Gold, USD And Rates: Lost In Transitivity

by: Evariste Lefeuvre

If A, B and C are economic variables and if we suppose that A and B are correlated and that B and C are also correlated, then that means A and C are…not necessarily correlated! As a mathematical binary relation, correlation is not transitive. The table below provides a financial example:

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  1. The correlation between USD and US Treasury yields is slightly less robust but negative (weaker USD à higher yields), which may come as a surprise to readers, but this is what data show (see chart above, right);
  2. The correlation between Gold and US Treasuries is close to zero and highly unstable. Many investors would have expected gold to rise when sovereign yields decline (see my discussion below), but the link is not statistically significant (note that the transitivity mentioned above would have led to an unexpected positive link between gold and yields).

If there is no statistical reason (no transitivity) for gold and yields to be correlated, we could stop our analysis here. However, there might be a missing link: inflation.

The link between gold and inflation (1-year change in the aggregate price level) and the acceleration of inflation (the 3-month change of inflation) is weak. As can be seen below, the correlation is highly instable, regardless of metric used (inflation or the change in inflation). Even the correlation with market-expected inflation (Breakeven inflation from TIPS), albeit positive, remains below 0.35 - an insignificant number.

Yet, the correlation between real rates and gold remains robust. It weakened somewhat in 2012 (chart below, right). Adjusting nominal yields (whose correlation with gold is nonexistent) with inflation may help us to establish the "gold-dollar-yield" trinity.

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The negative correlation between real yields and gold leads us to assess whether there is a solid link between real rates and the USD. This would enable us to have near-perfect correlation transitivity. Unfortunately, the correlation between real rates and the USD, which used to strive to be close to 1, has been very unstable and close to zero on average since late 2011 (chart below).

As I wrote before, the best way to have a directional view on gold prices is to know where the USD is heading. I have to acknowledge that the relationship between real rates and gold prices has weakened but remains significant:

1. Lower nominal rates suggest a lower opportunity cost for holding gold (paying no coupon and no dividend);

2. The higher is inflation (for some investors, a reason to hold gold) the lower the real rate.

Nonetheless, the drivers of real rates are not straightforward:

  1. Higher real rates should reflect a scarcity of savings. All things being equal, a widening of the public deficit should come along with higher real rates. The chart below suggests otherwise. Between 1989 and 2008 a higher public debt would come along with much lower real yields. The relationship has collapsed since 2009 (blue circle). It is true that since 2008 private saving has increased, but it cannot compensate for the huge decline that has already occurred.

2. Real interest rates should also reflect the pace of growth of GDP. The chart below shows a significant disconnect since 2011.

Those apparent anomalies can be explained by one factor: the monetary financing of the US deficit and the Japan syndrome that the US economy is facing.

So here we are, lost in transitivity. The missing link between gold and nominal yields makes gold forecast dependent on USD views. Alternatively, the missing link between the US dollar and US real yields calls for a view on real rates to gauge the future path for gold. Unfortunately, the traditional and theoretical drivers of real rates are useless in a context of debt-monetization/quantitative easing.

My advice for investors is the following:

  1. Long run or even short run fluctuation in inflation are useless to predict gold price direction;
  2. The link between gold and the USD remains the most robust so far (for those that reject the view that GOLD/USD is naturally correlated to the USD and that the correlation could be spurious, the Gold/Oil ratio is also negatively related to the USD, meaning gold loses its attractiveness when the USD appreciates);
  3. For those who favor the gold/real rate relationship, beware. Not only do traditional divers not work but they suggest much higher real yields. Only Fed-watching (exit talks, relative efficiency of different bond programs in capping long yields) would help to figure out where gold prices are headed.

I am not sure that Draghi will be able to shore up the euro for along time. My positive view on USD would call for lower gold prices ahead.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.