at the amount of (housing) inflation of the purchase price of the home needed to break even. But the probability of realizing that level of housing inflation depends, of course, on (a) the overall level of inflation itself and (b) the level of home prices relative to some notion of fair value. This is similar to the way we look at probable equity returns: what earnings or dividends do we expect to receive (which is related to nominal economic growth), and what is the starting valuation level of equities (since we expect multiples to mean-revert over time). That brings me back to a chart that I have previously found disturbing, and that’s the relationship between median household income and median home prices. For decades, the median home price was about 3.4x median household income. Leading up to the housing bubble, that ballooned to over 5x…and we are back to about 5x now.

That’s the second part of the question, then – what is the starting valuation of housing? The answer right now is, it’s quite high. So are we in another housing bubble? To answer that, let’s compare the two pictures here. In the key chart below, the red line is the home price/income line from the chart above (and plotted on the right scale) while the blue line is the difference between the breakeven inflation for housing versus breakeven inflation in the bond market.

In 2006, the breakeven values were similar but home prices were very high, which means that you were better off taking the bird-in-the-hand of inflation bonds and not buying a home at those high prices. But today, the question is much more mixed. Yes, you are paying a high price for a home today; however, you also don’t need much inflation to break even. If home prices rise 1.5% less than general inflation, you will be indifferent between owning real estate and owning an inflation bond. Which means that, unlike in 2006-7, you aren’t betting on home prices continue to outpace inflation. It’s a closer call.

I can come up with a more quantitative answer than this, but my gut feeling is that home prices are somewhat rich, but not nearly as much so as in 2006-07, and not as rich as I had previously assumed. Moreover, while a home buyer today is clearly exposed to an increase in interest rates (which doesn’t affect the cash flow of the owner, but affects the value the home has to a future buyer), a home buyer will benefit from additional “tax shelter value” if income tax rates rise (as long as mortgage interest remains tax deductible!). And folks, I don’t know if taxes are going up, but that’s the direction I’d place my bets.

CPI Forwards Show Inflation Concerns Aren’t Ebbing

August 9, 2021 1 comment

One of the most important things I learned as a markets person was the relationship between “spot” prices and “forward” prices. A spot price is the price today, if you buy a particular investment or commodity. A forward price is the price that you agree today to pay in the future on some date for delivery of that investment/item.

To a non-markets person, this seems odd. If I want to buy a carton of milk, but the grocery store is out of milk so I tell the grocer “hold one of those cartons for me when they come in,” it wouldn’t occur to me that I should pay a different price than is on the shelf. Or, maybe, I might expect to pay whatever the price is, when the milk comes in. But I wouldn’t think that today I should arrange for a different price for that milk just because I get it in the future.

But of course, the idea of the present value of money is super important in investing. A dollar received in the future is worth less than a dollar received today. (That is, unless interest rates are negative. In that case, a dollar in the future is weirdly worth more than a dollar today, and we are in that bizarre situation I described once, in a really neat post, as ‘Wimpy’s World.’) But it isn’t just money that has a different value for future delivery than it does today. There are at least two ways that I can own a pound of gold six months from now. One is to buy a pound of gold, and pay for storage and for insurance for six months. The other is to arrange with someone today to deliver me a pound of gold in six months. In that case, I don’t have to pay for storage and insurance, so I’ll be willing to pay more for gold in the future. In commodities markets, we say that this curve is in “contango,” where futures prices are above spot prices.

The important thing to realize, though, is that all of these things converge. The spot price of gold will eventually converge to the 6-month forward price of gold…in, as it happens, about six months. If there is no change in the price of insurance and storage, every day the spread of the futures price over the spot price will decline by one day’s worth of those expenses. (n.b. – there are other parts of the carry, too; I’m abstracting here for illustration). If nothing else in the market changes, then the spot price will gradually rise towards that forward price. Here is the important bit that markets people learn: in some sense, that is not a true profit:

Buy today: $1700 plus $10 storage plus $10 insurance = $1720 cost of gold 6 months’ forward

Buy for forward delivery: $1720.

In both cases, if I sell the gold six months and one day from now at $1720, I have made zero money, even though in the first case I paid $1700 for it. But it looks like gold rallied.

I’m not really here to talk about gold. I’m here to talk about economists.

