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Volume One

Smart Volume Analysis

In previous posts I gave the Smart Money perspective for Candles, Chart Patterns and Indicators. Before moving on to the background study of charts, understanding price spread, and getting into strategies, I want to establish a clear understanding of what volume means.

The definition of volume:

In the stock market, volume refers to the total number of shares that exchange hands over any given time period.

In any volume bar several types of transactions might be taking place all at once. They are : buying, covering short sells, selling, selling short.

By itsself, volume only shows activity. VSA is not volume analysis, price spread analysis, nor volume and price analysis on a single bar or candle. For instance: high volume on an up move does not necessarily mean the next move will be up. There could have been hidden selling within that move.

VSA teaches that weakness comes in on up moves and strength comes in on down moves. From my last blog post, remember:

1. Bullish volume is increasing volume on up-moves and decreasing volume on down-moves.
2. Bearish volume is increasing volume on down-moves and decreasing volume on up-moves.

To Smart Money "accumulate means to buy as much of the stock as you can, without significantly putting the price up against your own buying, until there are few, or no more shares available at the price level you have been buying at. This buying usually takes place after a bear move has taken place in the stock market as a whole...The lower prices now look attractive." [TW]

This is a good time to incorporate Williams perspective on The Path of Least Resistance:

1. It takes an increase of buying (demand), on up-days or bars, to force the market up.

The appearance of no Demand (low volume) on an up-move, shows little or no buying. Which means, if there is no trading going on in one direction, the path of least resistance is generally in the opposite direction.

2. It takes an increase of selling (supply), on down-days or bars , to force the market down.

The appearance of no Supply (low volume) on a down-move shows little or no selling pressure. Which means, if there is no trading going on in one direction, the path of least resistance is generally in the opposite direction.

VSA is the combination of analyzing volume to price spread in the context of the background which includes the general market and multiple timeframes. It is within the context of the background that volume shows it's weight in the final analysis:

"It [volume] is often looked at for confirming evidence of price trend and price reversal patterns. For patterns such as triangles that are the product of a period of indecision or consolidation in stock price, volume is usually light during the formation of the pattern and increases on a breakout from the pattern. For any pattern or trendline penetration, a breakout with increasing volume is more an indication that prices will continue in the direction of the breakout than a breakout on low volume." [Trade10.com]

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http://www.informedtrades.com/blogs/magic/

A cube of unit edge is rotated 30 degrees about one of its diagonals. What is the volume of the solid that is?

A cube of unit edge is rotated 30 degrees about one of its diagonals. What is the volume of the solid that is the intersection of the initial cube and the rotated one?

Volume is approximately 0.803847577293 cubic units.

Brief explanation:
Intersection solid is irregular dodecahedron whose sides are twelve acute triangles each having sides:
a = √(5-2√3) ≈ 1.239313674927
b = 2√(2-√3) ≈ 1.035276180410
c = √(11-6√3) ≈ 0.779548045079

Angles opposite to sides a, b and c respectively:
cos A = 7/(2 √(40-23√3)) - 2 √(3 / (40-23√3))
A = 84.896091°
cos B = 4 / √(13 (7-4√3)) - 2√(3/(13 (7-4√3)))
B = 56.309932°
cos C = √(4/13 + (9√3)/52)
C = 38.793977°
We don't need these angles. I calculated them (using cosine law) just for purpose of visualisation, that is to show that sides of dodecahedron are indeed acute triangles. They can also be useful in case that someone decides to make a cardboard model of this solid.

We can find the area A₁ of the acute triangle through Heron's formula:
A₁ = √(s(s-a)(s-b)(s-c))
where s is semiperimeter:
s = (1/2) * (a + b + c)
s = (1/2) * (√(5 - 2√3) + 2√(2-√3) + √(11-6√3))
s = 1.527068950208
Area of one side of dodecahedron:
A₁ = 0.401923788647

We can divide this dodecahedron in twelve equal irregular tetrahedra in such way that each side of dedecahedron is base of one tetrahedron, and the apex of tetrahedron is the center of dodecahedron.
Height from the base to the apex is exactly 0.5 units.
The volume of a tetrahedron is given by the pyramid volume formula:
V₁ = (area of the base) * (height) * (1/3)
V₁ = A₁ * 0.5 / 3 = A₁ / 6
V₁ = 0.066987298108

Dodecahedron consists of twelve tetrahedra so its volume is
V = 12 * V₁ = 0.803847577293 cubic units

As a byproduct of this method, we also find area of dodecahedron as
A = 12 * A₁ = 4.823085463759 square units
This is all basic geometry, and will be more clear when I post some pictures. I'm not done yet.

Edit: I've just sketched this on paper for the first time and realized, what Gianlino said, that this is unit cube minus six right tetrahedra.
Very straightforward, but I didn't see that because I drew everything in my head, and only now I'm converting it to real drawings. Too bad I missed that, but I'll continue according to what I originally "saw".

Edit 2:
Unit cube and the diagonal:

http://img94.imageshack.us/img94/4386/slika001.png

View along the diagonal. Cube projects as regular hexagon and halves of its sides project as equilateral triangles.

http://img21.imageshack.us/img21/5280/slika002.png

Now we add another cube rotated by 30° around the diagonal.
From the original view:

http://img135.imageshack.us/img135/3471/slika003.png

Parts of the original (blue) cube, in shape of right tetrahedra, which are not hidden inside the rotated (copperish) one, represent the difference between volume of unit cube and volume of intersection solid.
I missed that and continued to "observe" along the diagonal:

http://img820.imageshack.us/img820/2355/slika004.png

Here x' and y' are projections of segments whose actual lengths are x and y, respectively. We're interested in ratio x/y. Because of linearity, x'/y' = x/y. Ratio x'/y' is easy to find observing the equilateral triangle outlined in red and using law of sines yielding
x'/y' = x/y = (√3 - 1) / (√3 + 1) ≈ 0.267949
Since y=1,
x=(√3-1) / (√3+1) units
Now we have everything we need to find a, b and c which are sides of triangle here outlined in red. This is normal view to side of a cube.

http://img824.imageshack.us/img824/4962/slika005.png

That triangle will be one of 12 (equal) sides of intersection solid. Notice also that it is coplanar with the side of the cube.This seems trivial now but will become important later.
Intersection is dodecahedron resembling hexagonal dipyramid, view along the diagonal and side view:

http://img852.imageshack.us/img852/132/slika006.png

Here, it's divided in 12 equal tetrahedra as explained.

http://img834.imageshack.us/img834/7674/slika008.png

Three tetrahedra are removed for better view, three are visible in the front and there are six more on the back side.
Because sides of this solid are triangles cut out from sides of cubes, normal distance from sides to the center (=height of tetrahedra) is equal to distance from side of a unit cube to center of a unit cube, that is 0.5 units. Now we find volume of a tetrahedron and multiply by 12.

Storm Freerun - Volume 1