The Silver Singularity

We all know that a line on a log chart depicts steady growth, where price = ab^t, where t is time, and the price increase per unit of time is equal to 100(b-1) percent. 
But what about a parabolic curve on a log chart, such as the one below? (The chart depicts the $TNX/$SILVER ratio, which can be interpreted as the number of ounces of silver you get in return for lending the US Government $1000 for ten years.)

The above concave down parabola should take the form ab^-(t^2) + c = r (where r stands for the ratio the chart is measuring) (To see why, take the log of both sides to get a function of -t^2). The constants a,b,c can easily solved for by substituting points that touch the curve. The thing to keep in mind is that the first three points that touch the above curve (events that occurred a decade ago) determined its shape into infinity (the same way that connecting two points 10 years ago will determine a line to infinity). So theoretically I could've solved for the equation (and drawn the curve above) many years ago, well before it swooped down in an accelerated decline.

Another interesting thing about the curve above: the same way one duplicates and then shifts a trend line (without changing its slope) to make a trend channel, I only had to shift the above parabolic curve down (~40%) and to the left (~1.5 years) to complete a parabolic channel. In other words, I didn't have to change the important variables a and b in the formula ab^-(t^2) + c that determine the shape (and thus the rate of decline). 

Now, the astute reader might be thinking "Wait, as you say, the above curve takes the form ab^-(t^2) + c, but c is obviously negative, so after a certain amount of time, the ratio will cross zero and start to take on negative values . . . whereas, a log chart can never go negative!" Bravo, astute reader, you have anticipated the point of this post. The above parabolic curve, which caps the $TNX:$SILVER ratio, is now at 0.48 oz of silver (whereas it was at 13 oz of silver throughout most of the 1990's -- see the horizontal regression line in top left of first chart), and, as is the nature of a downwards parabola on a log chart, the "half life" of the ratio gets smaller and smaller at a faster and faster rate. As the value of the equation ab^-(t^2) + c gets very close to 0, the ratio begins to lose half its value every week, then every day, then every second, then KABOOM! And knowing the equation for the curve, we can predict the date of the singularity. It is right after New Years 2014. We can also calculate the minimum price of silver on any given date, for any value of the long bond yield:

w/ Yield = Minimum Price of $SILVER on:
Apr-13 Jul-13 Oct-13 Jan-14
0.05% 1.44 2.23 4.62 1212.83
0.50% 14.39 22.33 46.17 12128.35
1.00% 28.77 44.66 92.34 24256.7
1.50% 43.16 67.01 138.52 36385.05
2.00% 57.55 89.33 184.69 48513.39
2.50% 71.93 111.66 230.86 60641.74

Yup, if we assume that the above parabolic curve will continue to function as resistance forever (and how big an assumption is that, really?), then even if 10-year yields are virtually zero (0.05%), silver would still be at least $1212.83. 

I also fit a less concave "last support" curve that touches all 3 obvious "bottoms" over the past 12 years. It crosses the upper curve . . . right around January 2014 (see dotted vertical line). 

Looks like the Mayans were off by a year.


Warren James said...

exciting times for silver .. nice work GM. Halleluiah. 24 months is a very short time, I will watch this ratio with great interest.

milamber said...

I have wanted to post this clip numerous times. This seems apropos.


Louis Cypher said...

So by 2.13 PM Jan 5th 2014 we should be well stocked up on squirrels and Silver ? :)

Jokey comments aside ... very interesting GM. A lot can happen in a year or three but the big trend is in place.

Byzantium said...

I'm not sure whether this is serious analysis or just mental doodling, but taking it at face value:

Silver is presumably incidental in this analysis, and you could have used several other commodities to have achieved similar results?

Interesting read though, including to remind me how much I have forgotten about statistics as a discipline.


Byzantium said...


If Eric King gets a hold of this, you may rue the day.....

"In a powerful piece posted today that shocked KWN, top blogger and trends forecaster, G.M. Jenkins forecasts 4 digit silver as a minimum by Jan 2014, and a thousandfold increase from spring 2013 in any scenario."


GM Jenkins said...

Warren, I hate to break this to you, but you don't have 24 months ... only 12. I know your home renovations aren't quite done yet, but I suggest you move up the bunker on the timetable. And don't let your contractor skimp on the wine racks and humidor. And some apparatus for smoking squirrel meat . . .

I've never really watched star trek, milamber, but I think I know the story line to the episode at 0:18 into your link. Spock had his way with those hot twins after drugging them, am I right??

