Gibson's Paradox: Everybody Out Of The Water

 |  Includes: DIA, IVV, QQQ, SPY, VTI
by: John Overstreet


The Barsky-Summers variant of the Gibson's Paradox is starting to show its age.

Gold and copper predict real interest rates.

A jump in real interest rates will suppress and possibly damage equity prices, suggesting it would be best to cash up.

A reader questioned my advice for bond holders to move into financial stocks in order to protect themselves from the growing risk that yields could jump over the course of the next year or so. One shorter-term indicator pointed to a trough sometime around August, and a medium-term cycle indicated that a trough followed by a sharp rise in rates was likely next year but could be as soon as this year.

The question was very astute, because he pointed out the case of 1981-1982, when interest rates skyrocketed and the stock market got pummeled pretty bad.

So, when are rising interest rates good and when are they bad?

I don't think we're going to come to any final solution to that problem here, but by thinking about these questions, it forces us to reconsider Gibson's Paradox. By modifying the orthodox interpretation of that phenomenon, we can change our understanding of market dynamics and hopefully protect ourselves from unnecessary losses. For readers who want to know, "What do I do now?" you may want to skip to the end, but the short answer is be very cautious of virtually every asset class for the rest of the year.

Gibson's Paradox

Without getting too much into theory, Gibson's Paradox has been the orthodox explanation for movements in the price of gold for a good quarter century. This orthodox explanation was crafted by Robert Barsky and Larry Summers in a famous paper called "Gibson's Paradox and the Gold Standard", and it said that gold (and other metals, especially "non-ferrous metals") is inversely correlated to real interest rates. When real interest rates go down, gold goes up.

Gibson's Paradox is actually a fairly old phenomenon mentioned by Keynes who picked it up from Gibson. Gibson had pointed out that, contrary to expectation, interest rates were strongly correlated with general price levels rather than the rate of change in those price levels.

As Barsky and Summers showed, prior to the collapse of the gold standard, if interest rates dropped, so did prices. But, since the gold standard fell in 1971 (and shortly before), when interest rates drop today, prices are likely to slow in growth or stabilize, but not fall.

They observed, however, that Gibson's Paradox had not actually disappeared. Instead, we should look at real interest rates rather than nominal ones; when we do so, we will find that, at least with gold and other metals, the real price level follows inverted real interest rates.

This causes a problem however, which I have alluded to before, and to which I think I have at least part of the answer. I don't want to get too far into describing the nature of the problem, but let me try to present it simply. I'm going to skip a few steps, but bear with me.

Prior to the demise of the gold standard, under the classical version of Gibson's Paradox, a rise in prices meant a rise in prices in terms of gold. So, if interest rates rose, then, say, the price of copper (in terms of gold) would rise, too. Today, we call this the copper/gold ratio.

Barsky and Summers, of course, pointed out that since the gold standard ended this doesn't apply any more, but it raises the question of why Gibson's Paradox should be inverted now. In other words, during the gold standard, the copper/gold ratio could be imagined to be strongly correlated with nominal interest rates, but now the copper/gold ratio appears to have a strong inverse relationship with nominal yields. That is, the gold/copper ratio is now correlated with yields.

(click to enlarge)10y yields vs gold/copper ratioClick to enlarge(chart based on data from St. Louis Fed and UNCTAD)

This is very strange. Under the Barsky and Summers model, we might expect this relationship to have changed somewhat, but for it to have become inverted is very odd.

Moreover, the Barsky-Summers variant of the Gibson's Paradox is, I think, starting to show it's age, and a way to reconcile the classical version of Gibson's Paradox with the Barsky-Summers model is possible now that more historical market data is available.

Simply put, the gold/copper ratio is correlated with real interest rates (see chart below). Thus, when real interest rates rise, copper priced in terms of gold will fall. Not only does this make a better fit than does the Barsky-Summers model, but it also accounts for the divergence that they note in their paper regarding gold and "non-ferrous metals" such as copper. Finally, I think this conforms with the original observation made by Gibson as it was reinterpreted by Summers and Barsky. Ultimately, though, that debate is for another time.

