Econometric Modeling Of Gold Prices

| About: SPDR Gold (GLD)

Summary

I model gold prices using structural multivariate regression models through four different parametric approaches (OLS, t-distribution, quantile regression, and log-normal).

Higher US inflation, a higher federal funds rate, larger budget deficit (or smaller budget surplus), and larger M2 money supply were all bullish for gold.

The influence of the US current account saw mixed results, while US real GDP and total world reserves had no statistically significant impact.

When modeling intrinsic price estimates for traditional commodities, it's largely a function of supply, demand, and inventories, which results in the formation of a fairly straightforward market. This formula works on oil (NYSEARCA:USO), coffee (NYSEARCA:JO), corn (NYSEARCA:CORN), industrial metals (NYSEARCA:DBB), and virtually all other consumable or utility-rich commodities.

However, gold (NYSEARCA:GLD) functions a bit differently. While it is true that supply and demand can and does influence gold prices to an extent, such as new mines opening up and demand in certain parts of the world (e.g., wedding season in India), gold has little practical utility unlike the aforementioned commodities, so these aren't the predominant factors driving the market. Gold has value given that it's been treated historically as an alternative form of currency. Humans have imbued the metal with value, in large part, because of purely psychological reasons.

Therefore, due to its treatment as an "alternative currency," its price responds to economic factors outside of the conventional elements that make a traditional commodities market. Given the US is the largest economy in the world, and is attributed with about 25% of global economic activity (using figures of $18.7 trillion for US GDP and ~$75.2 trillion for world GDP), gold also tends to be US-centric. Namely, gold tends to be most responsive to factors impacting the US economy.

Accordingly for purposes of this exercise, I am introducing models (or more than one parametric approach) by which gold prices are regressed on the variables of real US GDP growth, inflation rate, current account, budget deficit/surplus, M2 money supply, the effective federal funds rate (set by the Federal Reserve), and total world gold reserves.

There are of course many other factors that influence gold prices, including bond prices, stock prices, additional supply/demand elements, its price relative to other precious metals such as silver (NYSEARCA:SLV), and so forth. However, the issue with including these is that it creates numerous chicken-and-egg problems throughout. Throwing the S&P 500 index (NYSEARCA:SPY) or US Treasury yields (NYSEARCA:TLT)(NYSEARCA:IEF) into the regression may make intuitive sense given that money flowing out of stocks or bonds may end up benefiting gold. But the causation can work both ways.

Consequently, capturing only the rawest, fundamental elements is likely the best strategy. Gold very much trades on sentiment, or with respect to the broader macro components of the economy. If one were to form a structural model, plug in the current values of each independent variable listed above and it spit out a gold price figure that was $100 per ounce higher than the market price, that would be a very poor reason to enter into a long trade. Markets change over time and even if genuinely out of whack can remain that way for elongated periods in the absence of any catalyst to alter the trajectory of the market.

Data

Data was collected on each variable back through Q2 1968. All of it, with minor exception, was obtained from the St. Louis Fed's economic data site, which provides one of the largest public economic databases. YCharts supplied US current account data through the present-day given the St. Louis Fed's site went through only Q4 2013. Moreover, because data for this exercise was taken at quarterly intervals and fiscal deficit/surplus data is released annually, I linearized the data between data points to ensure no gaps were present. Otherwise 75% of the observations would have been missing from the regression entirely if only annual fiscal deficit/surplus data had been included. The fiscal deficit for 2016 hasn't yet been released, but I also linearized the intervals through the end of Q3 based on the estimate obtained here.

Results

I made four separate structural models based on distinct distribution parameters: OLS (normal distribution), t-distribution, quantile regression (estimates conditional median and other quantiles, rather than the mean), and log-normal.

In each model, five of the seven independent variables came back as highly statistically significant in each regression: US inflation (based on the personal consumption expenditures price index, or PCEPI), the federal funds rate, current account as a percentage of GDP, federal deficit as a percentage of GDP, and the M2 money supply.