Good to hear from you, Byzantium. Lol'd at your Eric King quip. Re: the ratio, it's not ust dependent on the $TNX, as that isn't falling parabolically on the log chart. But yeah, yields/commodities are all falling, not sure if you saw my recent post on $TNX/$CCI. Interestingly, the trend i fund there via regression is also only sustainable until 2014-ish

Byzantium said...

Hi GM Jenkins,

happy to provide the LOL, but to a serious question now:

The way I read your article, was in the spirit of 'there are many mechanisms and bases on which to extrapolate the past, but this intriguing little one (being one among many) suggests that a big shock is coming soon. Just something to bear in mind...."

I had the screwtape crew down as sympathetic to the price potential of PMs ('gold-bugs lite') but with their feet firmly on the ground. So I was surprised to find you going all KWN on us, unless it is as mentioned before, just 'what-if' doodling.

clarification sought.


milamber said...

@ GM,

Then you haven't lived Sir!

And for the record, Spock had his way with anything and anyone at anytime.

That's the power of the Vulcan mind meld at work; unlike KWN podcasts, it has a basis in reality!


Anonymous said...

So let me get this clear GM. Are you saying Silver is a buy?

anon said...


I don't think he's saying anything, he's showing some stats.

GM Jenkins said...

So let me get this clear GM. Are you saying Silver is a buy?

duggo, you know I don't give investment advice. I can only tell you what I am doing with my money, and you do with that information as you please. And as far as what I'm doing with my own money is concerned, I'm ... er.. well I probably shouldn't publish it on the internet, but let's just say the other party to my transaction is late and it's cold out here on the street corner.

milamber said...


Sorry, my bad.

(S)he will be there momentarily.

heading off to take a shower now...


GM Jenkins said...

@Byzantium - the specific curve I drew could be broken tomorrow for all I know. I'm not betting anything on its mathematical precision, obviously; I only worked that out to extrapolate a date. But as with any trend line, the more times it functions as resistance the more you take note of it, and I also wanted to raise the point that as the government's demand for money grows exponentially, the cost for it to borrow money (in silver, the historical currency) has been decreasing not at an exponential rate, but at an exponentially exponential rate. In 1990 the gov't paid you a 20 coin tube of silver every year for lending it $1000. Now it's paying you less than half a coin.

costata said...


While you're waiting for your "friend" to finish showering.... TA isn't my forte so forgive me if this is a stupid question.

Do you think this could be indicating a timeline for hyperinflation of the US dollar?

Byzantium said...

@GM Jenkins,

cheers, that's what I thought; you are merely bringing our attention to an interesting trend.

It is for the individual reader to decide whether this provides any basis to divert part of their hooker budget to silver or similar.

decisions decisions


GM Jenkins said...

@costata, even if you assume the above hyperbolic trend can't possibly last (and I suppose the main reaosn for this post was to point out that it can't possibly last) it's still the case that the real value of yields in any currency (as Byzantium pointed out) is decreasing exponentially. That can technically last without hyperinflation I suppose if yields are allowed to go negative, as we discussed in the comments in my Timeline to the Apocalypse post.

I think hyperinflation should be the topic of this years Screwtape christmas pow-wow. Unfortunately we can't invite Mish Shedlock as guest speaker again after Louis called him out last year for double dipping in the fondue pot.

GM Jenkins said...

*correction, above i meant in any commodity, not currency

costata said...


double dipping in the fondue pot

Mish Shedlock, clearly a man with no conscience.

I pointed the discussants over at the FOFOA blog to this post. 'Edwardo' made an interesting observation about the number of analysts (using different methods and approaches to TA) who are looking to this 2014/2015 period for a climax of some kind. Though you seem to be hedging your bets and hinting at a series of them between now and 2014.

S Roche said...

Now would be good!

Anonymous said...

Silly me GM. I now see you were using the word "silver" as euphemism for cocaine. The charts now make perfect sense. The price of "blow" must be subtly indicating the state of the World economy. You shouldn't stand on street corners waiting for your pusher though, you'll catch your death.
I am encouraged by your "longterm" speculation that there actually will be a 2014/2015.
Once we get through the "End of the World" 21 December 2012 it should all be plain sailing.

Bullion Baron said...

Forget Freegold, looks like we are heading for Freesilver! ;)

Anonymous said...

Lovely shiny silver porn ! And right before Christmas too.

Another confirming indicator for those of us stacking the stuff at the expense of consumption.