It never ceases to amaze me how price movement is so intricately related to itself. Here, I would like to present one of my own geometric approaches (Relative Charting) in a step-by-step procedure which outlines the S&P 500’s rather steadfast up trend since the major low of 666.79 on the week of Mar 2, 2009, as well as ties together the last 18 years. These perspectives will be offered from the previous large uptrend from the major low of 768.63 on the week of Oct 7, 2002 to the all-time high of 1576.09 on the week of Oct 8, 2007. (Notice the 60 month cycle which repeats this October.)

**STEP 1: Calculate the Vector Ratio**

Every trend can be mathematically quantified by its exact low and high. In this case, the market moved 807.46 points (from 768.63 to 1576.09) over a period of 261 weeks. This is an average movement of 3.0937 (rounded) points per week, arrived at by simply dividing the points gained by the time elapsed. This is represented on the chart as a straight line from the low to the high, or ‘vector’. (For great vector work, check out Michael Jenkins’ Secret Science of the Stock Market.)

Before we get to the second chart (hey, no peeking!), first imagine lifting this line and placing it directly starting on the next major lower low. Hmmm…

**Step 2: Apply the Vector to the Next Major Lower Low**

Here, the newly placed vector gives great support to the major pullback of this large uptrend. What this says conceptually is that this up trend is stronger than the average force of the previous up trend.

Although one could get that visually from a casual observation, this procedure quantifies this comparison (3.0937/W), and even offers functional support.

Certainly, a sustained break of this support would indicate an end to this up trend, with either a down trend or a sideways market of similar magnitude to follow. But this now seems close enough to a basic and very obvious trend line drawn from both lows, which certainly most analysts are aware of. What’s the big deal?

Well, WHY did the market bottom twice in this relationship, and exactly at this placement? In other words, was this vector placement there already, like a ‘pre-existing trend line’ of sorts? Are these two lows just ‘following orders’ in a larger scheme related to the previous up trend? And more importantly, if so, what else can be gleaned from such a possibility to derive additional support, or even resistance for future price action?

To find out, we gotta get geometric…

**Step 3: Set the Chart Scale to the Vector at 45 Degrees**

(for additional details, please see Appendix concerning the chart scale)

By setting the geometric perspective to this up trend, we can now ‘see’ all price movement from this trend’s perspective of 3.0937/W, set at 45 degrees. This is the basis of Relative Charting (refer to my February and April ‘Back to the Drawing Board’ articles in this newsletter). This is opposed to the traditional Gann environment of using an ideal quantity per time, such as 1 point/W, 50 cents/TD, $1/M etc.

Note: Using a trend’s vector as the geometric basis just offers a different perspective, relative to price itself. I find that it complements, rather than competes with the traditional geometric method.

Thanks to mathematical procedures for accuracy, as you will see, the vertical scale does not have to be perfectly accurate with this vector seen exactly at 45 degrees for our purposes today. But for now, if you do not have a geometric locking feature on your charting program, then draw the height and width of the vector (forming a square) and adjust your chart vertically until all sides match closely enough. If greater visual accuracy is desired, you can place a right-angle tool on the screen, and use the 45 degrees side as a guide for the vector.

Now that the scaling ratio is defined, we can begin to turn the vector into a circle, which is a great place to start digging for geometric relationships.

**4. Find Circular Dimensions by Multiplying the Vector Height and Width by ****the Square Root of 2**

A circle drawn from the vector (the high is the center) will represent the vector length in all directions, most importantly straight up, down and sideways, as in north, south, east and west. These ‘cardinal cross’ points (as well as NW, NE, SE & SW or ‘ordinal cross’ points) are great for extended geometry, and really come in handy. Here I calculate just the south and west points by simply multiplying the vector dimensions of 807.46 points (height) and 261 weeks (width) by the square root of 2, or 1.4142 (rounded). This multiplier gives the new dimensions as 1141.92 points down from the high to a lower price of 434.17, and 369.11W back from the high to Sep 11,1999 (both figures are rounded). The chart view must be zoomed out a bit to fit in all to follow:

I also included the east side of 369.11W after the high which gives Nov 3, 2014: an election Tuesday!?! The circle top price (north) would be 2718.01, which is 1141.92 added to the high of 1576.09 (not shown for clarity). And now, we use these points to draw a perfect circle.

