Regression Analysis of the Gold Bull Market




As we approach the end of 2012, there's a lot of talk about this being the 12th year of the gold bull market. While true, it's worth noting that with respect to charts, as late as 2005 there really was nothing all that special going on in the gold market (the fundamentals were a different story). What I mean is that gold had entered the $380-$500 range several times after the 1980 crash, where it was still meandering for virtually all of 2004-2005. For example, most of 1987 and 1996 were spent in that range. So, if we want to settle on a date when the 21st century gold bull market began, we have several possibilities. 

As a lower boundary, of course, we can pick the earliest date on which gold hit a price that it never touched again. That occurred in Dec 2001, with gold hitting $270 for the last time.   

Then, we can focus on the all-important $370-$500 range, choosing the date gold finally busted its ceiling since the 1980 crash. That day occurred exactly 7 years ago, around Thanksgiving of 2005. We can also pick the date when gold hit $370 for the last time and never looked back. That occurred in May 2004.

Finally, we can narrow our horizon somewhat and just look at the "QE" period since the crash low of 2008, after which gold has climbed up at a strikingly fast and regular rate, its narrow channel only broken in April of this year. (It made a low shortly thereafter, but has actually continued to climb at a similar rate, just shifted ~$75 lower.)

I'm getting into this because I chose to look at linear regressions of the gold price, and I had to pick critical dates on which to begin the analyses. A linear regression will find the line that minimizes the squared distance of the prices around it. The slope of this line will give you a good estimate of the average daily increase in price during the period you're looking at. It should be kept in mind, however, that in this analysis the residuals from the line of best fit are not independent; if price is far below the line of best fit today, chances are it will still be below it tomorrow. So it's not as good a predictive tool as would be the case if the "errors" from the line were independent of each other. But it is still informative and illuminating.

So with no further ado, here is the weekly candlestick chart with the regression lines. The vertical lines denote the critical dates I described above. (Note that they are opaque, so they cover the candlesticks for that week, but rest assured they are at minimum points). Each regression line begins at its corresponding vertical line. (You can ignore the lines parallel to the "center" regression lines for this analysis.)

The light-blue regression line is a lower bound of sorts. It captures the action of the bull market since it's very beginning in 2001, reflecting a price increase of ~$12/ month. The light-green regression line is an upper bound. It captures the rate of price increase since the 2008 low, at ~$24/month. Gold is not unexpectedly between these 2 regression lines. In fact, it is smack on another line I drew midway between them (pink), which also covers the other 2 regression lines I drew (rationale described above) which start in May 2004 & December 2005.

As you can see, I've "widened" the upper and lower boundary lines somewhat, because as price moves, the actual regression lines will slowly change in slope. But the widened light-blue and light-green bands should capture the true regression lines for awhile. Again, gold is right in the middle of those 2 lines, so right now the direction it goes is anyone's guess (i.e. it's not underperforming or overperforming). I'll be watching the action over the following weeks closely for a hint. Is the nearly perfect cup and handle that is forming going to amount to anything?

My guess is we'll continue to see a lot of volatility between the two boundary regression lines until one is emphatically breached. The lower boundary is approaching $1650 -- and as I've been saying for awhile, I don't think that level will be broken.  Nonetheless, I'm thinking $1800 won't be decisively cleared either, not until earliest April 2013 (see red circle), about 3/4 to the end of the obvious ascending wedge (see red lines). So I think gold bugs should be patient.

**Update: here is an analogous monthly chart with regression lines drawn from significant dates. The 7-year linear fit to gold since December 2005 (dark blue) is quite good, indicating that gold has grown more linearly than exponentially during that period, at ~$16/month.



Regarding the 2001 date I considered the earliest start of the gold bull market, let's look at another weekly chart. The green 89-week MA (a Fibonacci number, perhaps worth mentioning), as well as the 89-week MA of weekly highs and lows (above and below it) make as good a "natural" support system as can be. And we see that the time in 2001 I picked as the earliest start of the bull market was also the period when the 89-week MA was first touched, after which its slope has never been negative (i.e. it has gone only up).
Now, some updated charts from my long post last week. As I predicted, the PPT did not let us down, and the S&P 500 is now outperforming gold for the year.

And the DOW:GOLD ratio indeed bounced off its Fib retracement line. So, I sold my SPY holding (although there's probably further upside, seeing as the DOW's 200-day moving average was cleared Friday).

 Gold in euros still hovering around its all-time high, and bullishly, re-approaches the bottom of its channel.

The 9-year daily gold chart:

On the monthly gold chart, November looks like it will finish in the 40% channel, as I was betting on.


And some long-term silver charts... 
the linear daily:



 And the weekly:

17 comments:

duggo said...

