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Gold and short-term interest rates [ClearOnMoney]
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Gold and short-term interest rates

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Commentary

Gold and short-term interest rates

7 Oct 2010 by Jim Fickett

History suggests that as long as real, short-term interest rates are negative, the gold price is unlikely to drop.

Reader Barry Hillman pointed me today to an interesting post at EconomPic, On the Value of Gold, which was in turn inspired by a post from Eddy Elfenbein at Crossing Wall Street, A Possible Model for the Price of Gold. Here is Elfenbein's main thesis:

The key is that gold is tied to real interest rates. …

Here’s how it works. … Whenever the dollar’s real short-term interest rate is below 2%, gold rallies. Whenever the real short-term rate is above 2%, the price of gold falls. Gold holds steady at the equilibrium rate of 2%. …

for every one percentage point real rates differ from 2%, gold moves by eight times that amount per year. So if the real rates are at 1%, gold will move up at an 8% annualized rate. If real rates are at 0%, then gold will move up at a 16% rate (that’s been about the story for the past decade). Conversely, if the real rate jumps to 3%, then gold will drop at an 8% rate.

Both sites post graphs showing a model versus the actual gold price. In the model, the amount by which real returns on T-bills exceeds a fixed 2% rate of return is calculated for each month, multiplied by -8, and then the modeled gold price is moved by that much. Over the long term, the lines for the modeled price and the actual price can be superimposed fairly well.

Superficially, it would seem Elfenbein has discovered that the magic numbers 2 and 8 play a key role in human psychology worldwide. That seemed rather implausible to me, so I spent a bit of time looking into the model.

Consider separately the agreement in the long-term growth of the price, and any agreement in shorter-term movements. The longer-term growth in the model price will look pretty good as long as the following (rather loose) conditions are met:

  • the model, like any nominal price in an inflationary environment, is roughly exponential
  • the average growth rate in the gold price, and the average growth rate in the model, are in rough agreement

Over the 20 years considered by Elfenbein, the real return on T-bills was at a compound annual growth rate (CAGR) of 1.1%. The nominal price of gold rose, meanwhile, at a CAGR of 5.1%. The model price of gold rose at a CAGR of 7.1%. The reason the magic numbers 2 and 8 work is that (1.1 - 2) * -8 is approximately 7.1, and 7.1 is close enough to 5.1 to make a good looking graph.

In other words, the main thing Elfenbein has done is make a simple compound growth curve with the right underlying constant. Or, to put it another way, just taking a model gold price that grows at the right CAGR would not look too bad over the last 20 years.

Now consider shorter-term movements. To be fair, the Elfenbein rule does give somewhat better agreement than just a compounding curve. Specifically, as shown in the EconomPic graph, it does a decent job of catching the 1980 peak. How about more generally?

Monthly data on both rates and the gold price are quite noisy, but if real rates on T-bills are actually a main driver of the gold market, I would expect the correlation to show up year-on-year. Below is a scatter plot for annual data.

(Real rates are approximated by nominal rates minus the CPI. Data are for 1970-2009, since Nixon set the dollar free from gold in 1971. The last 10 years are shown in red.)

The correlation is quite weak, and does not provide much support for the particulars of the model. It is perhaps significant that whenever the real short-term rate has been negative, the gold price has almost always risen. This is not a strong conclusion, with only 11 data points, but it does seem to be a pattern. And it makes sense from the point of view of market psychology: when people know they are losing money in their bank accounts, it pushes them towards gold.

Currently the three month T-bill is paying about 0.1% and inflation is running at about 0.9%. The above analysis does at least suggest that gold is not very likely to see a big drop soon.