Real GDP and the supply/demand element of gold reserves were not statistically significant in any model. As a result, those variables were tossed out when forming the final model for each parametric approach.

(Source: author)

The results of each model came back as follows:

OLS

T-Distribution

Quantile Regression

Log-Normal

(Source: author)

To test what each model might predict based on an approximate representation of the current economic situation, I inputted the following parameters for each variable: PCEPI (1.5%), effective federal funds rate (0.625%), current account as a percentage of GDP (-2.8%), federal deficit as a percentage of GDP (-3.0%), and M2 money supply ($13.2 trillion).

I obtained the following estimates for each in price per troy ounce:

(Source: author)

These models estimate a gold price anywhere from $1,426 to $1,758 per troy ounce. The quantile regression model also provides upper- and lower-bound estimates of each coefficient at a 95% confidence interval. This provides an estimation range of $1,337-$1,594, with $1,468 at the median.

Also note that the log-normal distribution estimates the natural logarithm of the dependent variable (i.e., gold), as we are fitting that value to the distribution rather than its actual numerical quantity. This approach helps reduce the influence of outliers in the data that are often difficult to rein in under traditional mean-centered parametric methods. The actual value obtained from the log-normal regression was 7.47. The estimated gold price is estimated by taking Euler's number (e = 2.71828…) to the power of 7.47, which provided the $1,758 price.

The log-normal model came to be a bit of an outlier. The average of the OLS/t-distribution/quantile regression ("OTQ") set came to $1,468 per ounce, with the log-normal estimation coming in about 20% higher. Overall, the OTQ set estimates gold at about 20% higher than its current value, based on a spot price of $1,227.

General Findings

In general, there were few surprises from this exercise. Higher US inflation, higher interest rates, a higher federal deficit (or lower federal surplus), and a higher money supply are bullish for gold.

The results on the effect of the US current account were mixed. The log-normal model saw that a higher current account deficit (or lower current account surplus) was bullish for gold. This might be expected given this is a net negative for the US economy, in light of the trade balance weakening and/or a reduction in other foreign income. It's been traditionally established that lower current account and fiscal budget numbers ("twin deficits") would be negative for the US dollar. With the inverse correlation between gold and the US dollar, it would be expected that the bearish elements for the dollar would be uniformly bullish for gold, and vice versa, but we obtained mixed results.

For every 1% increase in the current account (as a percentage of GDP), the OLS model tells us that gold would increase in price by 2.1%; 2.3% for the t-distribution model; and 2.2% for the quantile regression model. The log-normal model, however, predicted a 2.6% decrease in gold prices. So while we see statistical significance suggesting it should be included in each model, the economic significance may be somewhat suspect.

Conclusion

I sold my gold position after last week's election results, given that the "fear" element that gold traditionally benefits from was notably absent in the market. A simple analysis might suggest a Trump election may favor a boost to gold - inflation up, federal deficit possibly up (i.e., getting worse, with tax cuts and fiscal spending initiatives likely forthcoming), and money supply likely neutral. A fed funds rate increase is already 90.6% priced in as of the time of this writing, although the idea of no hike - bearish for gold - received some traction upon the potential of higher volatility.

The actual reason for gold's 3%-4% dip was likely derived from investors putting more money in the equities market on the idea that some/many of the incoming administration's future policy enactments - bank deregulation, lower corporate taxes, repatriation of overseas cash, infrastructure spending, etc. - would be bullish for US stocks generally.

Also note that any individual type of model should not be used exclusively to shape one's investment opinion. Any model can fail to include one or more relevant variables, existing variables may take on different levels of significance over time, and additional variables may eventually work into the picture to cause any given model to be wide of the mark in accurately estimating where price should lie. A combination of models and prudent fundamental (and/or technical) analysis is best used to estimate prices and cross-check for the sake of greater accuracy.

Disclosure: I/we 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.