What Do Stocks, Real Rates & Japanese Yen Tell Us about Gold?
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Miners on Cage, Catlin Shaft
Eureka-Croesus Mine, Eureka, Nevada
A surprisingly accurate gold model
What do stocks, real rates and Japanese yen tell us about gold? A whole lot, at least over the last several months. Falling domestic equities and declining real interest rates have helped propel an impressive gold rally since mid-November. The underlying uncertainty generated by turmoil in Washington, the U.S./China trade dispute and mixed signals from the Federal Reserve have created a “risk off” sentiment returning investors to safe havens like gold and the Japanese yen. My January 3 Kitco commentary posits that without resolution of these troubling issues, the first-half of 2019 will be a push-pull to higher $1,380+ gold prices underpinned by a trend of higher lows. Last week, prices paused as stocks rose from their December lows and real rates inched higher. The yen weakened and gold fell on new optimism for a U.S./China trade deal by this spring. Will this “push-down” by reversed by a “pull-up” as the propolonged U.S. government shutdown grinds on? A good gold model can help explore these interactions and suggest what lies ahead.
A model based on stocks, real rates and Japanese yen
Figure 1 shows a 3-month linear regression model that has Comex gold price as its output and the S&P 500, real rates and the Japanese yen as inputs. The previous commentary defines “real rate” as the inflation adjusted interest rate of a U.S. 10-year Treasury note. It is is computed by subtracting the 10-year breakeven inflation rate, also known as the 10-year inflation expectation, from the Treasury note interest rate.
Figure 1 – A gold model based on stocks, real rates and the Japanese yen
Actual Comex gold price (most active contract) is given by the orange trace; the model output or estimate of gold price is shown in blue. The period of regression analysis is shaded covering a range from October 18 to Friday’s clsoe, January 18. Diamond markers indicate key milestones: The S&P 500 all-time high on September 21, the CBOE S&P 500 Volatility Index (VIX) ramp up on October 3, and the S&P 500 plunge to bear territory on Christmas Eve.
My rule-of-thumb for a “good model” is an estimate error (1-standard deviation or -sigma) less than 1% over the period of interest and a “goodness-of-fit” (R-squared) greater than 0.85. The model in Figure 1 meets this criteria with surprising accuracy, an estimate error of $8.69 per ounce (0.70%) and an R-squared of 0.90.
A “useful” model can give us an idea of what high/low price range to expect in the near-term. The dotted traces show this range computed as +/- 2-standard deviations from the gold price estimate. As of Friday the lower bound is $1,255.3 and upper bound, $1,290.0 per ounce. This suggests the mercurial $1,300-level is likely out of reach for the time being but gold prices should remain above $1,250.
Another helpful attribute is the sensitivity of the output to a small variations in input. Figure 2 shows the gold price sensitivity to a +1% change for each input - S&P 500 (SPX), real rates and yen (USD/JPY). It is noteworthy that a move up in any of the three inputs causes a fall in gold price.
Figure 2 – Gold Price Sensitivity
Accordingly, if the S&P500 advanced 1% higher it is statistically likely that gold prices would fall $1.41 per ounce. Viewing the data in this light, a +1% changes in USD/JPY (i.e. yen weakening relative to the dollar) results in a much larger dip, $8.44 per ounce. The 10-year real rate moving 1% higher (e.g., 0.96% to 0.97%) causes the least change, $0.98 per ounce down.
Variance analysis of the same model allows combining the model sensitivities with the statistics of the inputs over 3-months as shown in Figure 3. The first chart (3a) compares the variance of the actual gold price and estimate expressed as a percent. For the current model, this measure is 90% suggesting the unexplained variance is only 10%. For scalar regression with multiple inputs, the unexplained variance is equal to 1- (R-squared ) in percent.
The second chart (3b) shows the variance contribution of each input to a measure of the model variance. Clearly the yen is still dominant (67.5%) but given the statistics of real rates over three months, interest rates move into second place (21.5%) compared to stocks (11%).
Figure 3 – Model Variance Comparisons
Finally, correlations come and go in markets and so do good models. If gold prices going forward exceed the dotted bounds shown in Figure 1, something fundamental has shifted in the markets and it is probably time to bin the model and retool. This was the case during a low volatility period for gold from last April to late-September. During this time, gold behaved as a currency with a high coreelation to the Chinese yuan (USD/CNY). A “good model” based on currencies blew up as fear crept into the markets and the yellow metal regained safe haven status. The model presented here became its replacement. So far so good.