Econometrics meets gold: a simple model with powerful insight.
KEY TAKEAWAYS
Gold’s rally explained using a regression model with real yields, the dollar, and the VIX
Adjusted R² of 0.3166 shows one-third of moves explained by the model
Real yields and the dollar are highly significant; the VIX is not
Coefficients show strong inverse relationship between gold and both real yields and the dollar
The rest of gold’s moves are noise–psychology, speculation, central bank buying
NEXT UP
Gold’s mystique is overblown; numbers matter more than narratives
One-third explained by math is good enough in finance
Fear only matters during full-blown crises
Real yields and the dollar remain the true drivers of gold
The rest is noise, but noise that can move markets dramatically; nothing is that simple in markets 😉
You can quote me: “If you think gold is a perfect hedge, show me the numbers.”
This is how we do it. Ok, it’s not Friday night–it’s early, early morning on Tuesday, but I’m feeling alright despite a long workday yesterday. If you haven’t figured it out, I am referring to a 1995 R&B hit by Montel Jordan. You may not remember him, but I am sure you remember the “this is how we do it” line. It is sort of ingrained in pop culture, so even if you weren’t born yet, you have probably heard it and have most likely–despite your age–done some sort of accompanying dance move. This morning, it’s not about dance moves, but about… well, finance–really econometrics, and how WE do it. You see, I can’t stop staring at the following chart. Have a look and keep reading.
Yeah, that is a chart of gold, which I am sure you have seen. Are you perplexed that gold has gone up and up and up? Well, most of us just assume that gold is going higher due to exposed nerves. When folks think that 💩 is about to hit the fan, one of the first things that come to mind for most investors is… well, gold. I suppose that there is some post-apocalyptic scenario where the banking system has completely collapsed and the world goes back to trading gold pieces for goods and services. Ya, maybe, and even possible, but highly improbable. Then there is a theory about global liquidity and central bank balance sheets. The global liquidity theory of gold says that when central banks expand money supply or their balance sheets, investors fear currency debasement and buy gold, pushing its price up. When liquidity tightens, real yields rise and gold loses appeal, causing prices to fall. So, really, what is it that is causing gold to surge to new highs on what seems like daily? Well, I am pretty sure that I can’t tell you EXACTLY what it is, but I can show you how a proper finance person may approach the question. OK, put your thinking caps on and hold tight.
Let’s start by looking at the numbers. We will examine the following regression model:
Gold Returnt = α + β1 ΔRealYieldt + β2 Dollar Index Returnt + β3 VIX Returnt + εt
What? You are not a quant with extensive training in econometrics? Don’t worry, I got you on this. This equation uses historical performance of gold, real yield, the dollar index, and the vix to see if the latter three explain changes in the former. In other words can gold prices be explained by inflationary forces, dollar strength, and market volatility? If so, by how much. Ok, so let’s write some R-code and run it.
Here you go--have a look, and I will explain. Be patient. 😉
Ok, now I know that my academic friends are all chuckling right now. Bear with me. Notice how I circled that Adjusted R-squared of 0.3166 on the bottom. That means that these independent variables explain 31% of changes in the price of gold. Now, I need to give you some context. In finance, if you have a simple 3-factor model that explains about ⅓ of your dependent variable, it is pretty decent. The reality is that, beyond these three variables, there is a bunch of noise, speculation, and possibly flows involving non-US central bank stockpiling. Those are all things that we really cannot observe on a daily basis.
Looking back on those cryptic numbers, we can learn a few more important facts. Two of those independent variables have very low P-values–they are the ones with the three asterisks ‘***’ next to them (I marked those with gold arrows). That means that changes in real yields and changes in dollar value are statistically, highly significant in explaining changes in the price of gold. The VIX, or volatility in markets, not at all; we know this because of its high P-value.
