Amount-Related Terms: Size, Base & Increment

Figure with amount coordinate items and terms

In earlier article we defined price-related terms and talked about discrete price levels. Now we need to look at the horizontal coordinate and define amount-related terms. In the article Coordinate System in use for Pyramids we saw that horizontal width of a particular pyramid rectangle corresponds to the amount of shares. Due to the nature of pyramidal shape, the pyramid gets wider towards the bottom. This is actually one of the key Pyramid Investing principles – the amount of shares purchased increases as the price of underlying stock goes down.

But before we can quantify the amount of shares that relates to particular discrete price level, we need to define a few terms. Let’s look at the following figure:

Definition of Amount-related terms: Size, Base & Increment

Look at the horizontal dimension of pyramid – the amount coordinate, and observe three new amount-related terms:

• Size
• Base
• Increment

Unit for amount related terms is share

All three amount-related terms use the same unit. However, we mentioned earlier that amount may represent either amount of dollars or amount of shares. Therefore, depending which one we use for a particular pyramid, the unit of amount gets to be either dollar or share, respectively.

We predominantly deal with the amount of shares and thus we assume that the unit for amount-related terms is share. Only on rare occasions when we explicitly mention so, we consider dollar as a unit for amount-related terms. One of those occasions is application of Pyramid Investing to 401(k) mutual funds. There, we use dollars in order to avoid dealing with units of different mutual funds.

I think it is worth mentioning that the logic and use of amount-related terms always remain the same regardless of unit we choose to apply for particular pyramid amounts.

Another obvious fact is that wider pyramids deal with larger amounts and vice versa. Looking at any single pyramid, we observe that pyramid gets wider towards the bottom, and consequently the amounts we deal with also get larger towards the bottom. With the increase of depth, we normally consider only linear increase of amounts, although alternative (and more complex) approaches may deal with exponential or some other relationships.

Definition of Size

Size is general term that we use in relationship with horizontal dimension of pyramid. Therefore, we have the following definition: Size is a measure of pyramid width at the specific price level.

For typical pyramids, size varies depending on price level within pyramid range. The smallest size is found at the top of the range and it becomes larger towards the bottom of the range. As you can see, term size is equivalent to the amount.

Definition of Base

Base is one specific pyramid size – the size at the top of the pyramid. Base is shown on the figure above. We can define this term using following definition: Base is the size of pyramid’s top.

As you can observe from the figure, our pyramid has a “flat” top. Base is the width of the pyramid at its top. Base is also the smallest width of a pyramid. Since we know that base relates to the amount of shares, it expresses the smallest amount of shares to deal with when applying certain pyramid.

As we are already aware, the whole idea of introducing pyramid shape is to help us determine discrete price levels and associated amounts we trade. But we need to be careful since it is not practical to trade extremely small amounts of shares. In addition to not being allowed to trade fractional shares, it is not practical to trade one or two shares of cheap or penny stocks. This makes even more sense when we account for trade commissions that are unavoidable factor in trading stocks.

Now you realize why we needed to “clip” the top of triangle when we performed our geometry play in order to obtain basic pyramid shape. We wanted to achieve some non-zero size at the top of our pyramid due to practical considerations. Base is the smallest amount of shares we trade along the pyramid we specify.

In the process of shaping pyramids, we have a freedom of choosing appropriate base depending on other factors such as top of the pyramid, commissions and amount of trading profits we want to achieve. As we will discover later, shaping pyramids is somewhat an artistic act that determines risks we take and eventually profits we obtain. In other words, shape of a pyramid directly determines how aggressive or conservative our approach to the market gets to be.

One important distinction I want to emphasize regarding the term base is that it is used to measure the size of pyramid’s top, not bottom! You may want to naturally associate base with the bottom of pyramid, however, you need to remember that we always start from the top of the pyramid. Therefore, base is the amount we start with in building our position in a pyramidal way.

Definition of Increment

So we start from the top of the pyramid. We buy the base amount of shares at the price that corresponds to the pyramid’s top. When the price drops to the first lower discrete price level, we buy additional amount of shares at that level. We want this additional amount to be larger than base amount. How much larger the additional amount gets to be compared to the last amount bought is determined by increment. Thus we have the following definition: Increment represents the difference between amounts at two adjacent discrete price levels.

It holds that adjacent discrete price levels have consecutive depth numbers. Thus as the depth increases, each additional amount is larger for the amount of increment. In other words, to come up with new amount, we need to add increment to the old amount. Once the trade is executed, new amount becomes old and we repeat incrementation with the next trade.

Increment doesn’t necessarily have to be a whole number. If it is a fractional number, the amount of shares may happen to be fractional as well. Since we are not allowed to buy or sell fractional shares, we perform rounding of shares we deal with.

This article rounds up defining terms that relate to pyramid’s vertical and horizontal dimensions. There are still few terms remained that relate to cumulative pyramid measures – surface areas as well as pyramid names based on price range coverage. Those are going to be addressed in future articles.