Sunday, August 21, 2011

Gold's Parabola Equation

We all hear the talk these days about gold going 'parabolic' and that gold's secular bull market is itself making a large scale parabola. I decided to do a little investigating this weekend to see if I could prove or disprove some of these notions mathematically.

After blowing the dust off the cover of my high school algebra book, I found the equation for a parabola which is:  y = ax(squared) + bx + c.

Then it all came back to me what a hassle these kind of problems are to solve.

The x and  y variables are not so troublesome to figure out. X is the time across the bottom of the chart and y is the price of gold as it rises vertically.

But additionally solving for three variables (a, b, and c) will involve simultaneous equations. Yick! That can get really messy.

It took me a while but I finally solved the problem, then made this chart to show you.

I decided to set the first day of the secular bull market on April 1, 2001 as that was the day gold achieved its low of $256. Each year after this day is expressed in increments of 10 (i.e. 50 would be 5 years after April 1, 2001 OR April 1, 2006).

This is a daily chart of gold. The red line running along with price is the 200 dma. The blue line is defined by the parabola's equation.

The equation I came up with seems a pretty good fit considering it covers over 10 years of gold's daily price movement. There are a few tweaks I could do to the equation to have it match price movement a little more closely at specific points in time, but overall I think it shows me what I wanted to figure out.

And indeed, I think we can conclude that gold's secular bull market is making a long term parabola.

I found it interesting to visually compare the 200 dma (red) with the parabola equation (blue). They are quite similar.

Also, it appears our current high of $1881 has strayed noticeably higher from either the parabola or 200 dma than at any time in the past 10 years. But that is a visual perception error. Price, as measured by a percentage comparison, is no higher today from these bench marks than in 2008 and in fact, price would need to barely surpass $2,000 to equal 2006. And who knows - as this is the largest C-wave to date, it may break every record on the chart.


  1. TSI trader I appreciate your blog and your trading advise, and I thank you for all. Lately, your writings and advise have gone into a wondering mode, reflecting the current market environment no doubt. My suggestion is to mentally or physically to close out of your current losing positions and start fresh based on your very good trading system. Thank you.

  2. I have often wondered why "going parabolic" is used as the model in charting. It seems to me that the growth curve (y=e^x) is more appropriate. The right side of the two curves are very similar but the growth curve becomes steeper as we move further out to the right. I wonder if the increase in slope of the chart for gold is because gold is following the growth curve rather than that of a parabola.
    Either way, I really appreciate your efforts and the time you must put in to do all these analyses. They are very well done and enlightening.

  3. what makes more sense to me is Adam Hamilton's analysis of the distance from the 200ma

  4. Anon - thanks for the suggestion. I am more likely to stop writing this blog altogether than be overly concerned by my current stock positions.

    Hi Loren - I have not plotted the growth curve you shared, but if it becomes steeper than the parabolic over time, you are probably onto something.

    For the heck of it I tinkered a little with the 1980 gold 'parabolic'. That thing was relatively flat over three years and then the final 6 months (and especially the final 5 weeks) went bonkers. I could not easily get a parabolic equation to fit it.

    Anon - Adam Hamilton has been a favorite of mine for a long long time. Thank you for the link - I just gave it a quick read. I personally am more in tune with his thinking than others who are convinced gold is never coming back down. Maybe this time will be different. But I am skeptical.

  5. Nice work John. Thanks. Bruce

  6. Hi John

    Im still holding TNA at 64.50

    any advice on what to do?

    Thank You

  7. Bruce - you are wecommed.

    Anon - I am still holding on in hopes of a bounce, as that seems like it has better than even odds of happening. But playing the odds is just that - and it is much better to not get in this situation in the first place, obviously.

    Oct. 2008 dropped 400 S&P points in 3 weeks. Then it bounced on the 4th week - 200 points. Of late we have dropped 250 S&P points so who knows if there is more down to go?

    The stock market and gold market are both extremely stretched - way out of whack with 'normal'. It's tempting to think the current market conditions will never reverse, but they always do. For myself, I am just practicing patience.

  8. I see some divergencies in TNA but no outright buy signal yet. Maybe in a day or two.

  9. Hi Loren - well, the S&P (/ES) is threatening to make a trend line break buy signal this hour on the 4 hour chart and looks good. Gold is looking shaky. The situation in Libya just may take some money out of the gold security blanket and put it into a severely oversold stock market - and soon.

  10. hey john,

    read armstrongs recent letter... 2200 is just a normal part of the market... no real phase transition my friend.

  11. John, Great stuff, creative, technical and inquisitive! Thanks and please keep up the good work.

    I agree that Gold is parabolic and due for a respite so manana I sell my calls and then will wait for the correction to bottom out before buying back in as I think gold has still a long way to go.