We can take away one final thing from those results. Check out the coefficients (the betas: βn) which I drew a gold square around. They tell us that there is an inverse relationship between real yields and gold, and similarly between the dollar and gold. Specifically, one point move lower in real yields translates into about a 6% gain in gold on a monthly basis. A 1% move lower in the dollar index translates into about a 0.85% gain in gold. And, as mentioned before, the relationship between the VIX / volatility and gold is noisy.
That should make intuitive sense. Gold pays no income. If you can suddenly earn a negative real yield in Treasuries (that is TIPS/inflation protected yield minus treasury yield), that shiny lump of metal looks… well, a bit shinier–less competition from yielding treasuries. And since gold is priced in dollars, a weaker dollar automatically makes gold cheaper for the rest of the world–increasing demand.
As for the VIX, the “fear gauge,” it only really matters in crises. During normal times, equity volatility doesn’t drive gold much. But when the world falls apart–think 2008, March 2020–gold usually benefits. That’s why the regression picks up a weak positive coefficient, but one that isn’t consistently significant. I am going to leave you with one final chart. Check it out and then follow me to the finish. This is a cool one–trust me.
This chart shows us the predictive power of the statistical model we just analyzed going back to 2005. The red line shows actual monthly changes in the price of gold, and the green line shows what our model would have predicted with input from changes in real yield, changes in the dollar, and changes in the VIX. Just by eyeballing it, you should notice that it is pretty accurate!
Ok, now you can breathe, the math is over. 😌 Take off your thinking cap and grab your tea. If you’re trying to understand or forecast gold, our fancy statistical model says you should keep your eye on two things above all else:
👉 Real yields. When inflation expectations are high but nominal yields are stuck, real yields fall and gold rallies.
👉 The U.S. dollar. When the dollar weakens, global gold demand picks up.
Those are the main ingredients–everything else is just seasoning. The VIX, liquidity stories, geopolitical risk–they matter during certain times, but they aren’t the consistent drivers.
Now, I would be remiss if I didn’t mention that these models are limited, that is, they don’t explain everything. They do, however, validate inflation expectations and currency value as key drivers. What about that other 66%? Look, we know that there are lots of other factors such as psychology, narratives, and sudden surges in demand from places like India and China. Those were not factors we tested in our regression. Those are not necessarily numbers-based, making them difficult to test as model inputs. Look, we know they are there, but we would like to find a solid numerical explanation, and we have found some important clues.
Gold isn’t perfectly inverse to the dollar, and it isn’t a perfect hedge against anything. But it does have clear, measurable relationships to real yields and the greenback. That’s the core truth the regression uncovers. The rest is noise. Sometimes that noise is small. Sometimes it’s deafening. But it’s always there, and it’s what makes gold both frustrating and fascinating all at once.
So the next time someone tells you gold is just about global liquidity, or that it’s a perfect hedge against inflation, or that it always goes up in a crisis, remember this regression. Remember that about one-third of gold’s moves are predictable, and two-thirds are just gold being… well, gold. Right now, it should be pretty clear, both intuitively and statistically why gold is having a moment. How long will it last? To answer that question, we need to look at TIPS yields and the dollar index and what drives those to get a clue… for at least ⅓ of the answer. That’s the beauty of markets. These numbers, they aren’t perfect, but they don’t lie. And yes, this IS how we do it.
All this analysis was done in R-programming language. Happy to share my code. 😉
YESTERDAY’S MARKETS
Stocks rallied yesterday as hopes of Fed rate cuts in today’s / tomorrow’s FOMC meeting hit a fever pitch. A 25-basis point cut is very much priced into markets–anything less will be painful. Bond yields declined and gold gained. 🤔☝️
NEXT UP
Retail Sales (August) is expected to have risen by +0.2% for the month after gaining 0.5% the month before.
Industrial Production (August) may have slipped by -0.1% for a second straight month.
NAHB Housing Market Index (September) probably rose to 33 from 32.
The FOMC meeting starts today, but we won’t hear anything about it until tomorrow afternoon–be patient. 😉