What is the real real interest rate measured in? (If you didn't say "gold" then go directly to King World News. Do not pass go, do not collect $200. And for f#@%'s sake, stop reading Jon Nadler.)
Let's extend my previous analysis. First, if we wish to fit a parabolic curve of the form ab^(-t^2) + c to a series of descending price points (or ratios of prices, as I've been doing), the constant c is important, because a "singularity" only happens if c is negative (as we saw with 10-yr yields measured in ounces of silver).
That doesn't look to be the case with gold.
Yes, the $TNX/$GOLD ratio is also descending parabolically on the log chart. And, as usual, we can interpret the $TNX/$GOLD ratio as the amount of gold the US Government gives you every year for lending it $1000 for ten years. Throughout the 1990's, that amount stayed constant at 1/5 of an ounce (almost literally; see horizontal regression line in chart below). Nowadays, it's below 1/100 oz.
Note also in the graph above that, as with silver, I had only to shift the upper curve down and (slightly) to the left to get a nice parabolic channel.
Because the equation of the above curve has a positive constant c added to it, it stabilizes at that value (asymptotically), never hitting zero. Meaning the maximum value of $TNX/$GOLD will stabilize at c = 0.0037. Theoretically, that means that the price of gold can keep falling towards zero, as long as yields fall even more.
So, unlike the chart with silver, this one is telling us the "singularity" (interpretable as "hyperinflation") won't happen. Is there a key date we can extrapolate nonetheless?
We could find the inflection point of the curve, which gives us the day the ratio starts falling at a slower rate than the previous day. That occurred in the spring of 2010. But the inflection point is not too interesting, because the rate of descent can slow down in relative terms while the ratio is still falling damn fast.
What we're really interested in, then, is when the curve changes "qualitatively" on the log chart: i.e. the moment when the infinite journey to its asymptotic final value visually "begins". That can be calculated by finding where the third derivative (i.e. the "jerk") of the log of the curve equals zero. See the graph below to see what I'm talking about.
On that day (January 2015), if nominal yields are where they are now, at 1.60 (note that's 16.0 on $TNX), that would imply a minimum of $2,850 gold. If yield falls to 0.50, then gold's minimum price is at Nadler's price target of $877.
If yield rises to its 10-yr average of ~3.5%, gold would be at a minimum of $6,150.