What gold's negative lease rate teaches us about the zero-lower bound

When people talk about gold, they usually talk about the gold price. But there are a few other key gold market metrics that often go unmentioned. The chart below stacks the gold price on top of the gold forward rate (GOFO), LIBOR, and the lease rate. The gold lease rate is an interest rate. Just as you can lend your cash to a bank at the bank's deposit rate, you can lend your physical gold to a bank at the lease rate.

Understanding GOFO and the lease rate is important not only for gold bugs, but for anyone who wants to get a good grasp of the phenomenon of interest rates. GOFO and the gold lease rate demonstrate that interest rates are not phenomena solely confined to paper assets. The ability for an investor to lease their gold and earn an interest return makes up part of gold's peculiar "own-rate". All commodities have own-rates. From our perspective as consumers, we rarely get to see these markets, but they do exist. I've illustrated them in the following chart:

Go to this scribd link for a high res version if you want to understand how GOFO, LIBOR, and the lease rate interact.

One thing you may have noticed from the chart is that gold's three month lease rate (at bottom) is negative. Back in November 2011 the one month lease rate fell to a record low of -0.5%. Now anyone familiar with the idea of the zero-lower bound may find this surprising. Interest rates aren't supposed to be able to fall below 0%. If they do, people will simply redeem the underlying 0% yielding asset and store it themselves. Why keep gold on loan to a bank only to pay a -0.5% penalty when you can withdraw it and keep it under the mattress for free? Yet the market was willing to bear negative lease rates.

The reason for this oddity is that as the yellow metal's price rises, it becomes ever more attractive to robbers. One ounce to a robber at $300 is tempting, but not as tempting as that same ounce at $1750. So it costs more to insure gold. Secondly, storing gold is somewhat costly. Do you hide it under granny's bed, or do you buy a home safe for it? At which point do you rent a vault at a bank? Anecdotal evidence suggests that banks specializing in gold storage have been running out of space over the last few years, implying rising storage costs.

In a nutshell, that's why people haven't withdrawn their gold as lease rates have turned negative. In keeping their gold on loan to the bank rather than bringing it at home, they avoid all the headaches of storage costs, insurance, and the fear of theft, yet still get exposure to gold price appreciation. The negative lease rate is the fee they pay in order to have someone else incur all these headaches.

Like the gold market, the currency market also has the capacity to bear a negative interest rate. If the rate on bank deposits falls to say -0.25%, depositors would likely keep their cash on loan to the bank since storing it at home or in a vault is costly. How low can deposit rates fall before people start to withdraw cash? -1%? -2%? Cash, after all, is thin and light, surely easier to store than gold. One way to prevent cash redemption at negative deposit rates is to make cash storage costly. If someone wants to withdraw $100,000 in cash, make them take it all in $5 bills. The high cost of storing low denomination bills will get anyone to reconsider withdrawal. I've discussed the idea of varying redemption denominations here.

So as the gold market shows, the zero-lower bound is a soft bound, not a hard one. As for all you gold bugs out there, I'll write more about negative lease rates sometime soon.

Zero percent interest rates forever

Noah Smith asks what would happen if the Fed kept interest rates at zero forever. Specifically:

Suppose that the Fed targets only one interest rate, a short-term nominal interest rate, and that its only tool is Open Market Operations (it cannot provide any "forward guidance" or communicate with the public at all). Suppose that at date T, the Fed decides to keep the interest rate at zero in perpetuity, and remains unwaveringly committed to this decision for all time > T.

He asks this because Nayarana Kocherlakota, head of the Minneapolis Fed, once said, somewhat counter-intuitively, that over the long run, a low fed funds rate must lead to consistent—but low—levels of deflation. This seems odd at first blush because we've been conditioned to assume that low interest rates lead to inflation, not deflation.

I'm going to try and give an answer that financial types will understand. The spoiler is... over the short term we'd have inflation, but Kocherlakota is probably right that after some time passes, an artificially low federal funds rate will lead to a steady deflation.

Imagine that you're an investor who can hold either deposits at the central bank or units of some durable good. In order for these two assets to be willingly held by both you and your fellow investors, each must provide attractive returns. If one of these assets provides excess returns, arbitrage dictates that you'll all try to switch to that asset until those excess returns cease to exist.