Dear Gm
I've noticed you haven't had any comments for your obvious hard work. So in the spirit of comradeship here is my comment.
I do not think graphs have any value other than a "comfort blanket". A graph is a magical mirror into the "what has been" land. In the past we relied on crystal balls, tea-leaves and the runes. Science has taught us that we need modern mumbo-jumbo to be convinced so we use a lot of mathematics and pretty colours combined with computers to give that aura of mysticism that somehow the crystal-ball lacks.
I think there is a deep longing in the person using charts to be protected from their perceived foe called "The Future". He is so unpredictable that "Chart Man" must gather about him a multitude of charts in order to predict "The Futures" next move. Chart Man wins a few lucky battles but is always destined to lose. Somewhat like Sisyphus and his boulder.
Please do not be down-hearted. There is something of value in the hard work involved. The sheer act of gathering and computing does feed the subconscious with valuable information that does eventually help in major decisions.

Warren James said...

I have high hopes for silver - I still see the current leg up as part of the start of the 'handle' in the 30-year cup and handle (time will reveal all).

I think with enough good data points, 'Chart Man' wins the day. It seems we're mapping human psychology and if that has recognizable patterns then an advantage can be gained in the real world. my 2 cents.

mr pinnion said...

@Duggo

That was a bloody good comment.My thoughts excactly.
Regards
Ozzy

Michael H said...

GM Jenkins,

On the regression charts, are you able to do the analysis on log charts?

For longer time periods especially, a steady percentage increase would show up as a straight line in a log chart, but a parabola in a linear chart.

Also, have you looked at the long-term gold in Euros chart? If I recall correctly, it was flat from about 1999-2003 or '04, then started its upward slope. I think the upward channel of Euro-gold is less volatile than dollar-gold.

GM Jenkins said...

Hey duggo,
Thanks for your thoughtful comment. Keep in mind that there's a difference between (a) using charts and stats to analyze what has happened in the past (which is not "mystical" at all) and (b) making the leap to thinking that an analysis of the past will have value for predicting the future. Like a lot of people who comment here (including, probably, you) I enjoy (a) very much in itself. Shit, I spent a good part of my high school days trying to come up with better sabermetric analyses of baseball stats, or objective criteria for awarding the MVP, etc. When I started gambling on sports, I moved on to (2) with pretty good success (e.g. there's a certain set of circumstances in NBA basketball that when it periodically arises, there's a prop bet I make that has almost never failed). I'm scientific enough in appraising my success that if something seems to be not working or working at a rate no different than chance, I stop (e.g. I stopped betting on football long ago).

But to expand upon a point Warren made, let's assume you're right and that (b) is delusion. Even still, by spending enough time with charts and such, if only by assimilating enough data points, you have a better understanding of the past, and *reasons* for why things happened the way they did begin to suggest themselves. Cf. William Blake: "the fool who persists in his folly will become wise."

As a case in point, I remember as a kid I did some basic statistical analysis of home runs hit and concluded that sometime in the late eighties/early nineties MLB "juiced" the baseball (I didn't realize that it was in fact the players who were juiced.)

Slow Loris Larry said...

I would have beaten Duggo first thing yesterday morning when GM's new post first appeared down under here, but my comment disappeared into the Aether when I hit 'publish comment', and I hadn't the time to recnstruct it.

Although most of what I had intended to post was really just a long rant about the voodoo involved in some of Jim Sinclair's correspondents getting all hot and bothered when they can sort of match plotted price histories with segments of French Curves, I did congratulate GM for his sophisticated use of regression analysis, which is a legitimate, and quite valuable, form of sophisticated statistical analysis.

However, I concluded by saying that GM's first chart, like all other TA endeavors, can only provide an analysis of the past, and cannot possibly tell one what may, or may not, occur in the future. But, what they will show, as events transpire, is that the trend depicted on the chart has continued, or that it hasn't.

That alone is not without considerable value, as knowing when a trend has ended and in what new directions things have begun to move, can inform trading, speculating, and even investing decisions.

GM Jenkins said...

Hey Michael H,
The problem with regression on log charts is that the distance from a point down to a line is not the same as distance up to the line (i.e. vertical distance is percentage gain/loss, but distance X down from a high value is a smaller percentage than distance X up from low value). So I'd have to think about what alpha/beta would mean in such a case (open to suggestions). Clearly, trend lines on log charts are meaningful, e.g. the bottom of a channel is like someone deposited money into a bank account at X% interest, and by chance only checked his balance on days when it hit the bottom of that channel, happy to see his 1+X% growth.

I usually work with log charts, as growth is more important than linear gain (obviously after enough time, any linear increase will start to look flat on the log chart, meaning your investment is getting worse), but interestingly, the linear fit to gold since the late 2005 date I mentioned is excellent (I should've made that regression line the most salient, as it gets hard to appreciate amidst all the clutter). You can conclude that gold has in fact been growing linearly, not exponentially since ~2006, at about $16/month. On the other hand, th elinear model is terrible for the post-2001 set of data points (what I call the lower bound regression line), not least because the intercept is -$250 or something, which makes no sense.