**5. Draw a Vector Circle from the High Center Using Extreme Points**

If your charting program offers a scaling ratio feature in the circle tool, by all means use it. If not, draw a circle from the vector high using the expanded height and width points. If your program does not have a circle tool, strongly consider getting a new one that does!

As stated earlier, this circle truly represents the vector length in all directions emanating from the vector high, and therefore truly represents the actual up trend in all directions from the high, as seen by the uptrend itself. However, if drawn in a 1 point/W environment (Gann), the trend would be represented in all directions as seen through the perspective of 1 point /W, and therefore different points on the chart would be given by the resulting circle, offering different geometric possibilities. Apples and oranges, and both are good for you!

The retrospective support offered by this circle clearly shows we are on track, just as the vector placed on the Mar ’09 low indicated as well. Unfortunately, price is not close enough to this circle to really offer anything at the moment, so let’s put emphasis on the S and E ‘points’ and go back to the vector.

**6. Connect the South and East Points (‘Pre-Existing Trend line’)**

Here’s the answer we’ve been looking for: The vector, when placed perfectly on the south point (which connects perfectly to the east point) provides support for both important lows. Hence:

Both lows are revealed to be geometrically in-line with the previous up trend’s average (vector), when placed on its extreme lower vertical expression (south point), but only when seen from its own perspective (vector set at 45 degrees – Relative Charting).

OK, so we got something regarding previous lows. What about something more useful like resistance or defining the current small up trend?

**7. Connect the Vector Low with the East Point**

By connecting the vector low with the east point, resistance for the uptrend is revealed. In addition, the east point is a focal point, drawing the market towards it in a defined large bearish wedge shape. If the S&P can successfully break out of this shape, then a prolonged bull market is indicated at least to the vector high of 1576.09. If a breakout of this level occurs, then the east point would become a potent location for a major pullback low.

Doesn’t the resulting small up trend of current price movement have a slight arc to it? Let’s nab that, and see what it brings.

**8. Add Internal Circle by Dividing by Root 2**

Yes, the return of the square root of 2. By dividing the circle by 1.4142 (or better yet, think of it as multiplying by .7071, a crucial retracement level revealed in circular geometry) the circle is automatically ‘shrunk’ to fit the vector square (thin blue circle). This means that the resulting circle’s radius is the vector’s width/height.

Current price is quite familiar with this resulting circle:

The S&P’s recent up trend is climbing perfectly up this circle, and is just underneath resistance: This intersection is a perfect harmonic location for either a push-through or a reversal! In addition, the circle naturally ‘ends’ at the next vector cycle point of 261 weeks (60 month anniversary) on the week of Oct 8, 2012.

In conclusion, almost every important aspect of the S&P 500’s large up trend since Mar ’09 is accounted for, simply by viewing it from the previous up trend’s relative geometric perspective. Currently, the market is at a crossroads of rising circular support meeting ascending angled resistance.

Current price can either reverse back down, staying in a clearly defined ascending wedge, or break out into an extended bull market.

And now for dessert, a grand finale of sorts, since the circle low of 434.17 is just a shave under the 1994 correction low of 435.86 on the week of Apr 4… And hey, didn’t the 1990’s top out proportionately with the current large up trend (or vice versa), as seen through the trend in the middle, with lots of geometric harmony along the way?

**9. Perfect Balance – Tops, Bottoms and Trends In-Between**

I’ll let you peruse this one by yourself. Enjoy!

APPENDIX

The very basis of geometric charting is the exact chosen relationship between price and time, also known as a scaling ratio. (Market Analyst software uses the term ‘geometric lock’ – excellent term!). By linking a particular amount of price (vertical distance) with a particular amount of time (horizontal distance), the chart is now aligned by a specific ratio that reveals certain relationships (S/R, shapes, geometric angles etc.) that are either very difficult if not impossible to determine otherwise.( It is not necessary to do this on graph paper (where each square perfectly represents the scaling ratio), although I certainly recommend doing at least one chart this way, which can greatly aid your abilities).