A bank deposit's return can be decomposed into an interest component, expected capital appreciation (or depreciation), and a liquidity yield. Liquidity is a special benefit that a deposit provides since it more marketable than most assets. The durable good, assume it costs nothing to store, provides a return in the form of capital appreciation (or depreciation), but no interest and a liquidity yield that is so minimal that it may as well be nothing.

At the outset, the returns on the two assets are already equal. But the central bank suddenly lowers the interest component of the return it pays on deposits to nothing, catching the investment community by surprise. As an investor you're distraught. The deposit you held just prior to the announcement yielded, say, 5%, and now it yields just 0%. You'd like to sell it for the durable good, since the return on the durable good (which is composed, say, of expectations of 10% price appreciation) is superior. But investors holding the durable good won't sell to you, simply because the return they require on the 0% deposit must be similar to the return on the durable good they already own. And it isn't.

To convince them to accept your 0% deposit for their good, you must increase its return. You can do this by increasing the expected capital appreciation provided by the deposit. By marking down the current price of the deposit relative to its expected future price, you provide your trading partner with the necessary potential capital appreciation. Whoever buys the deposit can be sure that even though it yields an interest rate of 0%, it will provide a commensurate capital return of 5% or so.

In knocking down the market price of the deposit, you've caused immediate inflation. The purchasing power of money (the deposit) has fallen such that you can't buy as many durable goods with it as you could before. At the same time, you've cleared the stage for future expectations of deflation. That's because in low-balling the offer price for your deposit to attract buyers, you've increased the expected capital appreciation provided by the deposit. You've caused inflation in order to promise deflation.

Maybe the entire process happens immediately. But economists like to divide things into the short and long run. In the short run, all you'll see is inflation as the market gropes for a new and lower clearing price for deposits. At first, perhaps, most investors think that the central bank will only keep rates at 0% for a year and then set them back at their normal rate. But when the next year comes and the bank surprises the market by keeping those rates at zero, once again you'll have to rapidly lower the price of your deposit so as to provide potential deposit buyers with enough capital appreciation to compensate for the disappointing yield on deposits.

This yearly pattern of lowering the price you offer on your deposits continues until the market is no longer surprised by the central bank's intentions to keep rates at 0% for eternity. Only then will the inflation end. Deposits, which by now have been bid down to some terminally low level, will slowly and steadily appreciate. This is the "consistent deflation" that Kocherlakota describes.

There is one interesting caveat here. I started out the example by pointing out that one component of a deposit's return is its liquidity yield. Because the market puts a premium on liquid assets —a liquidity premium, so to say —deposits and other liquid assets can provide lower interest rates than not-so-liquid assets.

But if deposits (or any other money-like object) are constantly plunging in value, they cease to be attractive as medium of exchange. In general, people prefer to transact with relatively stable monies. Thus each time you mark down the deposit's value, its liquidity premium deteriorates as the market searches out for other assets that can serve as better mediums of exchange. With the decline in its liquidity yield, the overall return from holding deposits declines even further. This inferior return can only be compensated by a promise of more capital appreciation ie. yet another fall in today's market price relative to expected future prices. This process feeds on itself as the falling value of a liquid assets renders it less liquid which causes it to fall further in price. At some point, the deposit risks being demonetized.

What comes first? Will the deposits reach a terminally low price from which they commense their rise? Or will they become demonetised and valueless? What about the assets that back deposits... might these provide some lower limit for the price of a deposit, even if it pays 0% loses its entire liquidity premium? Fun questions, but I'll leave those for someone else.


Related blog posts:
Karl Smith here and here, and Andy Harless here.

More on own-rates

The discussion on own-rates, the natural rate, and Sraffa cropped again.

Andrew Lainton blogged here, followed by Nick Rowe here, Daniel Kuehn here, and David Glasner here.

It seems to me that Nick and David are more or less on the same side of the aisle. I commented on Nick's post here, and Nick provided a helpful response. I commented on Glasner here, and he gave me some good feedback.

The natural rate of interest and the own-rate argument

The Austrian vs Keynesian end of the blogosphere often battle over the existence of a natural rate of interest. The Keynesian side typically points to Piero Sraffa's argument that there are many natural rates of interest, or own-rates, and therefore an Austrian sort of monolithic natural rate of interest simply doesn't exist.

Over the last few weeks I've participated in the comments here at Jonathan Finegold Catalan's blog and here at Daniel Kuehn's blog. Here is an older comment in this vein on "Lord Keynes" blog. Bob Murphy also has a paper (pdf) on this subject and has commented on the above blogs on this subject.

