Gold's rising convenience yield

While I may have taken some jabs at the gold bugs in two recent posts, please don't take that to mean that I have it in for the metal itself. Gold is a fascinating topic with a history that is well worth studying. (See this, for instance). In that vein, what follows is some actual gold analysis.

Something weird is happening in gold markets. The future price of gold (its forward price) has fallen below the current gold price. Now in fairness, this isn't an entirely new phenomenon. Over the last year or two, the price of gold one-month in the future has traded below the current, or spot price, a number of times. However, this observation has grown more marked as both the three-month and six-month rates have also recently fallen below the spot price.

This degree of inversion is rare. Except for a brief flip in 1999 when near-term forward prices fell below zero for a day or two, future gold has almost always traded for more than current gold. See chart below, which illustrates the one-month to twelve-month forward price premium/deficit in annual percent terms:

Here's why this pattern has dominated:

Gold's forward price indicates the level at which a buyer and seller will contract to exchange gold at some point in the future. The seller must be compensated for a number of costs they will incur in holding the gold until the deal's consummation, including: 1) taking out a loan to buy the gold and stumping up interest expenses; and 2) paying to store and insure it in a vault. Together, these are called carrying costs.

The buyer of future gold needs to compensate the seller for these costs. Rather than paying the seller an up-front fee, the buyer builds a premium into the price they pay for future gold in-and-above the current spot price, say $5. The future seller of gold can use this $5 premium to cover their carrying costs, thereby coming out even in the end. So future gold trades above spot gold by the size of its carrying costs.

The current inversion of spot and future gold prices seems to break all these rules. The premium that sellers have traditionally required has not only shrunk to 0 but become a deficit. Put differently, sellers of future gold are no longer demanding a compensatory fee for storing and financing the metal. In fact, they seem willing to provide these expensive services at a negative price!

One explanation for the inversion is that with interest rates being so low, the costs of carrying gold have become negligible. This is only party correct. Minuscule carrying costs would imply a future gold price that is flat relative to the current gold price, when in actuality future prices are below present prices.

That leaves only one explanation for the inversion: there is some sort of hidden non-pecuniary benefit to holding the stuff. In futures-speak, this benefit is typically referred to as a commodity's convenience yield, a term coined by Nicky Kaldor in 1939. An analogy to oil markets may be helpful. Oil prices often invert because merchants see potential for future supply disruptions. Having oil on hand during these disruptions is immensely useful as it  spares our merchant the hassle of negotiating his or her way though an oil supply chain that may be severely crippled while ensuring that customer demand is smoothly met. So the convenience yield can be thought of as a flow of relief, or uncertainty-shielding services, provided to owners of inventories of a commodity. If that relief is sheer enough, than the convenience yield will be larger than the twin costs of financing and storage, resulting in inverted markets. (For an excellent explanation of the convenience yield in oil markets, check out this Steve Randy Waldman post).

That's what appears to be happening in gold. Gold merchants seem to be anticipating choppiness in the future supply and demand of the metal, and see growing benefits in holding inventories of the stuff in order to cope with this choppiness. The convenience yield on these inventories has jumped to a high enough level that it currently outweighs the costs of storing and financing gold, resulting in an inverted gold market.

Gold's convenience yield spikes every every few years due to market disruptions, with the last spike occurring during the 2008 credit crisis, the one prior to that in 2001, and the one before that in 1999 when central banks announced plans to limit gold sales. It just so happens that these earlier disruptions occurred when U.S. interest rates were already high enough that they continued to outweigh the metal's suddenly-augmented convenience yield. Inversions were brief and only on the 1-month horizon. Now that a disruption is occurring when interest costs are near zero, a more sharply inverted market is the result, dragging the 3 and 6-month horizons into negative territory. Going forward, all gold market disruptions could very well create sharp inversions of -1 to -2% in the 1 to 12-month horizons, insofar as we are living in an era of permanently low interest rates.

Is gold becoming money?

A number of gold bugs see the current inversion as something quite momentous. To understand why, you need to know that a gold bug's nirvana is when gold is once again 'money'. When something is money, it is highly liquid. The beauty of owning a highly liquid medium is that it can be mobilized to deal with almost any disruption to one's plans and intentions. Put differently, the convenience yield on stored money is very high. One measure of a paper dollar's convenience yield is the interest rate a government-insured certificate of deposit. Locking away cash for, say, 24 months means that the owner loses all the benefits of its liquidity. With 24-month certificates of deposit currently yielding 0.34% a year, the value of those forgone conveniences is 0.34%.

So when a gold bug's dream becomes reality and gold overtakes the dollar, yen, pound etc. as the world's most-liquid exchange medium, that is the equivalent of saying that gold is providing investors with the market-leading monetary convenience yield. And a permanently high convenience yield would result in a permanently inverted gold market (or at least a much flatter one).

Is the current inversion an indication that gold is becoming money? I don't think so. If the augmented convenience yield on gold was in fact rising due to gold's liquidity having surpassed that of fiat money, we'd expect this to be reflected not only in near-term forward prices but along the entire horizon of forward prices. Not only should the 3-month forward prices be inverted, but so should the 3-year forward price. Is this the case? Not really. If you've seen Crocodile Dundee, I'd suggest you go and check out this hilarious post by Bron Suchecki illustrating the extent of gold's inversion. If you haven't seen the movie (you should), check out the chart below.

The first data point is the spot price. Gold forward prices are inverted after that, but only over a narrow range of five or six-months. By mid-2015, forward prices return to their regular pattern of trading at a premium to current prices.

So no, gold is not becoming money. Rather, we are running into some short-term jitters, and merchants think that holding the stuff provides a few more ancillary benefits than before.

