So correlations between different assets tend not to be fixed, and instead tend to depend on the macroeconomic conditions of the relevant time. And, in the case of free-floating gold, whatever else might be involved in determining its speculative value.
Indeed, CCFs were much more popular here at one point when backtesting showed they apparently had negative correlations with both stocks and bonds AND stock-like returns. Here is a representative sort of analysis from that era:
https://www.nber.org/papers/w10595
Abstract:
We construct an equally-weighted index of commodity futures monthly returns over the period between July of 1959 and March of 2004 in order to study simple properties of commodity futures as an asset class. Fully-collateralized commodity futures have historically offered the same return and Sharpe ratio as equities. While the risk premium on commodity futures is essentially the same as equities, commodity futures returns are negatively correlated with equity returns and bond returns. The negative correlation between commodity futures and the other asset classes is due, in significant part, to different behavior over the business cycle. In addition, commodity futures are positively correlated with inflation, unexpected inflation, and changes in expected inflation.
Your backtest picks up right after that period, and it is quite true during that period CCFs did not at all behave like some people were hoping based on studies like that. CCF returns were much lower than stocks, and not negatively correlated.
What some people back then failed to understand, among other things, is that this synthetic CCF index was in part just reflecting that their study period included a period when inflation was unexpectedly high, and US stock and bond real returns were really bad. We haven't had a significant period like that until just recently, and both returns and correlations depend on such things.
Now if you take your test and set the beginning to March 1, 2021, which is approximately when inflation really started taking off, you will see a couple things of note:
https://www.portfoliovisualizer.com/ass ... &months=36
First, now IAU has the higher correlation with VTI, 0.25, and PCRIX is -0.07. Second, PCRIX now has a 46.79% (!) annualized return, versus 4.35% for VTI and 8.21% for IAU.
So CCFs did do what was expected of them--when the right macroeconomic conditions came around.
By the way, USERX is one of the oldest gold (mostly) funds I know of. VFINX is also one of the oldest funds approximating the US total stock market I know of. Using those instead in your test, you get back to September 1976, and the average correlation between USERX and VFINX is 0.20:
https://www.portfoliovisualizer.com/ass ... &months=36
But if you click on the rolling correlation, you get a better picture of the real story. That rolling correlation has been as low as -0.26 (in 1994), and as high as 0.65 (unfortunately, now).
Again, whether you are talking about CCFs or free-floating gold, there is no one particular answer as to how they will correlate with stocks. It all depends on macroeconomic conditions, plus in gold's case this speculative factor which is inherently unpredictable.
For the record, though, USERX has spent more time positively correlated with US stocks than negatively correlated.
When holding a low-yielding high volatility asset, it's quite crucial that it's not correlated with the rest of your portfolio (otherwise you get hit in two ways: lower returns, maximum drawdowns are magnified).
As an aside, a sub-zero return, high-volatility, uncorrelated asset generally is not expected to improve portfolio efficiency.
Indeed, if it were that easy, you could take a portion of your portfolio each month to Vegas, and put it on black on a roulette wheel.
Mathematically, that is a slight sub-zero return and high-volatility "asset", and it is totally uncorrelated to anything else!
And yet, it is a bad idea.