Normal backwardation in crude oil markets

James Hamilton at Econbrowser had an interesting series of posts (here and here) on determining the effect of naive commodity index funds in crude oil and other commodity markets. His hypothesis was that:

the more futures contracts the funds want to hold, the more risk the counterparties who short the contract are exposed to. According to the model, the futures price must be bid high enough to compensate the short side for absorbing the risk. This compensation comes in the form of an expected profit to the short side of the futures contract. 

I pointed out in the comments that this sounded very familiar to me:

...isn't this an attempt to prove a version of Keynes's theory of normal backwardation? Here is Keynes: "If supply and demand are balanced, the spot price must exceed the forward price by the amount which the producer is ready to sacrifice in order to hedge himself, ie. to avoid the risk of price fluctuations during his productions period."

Keynes wrote that speculators would require a premium if they were to bear the risk of price movements. In a way, it seems you are substituting Keynes's hedgers with a more modern sort of naive indexer from whom speculators demand an extra return.

Unfortunately Hamilton did not find the data to back up his hypothesis. Too bad, it is a very elegant theory.

Sraffa, Hayek, natural interest rate, and own-rates of return

I commented on the blog Social Democracy for the 21st Century: A Post Keynesian Perspective in a post called Hayek’s Natural Rate on Capital Goods, Sraffa and ABCT.

Specifically, the issues in the above blog post are continued in one of my favorite David Glasner posts,  Sraffa v. Hayek.

I requote Glasner: "the rate of return from holding all assets net of their storage costs and their current service flows must be equal in equilibrium. If not, you’re not in equilibrium. So all you have to do is find an asset with no storage cost and no current service flow and calculate its expected rate of appreciation and you have the real natural rate of interest."

Liquidity options, liquidity premium, natural interest rate, TIPS, and inflation swaps

Commented on David Glasner's Once Again The Stock Market Shows its Love for Inflation:

The only problem here is the one that we talked about in a previous post (Unpleasant Fisherian Arithmetic) concerning the liquidity premium that assets carry. The reason for the rising TIPS spread could be (though not necessarily must be) that the liquidity premium on treasuries is shrinking relative to that of TIPS, and therefore TIPS are rising in price relative to Treasuries. This makes it hard to pass judgment on the hypothetical rate of return on capital.

 Anyways, you have already commented on this problem in your paper: “One possible cause of distortion in the yield on TIPS bonds and in the TIPS spread during the autumn 2008 financial crisis is that the yield on conventional Treasuries was depressed because of a liquidity premium. Even though the ex ante real interest rate was likely negative, because TIPS bonds were perceived as much less liquid than conventional Treasuries, TIPS bonds could not be sold unless they were discounted, so that their yields rose well above the (unobservable) ex ante real rate on holding real assets.”

 We were talking in the comments of the “Unpleasant Fisherian Arithmetic” post about how one could measure liquidity. I thought a bit about this. If there were a market for financial products, say options, that managed to price the pure value of an underlying asset’s liquidity premium, then you would be able to measure the value that the market placed on assets’ relative liquidity premiums and, from there, get a better idea for what portion of an assets total return is provided by an own-rate and what is provided by a liquidity premium. These sort of financial assets don’t exist, but if they did they would probably be sort of like credit-default swaps… more like liquidity-guarantee swaps.

Note that is follows from a previous comment I had concerning the impossibility of computing the natural rate of interest because liquidity interferes. See Unpleasant Fisherian Arithmetic

David responded:

Have you looked at how the Cleveland Fed tries to extract the inflation expectation from the TIPS spread?

I responded:

 I looked at it this morning. It seems to me that the Cleveland Fed is using alternative measures to extract inflation expecations given the problems posed by illiquidity in TIPS markets. They are including the inflation swaps market. In an inflation swap, one party pays a fixed interest rate, the other pays the inflation rate.

 Apparently swap markets didn’t suffer as much as TIPS markets did from liquidity problems in 2008, and for that reason the Cleveland Fed is using swap rates as one of their main indicators of inflation expectations.

 That being said, swaps are still traded contracts and bear some sort of liquidity premium, so it is still empirically impossible to back out a real rate without knowing what that premium is.

 For your records, here is the quote page for the 2 year USD dollar inflation swap spread: http://www.bloomberg.com/apps/quote?ticker=USSWIT5:IND

The Cleveland Fed discuss their methodology here. http://www.clevelandfed.org/research/workpaper/2011/wp1107.pdf