In general though you're right. In my super-basic ana;ysis above, the goal was of course to capture the "true" linear relationship between gold and time, which--given the non-randomness of the residuals around the lines--is incorrect to assume exists; as you say a curve might be a better fit, such that the residuals may actually be more independent.

GM Jenkins said...

Thanks SLL, that's what I was trying to get at in my comment to Duggo. I checked the spam folder and your comment wasn't there. I've had posts in progress disappear on me enough times that I now write them in a text editor.

GM Jenkins said...

I updated the post, adding a monthly chart with regression lines starting from various critical dates. I think it more clearly shows the very nice linear fits since 2006 and 2008.

S Roche said...

Greatly comforted by:

"the fool who persists in his folly will become wise."

I'll let you know.

duggo said...

@ Slow Loris Larry

"as knowing when a trend has ended"

Question:-
What is the guaranteed time length length of a trend?

Answer:- When Duggo spots it and lays hard cash down. Then the "trend" immediately reverses.

costata said...

Warren,

Some data sources on gold in Turkey mentioned in this report:

http://www.goldcore.com/goldcore_blog/%E2%80%9Cgold-atm%E2%80%9D-turkey-gold-deposits-surge-turkish-banks

"Gold deposits in Turkey have grown from 3.1 billion liras to 16 billion liras in the past year, Bloomberg reported on news reported in the daily Turkish newspaper Aksam which cited Denizbank AS gold banking group manager Cem Turgut Gelgor.

According to the Turkish bank Denizbank, one of the largest in Turkey, it collected 1.5 tons of gold in 7 months.

Deposits have increased from 500 kg to over 6 tons or over 192,000 ounces (worth some €260 million) over an unspecified period.

Kuveyt Turk Katilim Bankasi AS has added 3.8 tons of gold, Aksam quotes Kuveyt Turk product development group manager Mustafa Dereci as saying. Dereci said that Kuveyt Turk is providing new products such as “gold from the ATM.”

The World Gold Council estimates that there are around 5,000 tons of gold remaining outside the financial system, gold which the Turkish people have prudently accumulated over the years as a store of wealth to protect from currency depreciation and debasement.

Gold jewellery producer and wholesaler Karakas Atlantis Kiymetli Madenler AS is “working to bring unregistered gold into the system,” Chairman Kamil Karakas says in e-mailed statement today reported on by Bloomberg.

The gold wholesaler is meeting regularly with jewelers and banks in effort to draw unregistered gold assets into financial system.

Separately Turkey is aiming to position itself as a leading player in the gold jewellery and bullion industry by also becoming one of the leading gold and precious metal refining countries in the world.

Turkey is at a level to compete with international gold refining centers like Germany and Switzerland, Istanbul Gold Exchange deputy chairman Osman Sarac said today according to Dunya newspaper.

Turkey imports scrap gold mostly from Germany and the United Arab Emirates, the gold is turned into standard bullion coins and bars in Turkish refineries and exported.

Turkey imported 114.8 tons of gold by Nov. 14 this year, of which 46.6 tons was scrap, according to Istanbul Gold Exchange data."

milamber said...

subbing comments

duggo said...

Dear GM
Sorry about this. Just a further thought on the futility of charts.
Charts are just complex enough to make a person believe that they hold some hidden secret that if uncovered could lead to enlightenment and great wealth.
My wife and I play a game of cribbage every evening and we have become experts at the game. When you become good at cribbage you are able to play the cards the you have been dealt in the most effective way.
Now if I was to apply charts to the game of cribbage I may take note of every hand dealt and work out a graph that would look similar to a financial chart.
Common sense would tell me that the chart would be useless for telling me what hand would be dealt to me next. The variables are too enormous. This is exactly what happens with the choice available in the financial World looking to the future. People use charts believing they can in some way predict the future. When they find it doesn't they look for further inputs rather than realising that the future is totally unpredictable. Unfortunately the "chartist" gets lucky every now and then which encourages the delusion.

S Roche said...

Milambering...

Funky Tape said...

GM - Unique work I've never come across in gold. Thanks for the time as always. For some reason, April 2013 comes up a lot as an inflection point in as many markets as I follow, too. Too many to list, actually.

Duggo - Unfortunately everyone gets lucky now and then. I don't know any trader worth half his ass in Twinkies that thinks they can tell the future by staring at a chart. You seemed to be confused what the purpose of the exercise is in the first place. The data is the data; it has no opinion, it wants nothing, it's going nowhere in a market that's never wrong and will do whatever it's going to do (usually to piss you off.) ;)

Having said that, justifying one's position in the rear view mirror is I think what you're talking about. Yes, waste of time. Those that whine and cry that they studied charts for years and finally gave up cause they could never "get it" are the reason the market exists in the first place; to keep those that chase it always one step behind. No one beats the market because the rules dictate that there can never be a winner.

S Roche said...

Mentions regression analysis, gold, bull market. Gibson's Paradox re-re-visited: http://www.tfmetalsreport.com/comment/240900#comment-240900

Thought you might be interested too.