Gold/copper ratio as 'prediction' of real interest rates

When I first brought up the relationship between the gold/copper ratio and yields, I argued that the ratio appeared to be 'forecasting' interest rates sixteen months in advance. And, this appears to be even more true of the relationship between gold/copper and real interest rates.

(click to enlarge)Click to enlarge

The correlation between these gold/copper forwarded sixteen months and current real interest rates is 0.6 compared to the Barsky-Summers model below (according to my calculations) which tends to range between -0.5 and 0 (so that metals prices are inversely correlated to real interest rates).

(click to enlarge)Barsky-Summers model of GibsonClick to enlarge

So, assuming that this is a legitimate relationship I am describing--and we're talking about markets and economics, so we should be skeptical--what does this mean for the markets this year?

If you look at the gold/copper chart above, there are a few instances where the ratio jumps significantly (say, by a factor of 2), like the spike that occurred last year and therefore should be indicating something about this year.

What does the past tell us?

First, let's look at 1980-1982.

(click to enlarge)gold/copper 1980-1982Click to enlarge

The gold/copper ratio spiked twice in this period, so we should be on the look-out for spikes in real interest rates sixteen months later, and we are particularly curious about what impact they might have on the stock market. We will also keep bonds and oil in view along the way.

(click to enlarge)spx 1981-1984Click to enlarge(courtesy

In the periods that corresponded with the spikes in the gold/oil ratio, it would appear that the stock market's performance was seriously blunted in the first case and listless in the second, while bonds were strong and steady, respectively.

The next case would be 1986.

(click to enlarge)gold/copper 1985-1987Click to enlarge

This ratio retested its old highs of 1980.

(click to enlarge)spx 1986-1989Click to enlarge

This is a little difficult to read. It is possible that the gold/copper rise was linked to the bullish market of 1987, but it appears to be foretelling its destruction instead. Interestingly, this is episode is one of the few in which a spike in real interest rates did not occur. (See graph above).

Now, 1993.

(click to enlarge)gold/copper 1992-1994Click to enlarge

spx 1993-1996Click to enlarge

The rise in the gold/copper ratio appeared to mark a powerful rise in interest rates but a flat performance for stocks.

Let's skip now to a rise in the gold/copper ratio the magnitude of which hadn't occurred in nearly thirty years.

(click to enlarge)gold copper 2008-2011Click to enlarge

(click to enlarge)spx 2009-2012Click to enlarge

This foretold a blunted stock market, specifically the one that followed the 2009 Leeb shock (an 80% yoy rise in crude oil prices).

And, so in 2011, we had another significant spike in the gold/copper ratio that would suggest a surge in real interest rates and, if precedence holds, a weak stock market.

(click to enlarge)gold copper to presentClick to enlarge

This jump in the ratio is dwarfed by those of the early 1980s and 2008, but the move is historically significant.


To summarize, the jump in the gold/copper ratio last year, if history serves as any guide, promises a jump in real interest rates that will suppress and possibly damage equity prices.

I should point out to that in mainstream economic theory, high real interest rates are very burdensome on countries with high debt loads, and that, probably not coincidentally, in each of the cases mentioned above, the gold/copper spike preceded a "global banking crisis" as listed by Reinhart and Rogoff in Table 15.1 of This Time is Different, except for two: the eurozone crisis which got into full swing after they published their tome and the spike that foreshadowed weakness in 1984. Somewhat like the present circumstances, the 1983 gold/copper shock, if we can call it that, was right on the heels of the 1981 shock, so that suggests that our current predicament is not necessarily a doomsday scenario, but 1984 did mark the beginning of the S&L crisis in the US, so there probably won't be a free lunch, either.

Based on a historical perspective, the best case scenario is probably something like 1987, when markets ran up before cavitating, or a 1984, when markets merely stalled for a while, but looking at the nature of the gold/copper chart in 2011, it suggests that it would be best to cash up until the end of the year.

Disclosure: The author is long BAC. The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it. The author has no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: I am long September WTI crude. I may sell BAC within the next 72 hours.