Could these short-term supply & demand problems crescendo into longer-term problems, resulting in inversion beyond 2015? I don't think so. Unlike oil and most other commodities, the supply of mined gold is never used up. Ounces that were brought out of the ground by the Romans are still in existence. This means that supply disruptions should never pose a significant problem in the gold market since gold necklaces and fillings can be rapidly melted down into bars and brought to market. While we care if Saudi stops all oil production or if the U.S. corn harvest is terrible,  if South Africa ceases to produce gold—meh.

This means that the convenience yield on inventories of gold will almost always be less than the convenience yield on stocks of oil, since the sorts of disruptions in the gold market will always be shorter and less extreme than in oil markets. Oil supply shocks can be so sharp and enduring that oil's convenience yield remains elevated for long periods of time. The result is an inverted oil market over the entire time horizon. Such inversions are fairly common events in oil markets (once again, see Bron's post).

Gold shocks can never be enduring, so the types of price inversions we'd expect will be fleeting and only appear in the near-term time horizon. Like the one we are seeing now. In sum, we've seen this all before, and no, it's not the end of the world.

Interest rates and gold

Nick Rowe recently asked what the point of repoing an object was when you could just sell it, repurchasing it later. He could see three reasons. Firstly, you might repo a particluar thing because you hold it dear and want it back. It might not be available were you to simply try buying it back. Secondly, you might repo an asset because future liquidity might be an issue. Thirdly, you might repo an asset rather than sell it because future prices are uncertain. My comment used gold markets as an analogy:

Nick, I think for financial assets you are right about points 2 and 3. In gold markets, for instance, you'd rather lend or swap (ie. repo) your gold than sell it (upon the anticipation of buying it back at some future point) because you might fear that, come time to buy the gold back, the future price could be much higher, or that the gold market could be illiquid and you might not be able to buy.

Incidentally, you can also sell your gold and buy a futures contract. Selling spot and buying a futures contract is financially equivalent to swapping (repoing) gold - in both transactions you'll lock in a guaranteed price and will avoid the risk of illiquidity. So your question: why repo? is similar to the question: should I sell some asset and simultaneously buy a futures contract or sell it and take the risk of buying back at spot at some future point in time.

Some people might recognize these various gold transactions. A gold swap — a temporary exchange of gold for cash — is transacted at the GOFO (gold forward) rate. A gold loan, which is an unsecured and temporary exchange of gold for nothing but a promise to repay, is transacted at the gold lease rate.

You can actually conceptualize both transactions as swaps. In the first, gold is temporarily swapped for a liquid and safe financial promise (cash). In the second, gold is temporarily swapped for an illiquid and safe financial promise (a promise to repay the gold ie. "paper gold"). Lingo-wise a swap is no more than a repo.

The different rates at which these two swaps are conducted — GOFO and the lease rate — will be determined by the relative subjective value gold owners place on the swapped-for assets. Because liquid financial promises provide more services to their holders than illiquid promises, anyone swapping away gold will prefer the former to the latter. That's why the gold lease rate — the rate paid by the person taking the gold to the person foregoing that gold - has always been higher than GOFO. After all, the party swapping away gold needs some increased financial incentive to take the illiquid "paper gold" asset rather than the liquid cash.

Indeed, liquid and safe financial assets are so valued, and so easily storable, that in general, anyone swapping away their gold will not receive a fee for foregoing the metal. Rather, they will pay a fee for the advantages of getting cash. This fee is what GOFO represents.

These ideas can be tough to conceptualize. A while ago I caught the folks at FT Alphaville mixing them up. For instance, the author maintained that a dearth of cash in markets now meant that

since their cash had become more valuable to the market than their gold, they could now make a return from lending cash against gold, as opposed to gold against cash.

The above comment implies that the gold swap rate — cash for gold, or GOFO rate — has somehow switched. But in actuality, those swapping away cash for someone else's gold always earn a return (GOFO). This is because they are foregoing liquidity. The gold lease rate has switched, but that is a different rate, and a different story altogether.

On the topic of gold, David Glasner asks why gold markets are rising due to hyperinflation fears but bond markets aren't:

Now my question — and it’s primarily directed to all those believers in the efficient market hypothesis out there — is how does one explain the apparently inconsistent expectations underlying the bond markets and the gold markets. Should there not be a profitable trading strategy out there that would enable one to arbitrage the inconsistent expectations of the gold markets and the bond markets?

I don't think there is any discordance to explain:

I think gold prices and bond prices have been rising over the last three years for similar reasons. In general, the economy-wide expected rate of return has been falling (towards zero, perhaps below it) as investors grow fearful of the future. This pushes people into safe bonds. It also pushes them into assets like gold that have very low storage costs, since buying some easily-storable durable asset and holding it over time provides a 0% return, better than most risky alternatives which are expected to fall.

So I don’t think there are segmented expectations in these two markets, nor do I think it is worthwhile trying to arbitrage them.

Returning to the discussion of GOFO, if today's gold markets were actually dominated by those who believed in the inevitability of hyperinflation rather than (fairly) rational actors, then GOFO would be inverted... in essence, anyone who swapped away their gold for cash would expect to receive the GOFO rate rather than pay it. The current practice, as I pointed out above, is to pay that rate, not receive it. The reason for the inversion would be because the destiny of cash in a hyperinflation is demonetization and, as a result, it will lose all of its liquidity premium, whereas gold's destiny is to be remonetized and gain a relative liquidity premium. As a result, any gold-for-cash swap based on a universal expectation of hyperinflation would require whoever foregoes the benefits of gold's inevitable superior liquidity to be compensated by a return. Needless to say, GOFO has not inverted. Those foregoing  their gold still pay up to those foregoing cash.

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.