Arnold Kling  

Gold and Treasuries

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Paul Krugman writes,

What effect should a lower real interest rate have on the Hotelling path? The answer is that it should get flatter: investors need less price appreciation to have an incentive to hold gold.

Yesterday, in my high school economics class, I posed this question:

Suppose you have a fruit tree that you know you can sell for $100 in five years. The value of the fruit will be 5 percent of the value of the tree each year. The interest rate is 10 percent. What price should the tree sell for today?

I wanted them to use the formula:

profitability of buying = rental rate plus appreciation rate minus interest cost = 0

We set it equal to zero because there should be no excess profits from buying the tree. In that case, the annual appreciation rate should be 5 percent. So the price of the tree today should be about $73, allowing for annual compounding.

Next, suppose that the interest rate falls to 8 percent. Then the appreciation rate should be 3 percent, and the price of the tree should be about $84, or something like that.

I think that is the same story that Krugman is telling. There is an assumption that the long-term nominal price is unchanged, in spite of the deflationary shock that Krugman is arguing is at the heart of this. And my guess is that you need a really spectacular drop in real interest rates to get the sort of increase in the price of gold that we have seen over the past few years.

In the end, I think my preferred model (and perhaps Krugman's as well) is that there are two different sets of expectations at work. Buyers of Treasuries expect deflation. Buyers of gold expect inflation. It is well nigh impossible to arbitrage across the two. You could try shorting both in some combination, but, as the past year has shown, the market can stay irrational longer than you can stay solvent.

Comments and Sharing

COMMENTS (15 to date)
Alex Godofsky writes:

Why not just, it's some combination of the fall in interest rates + expected demand from developing nations?

Floccina writes:

There is an argument that rising gold prices are due to income growth India and China and not so much a function of inflation fears. Also sometimes things start to go up just because they have gone up recently due to momentum players. That BTW is my definition of a bubble, things going up just because they have gone up recently.

mark writes:

There are many factors at work and rationality is not the only one. One factor not mentioned by anyone is that physical gold is one of the few hedges against political risk.

A second point is that the supply of gold is small - in dollars, a day's trading volume of GLD is something like 5 minutes of AAPL volume.

Last you have Keynes' insight that investment success is not achieved by identifying the best investment in the abstract, but the investment that other investors are most likely to select as the best investment.

fundamentalist writes:

Krugman’s “Hotelling” story about gold prices reminds me of the grumpy grandfather who wanted to get rid of the screaming grandchildren around him. He told them that grandma had baked some cookies, which caused the children to run screaming into the kitchen. A few minutes later the grumpy grandfather got up to leave, so his friend asked him where he was going. The grandfather answered “To get a cookie, of course.”

Krugman made up a fictitious story about gold and then proceeds as if it were true. Gold is not a resource that gets used up, like oil. Very little goes into manufacturing or teeth. Almost all of the gold ever mined is still available. The Hotelling story applies well to oil, but does not apply to gold at all.

But he is right that inflation fears aren’t the only cause of gold’s rise. Gold is also a refuge in times of trouble, including economic turmoil that can lead to deflation. However, central banks are buying gold for one reason, to protect their national money supply from dollar devaluation.

8 writes:

There's certainly a large cohort of those who expect inflation in the gold market. But if the deflation is bad enough, the banks will fail and gold may be a relative out performer, though it will probably lose to cash outside the banking system or in Treasuries.

As mark points out, the gold market is still very small and it hedges political risk. It only takes a small portion of buyers to view gold as money/safe haven to elevate the price during a deflation. If you look at demand, China and India combine for almost 10 times U.S. demand. One of the stories here is that the U.S. is no longer driving global markets. Political risk is high and the law is no obstacle to government-banking incest, see the German high court.

Everyone wants to weaken their currency, the Swiss just wrecked their paper. We either have a world where the central bankers succeed in destroying their currencies, or one where they fail. If they fail, it will be a nightmare deflationary scenario with almost total loss of confidence in government. James Rickards said if gold is $500 an ounce, the S&P 500 will be 100, to illustrate the point.

What is the most underowned asset, outside of the black market? Physical U.S. dollars.

Troy Camplin writes:

Actually, they can both be right. If one expects deflation over the short term and inflation over the long term, it makes sense.

Alex Godofsky writes:


The fact that gold is consumed very slowly implies that the effect Krugman identifies should be even stronger.

David Pearson writes:

The paradox of bonds and gold rising together has a solution.

-Gold prices rise as real rates fall
-bond prices rise as nominal rates fall

-when deflation risk occurs nominal rates fall
-when deflation risk occurs central banks threaten to fight deflation by reducing real interest rates.

Therefore, bonds and gold rise together when deflation risk rises AND the central bank promises to lower real rates to fight that deflation.

fundamentalist writes:

Alex, but gold consumption is incredibly small, which would make the Hotelling effect infinitely large, and it isn't.

And none of Krugman's explanation works for the low price of gold during the decade of the 90's.

fundamentalist writes:

PS, gold production relative to the total amount of gold in existence is very small. You'll go broke trying to predict the price of gold by the amount of production.

Krugman's thesis applies only to producers. Producers are the smallest segment of sellers in the gold market. They're almost insignificant.

Leonard writes:

People are moving money into both (US) bonds and gold for the same reason: it is the classic "flight to safety" that happens in the wake of a speculative bubble popping. Bonds are the choice of people who see gold as a normal commodity (it is not). Gold is the choice of those who see it as, IMO, it is: money.

Gian writes:

"So the price of the tree today should be about $73"

But isn't price set by the valuations made by buyer and seller?
If I badly need $50 today, I might sell the tree today for $50.
If someone else badly needs that tree, I could sell it for $90 today.

ezra abrams writes:

I think both you and Krugman are making the same mistake: assuming complex econ models hold in the real world
I listen to both right and left am talk radio in boston (am 1200 and 1510)
both stations are pretty similar in a lot of ways, including a large number of ads for gold.
The ads are always the same: The sky is Falling !!!
Buy Gold !! Gold has doubled !! Another Doubling Likely !!
So if this is what is driving gold sales, does it have any relation whatsoever with economists models ?

Matthew C. writes:

Treasuries are being bought by the Fed, the TBTF and ecosystem partners of the Fed / TBTF.

Gold (and silver) are being bought by those who think the current global fiat financial experiment is failing, like all previous fiat experiments have failed.

I guess we'll have to see who is right. I know where I am placing my chips. . .

David Clayton writes:

The answer's not about $73, it's $78.35.

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