Economists don’t really internalize this well. Case in point is the question about whether inflation expectations are ‘anchored.’ An economist – in particular, a Fed economist – looks at the following chart of 2-year inflation swaps since February and says “Expectations for inflation two years in the future rose between February and May, and then have been flat-to-down since then.”

But that’s not really what happened.

Someone who bought inflation swaps in early May got something that a buyer of inflation swaps today doesn’t get. The May 15th version of inflation swaps, because of the way they work with a 3-month lookback, got half of the 0.6% March CPI print, plus the 0.8% April print, the 0.6% May print, and the 0.9% June print. The person who buys inflation swaps today doesn’t get March and April, and only half of the May uptick (plus June). Ergo, if nothing else changes we would expect the price for a 2-year inflation swap today to be lower than the price in mid-May.

As the high prints from the last few months pass into the rear view mirror (although there will be some high ones to come, I don’t really expect +0.9% m/m any time soon), the inflation swaps and breakevens markets should look softer. It’s just carry. But how much softer?

One way to find out what is really happening to inflation expectations is to look at the forwards. Let’s pretend for a minute that the CME had actually launched CPI futures a few years ago, and we had a CPI futures contract that traded in December 2023 (settling to the November CPI print that comes out that month). Over the last few months, what would have happened to the price of that futures contract? The chart below shows that it would have enjoyed a very steady rise over the last six months. The CPI futures contract settles (or anyway, it would have) to a particular price level. We would almost always expect the futures prices to be above the current NSA CPI number, which was 271.696 in June. But these prices – which I’ve calculated from an inflation swaps curve I build every day – are showing that investors have responded to these higher CPI prints by steadily raising their expectation of future prices.

If investors thought these last few months were going to be reversed in the coming months, then the forwards wouldn’t have responded in this way. Investors would be betting that the high prints would be followed by low prints that reverse the changes. However, that’s not what is happening. Investors are taking these high prints and putting them in the bank. While they might think the rise in the inflation rate is transitory, they don’t think the rise in the price level is transitory.

This is a key distinction. The inflation we are seeing, even if it later slackens, represents a permanent loss of purchasing power. How much of a permanent loss have we seen in the last couple of years? Here are my calculations of the theoretical futures curve for CPI, as of August 1st, 2019 compared to last Friday. The last column shows how much higher investors think prices will be on those dates today, compared to what they thought two years ago.

Notice that this is from well before the crisis, and so takes into account the plunge in prices from early 2020 and the recent increases. After all of the zigzags, investors expect prices to be about 5% higher in 2023 than they would have thought previously, and about 8% higher in 10 years.

And I think they’re too sanguine.

Categories: Investing, Theory Tags: , ,

Some Thoughts on Gold, Real Yields, and Inflation

February 23, 2021 6 comments

TIPS-style inflation-linked bonds (more properly known as Canadian-style) pay a fixed coupon on a principal amount that varies with the price level. In this way, the real value of the principal is protected (you always get back an amount of principal that’s indexed to the price level, floored in the case of TIPS at the original nominal value), and the real value of the coupon is protected since a constant percentage of a principal that is varying with the price level is also varying with the price level. This clever construction means that “inflation-linked” bonds can be thought of as simply bonds that pay fixed amounts in real space.

I have illustrated this in the past with a picture of a hypothetical “cake bond,” which pays in units of pastry. The coupons are all constant-sized cupcakes (although the dollar value of those cupcakes will change over time), and you get a known-sized cake at the end (although the dollar value of that cake might be a lot higher). That’s exactly what a TIPS bond is essentially accomplishing, although instead of cupcakes you get a coupon called money, which you can exchange for a cupcake. This is a useful characteristic of money, that it can be exchanged for cupcakes.

The beauty of this construction is that these real values can be discounted using real yields, and all of the usual bond mathematics work just perfectly without having to assume any particular inflation rate. So you can always find the nominal price of a TIPS bond if you know the real price…but you don’t need the nominal price or a nominal yield to calculate its real value. In real space, it’s fully specified. The only thing which changes the real price of a real bond is the real yield.

All TIPS have coupons. Many of them have quite small coupons, just like Treasuries, but they all have coupons. So in the cake bond, they’re paying very small constant cupcakes, but still a stream of cupcakes. What if, though, the coupon was zero? Then you’d simply have a promise that at some future date, you’d get a certain amount of cake (or, equivalently, enough money to buy that certain amount of cake).

Of course, it doesn’t have to be cake. It can be anything whose price over a long period of time varies more or less in line with the price level. Such as, for example, gold. Over a very long period of time, the price of gold is pretty convincingly linked to the price level, and since there is miniscule variation in the industrial demand for gold or the production of new gold in response to price – it turns out to look very much like a long-duration zero-coupon real bond.

And that, mathematically, is where we start to run into problems with a zero-coupon perpetuity, especially with yields around zero.


[If you’re not a bond geek you might want to skip this section.] The definition of Macaulay duration is the present-value-weighted average time periods to maturity. But if there is only one “payment,” and it is received “never,” then the Macaulay duration is the uncomfortable ∞. That’s not particularly helpful. Nor is the mathematical definition of Modified duration, which is Macaulay Duration / (1+r), since we have infinity in the numerator. Note to self: a TIPS’ modified duration at a very low coupon and a negative real yield can actually be longer than the Macaulay duration, and in fact in theory can be longer than the maturity of the bond. Mind blown.  Anyway, this is why the concept of ‘value’ in commodities is elusive. With no cash flows, what is present value? How do you discount corn? Yield means something different in agriculture…


This means that we are more or less stuck evaluating the empirical duration of gold, but without a real strong mathematical intuition. But what we think we know is that gold acts like a real bond (a zero coupon TIPS bond that pays in units of gold), which means that the real price of gold ought to be closely related to real yields. And, in fact, we find this to be true. The chart below relates the real price of gold versus the level of 10-year real yields since TIPS were issued in 1997. The gold price is deflated by the CPI relative to the current CPI (so that the current price is the current price, and former prices seem higher than they were in nominal space).

When we run this as a regression, we get a coefficient that suggests a 1% change in real yields produces a 16.6% change in the real price of gold (a higher yield leads to a lower gold price), with a strong r-squared of 0.82. This is consistent with our intuition that gold should act as a fairly long-duration TIPS bond. Of course, this regression only covers a period of low inflation generally; when we do the same thing for different regimes we find that the real gold price is not quite as well-behaved – after all, consider that real gold prices were very high in the early 1980s, along with real yields. If gold is a real bond, then this doesn’t make a lot of sense; it implies the real yield of gold was very low at the same time that real yields of dollars were very high.

Although perhaps that isn’t as nonsensical as it seems. For, back in 1980, inflation-linked bonds didn’t exist and it may be that gold traded at a large premium because it was one of the few ways to get protection against price level changes. Would it be so surprising in that environment for gold to trade at a very low “gold real yield” when the alternative wasn’t investible? It turns out that during the period up until 1997, the real price of gold was also positively related to the trailing inflation rate. That sounds like it makes sense, but it really doesn’t. We are already deflating the price of gold by inflation – why would a bond that is already immunized (in theory) against price level changes also respond to inflation? It shouldn’t.

And yet, that too is less nonsensical as it seems. We see a similar effect in TIPS today. Big inflation numbers shouldn’t move TIPS higher; rather, they should move nominal bonds lower. TIPS are immunized against inflation! And yet, TIPS most definitely respond when the CPI prints surprise.

(This is a type of money illusion, by which I mean that we are all trained to think in nominal space and not real space. So we think of higher inflation leading to TIPS paying out “more money”, which means they should be worth more, right? Except that the additional amount of dollars they are paying out is exactly offset by the decline in the value of the unit of payment. So inflation does nothing to the real return of TIPS. Meanwhile, your fixed payment in nominal bonds is worth less, since the unit of payment is declining in value. Although this is obviously so, this ‘error’ and others like it – e.g. Modigliani’s insistence that equity multiples should not vary with inflation since they are paying a stream of real income – have been documented for a half century.)

For now, then, we can think of gold as having a very large real duration, along with a price-level duration of roughly one (that is just saying that the concept of a real price of gold is meaningful). Which means that higher inflation is actually potentially dangerous for gold, given low current real yields, if inflation causes yields (including real yields) to rise, and also means that gold bugs should cheer along with stock market bulls for yield curve control in that circumstance. Inflation indeed makes strange bedfellows.

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