Price-Related Terms: Level, Top, Bottom, Range & Step

Figure with price coordinate items and terms

In the previous article we inserted the basic Pyramid Investing shape into a 2-dimensional coordinate system. We defined vertical coordinate as price and horizontal coordinate as the amount of shares that depends on price.

Now, let’s move forward and add a few price coordinate items:

Definition of Price-related terms: Level, Top, Bottom, Range & Step

This figure helps us define very important terms that we are going to use frequently whenever we compare, analyze or apply pyramids. Terms defined here and in the following articles will comprise Pyramid Investing terminology. Put it simply, we will adopt specific language for Pyramid Investing.

This article observes vertical dimension of pyramid – the price coordinate. Using the help from the figure above, we will define five price-related terms:

• Level
• Top
• Bottom
• Range
• Step

Unit for all price-related terms is dollar

All five terms use the same unit, which is unit of price. I will always use dollar as unit of price. You may happen to be pyramid investor from some country other than United States, Canada, Australia or any other dollar-named-currency-country. In such a case, you may want to use Euro, Pound, Yen, Dinar or whatever the currency you use on your local stock exchange. Pyramids are universal so they work the same regardless of currency used.

The direction of price coordinate is up. That means price increases as we climb the price coordinate. In other words, higher points on price coordinate correspond to higher prices (more dollars). Just for the record, I would like to mention that we will always use linear price coordinate. That means the price difference between any two equidistant points on the price coordinate will always be the same.

Definition of Level

First, we define the term Level: Level is short for “price level” or “price”.

Thus any price on the price coordinate can be called level. Since our price coordinate is vertical, any point on horizontal line drawn in pyramid coordinate system will have the same price determined by the level of that horizontal line. Level is really one very general term. We are going to see later that we will mostly use discrete price levels that belong to the range of the pyramid.

Definition of Top and Bottom

Now let’s look at the figure above and define two more terms:

Top is the top level of pyramid or the highest price that the pyramid extends to in upward direction.

Bottom is the bottom level of pyramid or the lowest price that the pyramid extends to in downward direction.

Of course, top of the pyramid translates into higher price than the bottom of the pyramid. We will always look or start from the top of the pyramid. This is very important to remember. Thus the pyramid extends from the top to the bottom.

Definition of Range

Range is a collection of prices (or levels) between top and bottom of the pyramid.

We can also observe that any price or level on the price coordinate will either belong to the range or won’t belong to the range. Prices that do belong to the range also belong to the pyramid and vice versa. On the other hand we can also say that pyramid covers certain range of prices (or levels) between its top and bottom. We will see later that our tendency will be to extend the pyramid as much as we can so the pyramid would cover the broadest range we can handle.

Definition of Step

One of the most important terms in Pyramid Investing is Step: Step is the smallest difference between two discrete price levels.

Step actually makes general pyramid practically usable. Using technical jargon, we can say that step is used to discretize price levels in the pyramid range (step is resolution of discrete pyramid). In other words, pyramid range that comprises theoretically infinite number of prices, by virtue of step is brought down to some finite and practical number of discrete price levels. Thus we may be talking about the pyramid that has 10 or 20 or even 50 discrete price levels. The difference between any two adjacent discrete price levels is what we termed step.

The assumption I make here is that the step is constant regardless of which two adjacent discrete price levels are taken. It is possible to define variable step as well. However that would go beyond the scope of this article. At this time we can regard that the benefit of variable step is smaller than the downside of having to handle complex pyramids whose step changes with price.

Discrete domain

In the previous paragraph, where term step was defined, I mentioned several times discrete price levels. I think it is important to explain what “discrete” really means.

Since we use dollar as a unit of price, we express prices in dollars. Dollar also has its fractions – cents. One cent is one hundredth of a dollar. Therefore, when we express prices, we usually do that with precision up to two decimal points. So we say a price for certain share is $2.14 or $43.27 or $102.99. I am sure this is nothing new for you.

Considering that 1 dollar has 100 cents, there are 100 different prices that belong to the same dollar range. If we look at the range of 100 dollars, we see (100 times 100) or 10,000 prices! It is not unusual that our pyramid covers the range of 100 dollars. However, we definitely don’t want to deal with ten thousand prices! So we decide to eliminate most of them and focus only on remaining few. Let’s say we want to focus on 20 different prices. We divide 10,000 by 20 and obtain 500. 500 is our step expressed in cents. If we express it in dollars (divide by 100), we have $5 price step.

Now we can use $5 price step to obtain prices we want to focus on. We start from the top of the pyramid. Let’s assume the top level is $105. We go down step by step and select our price levels. We obtain the following prices: $100, $95, $90, $85, $80, $75 and so on until we have 20 of them. By doing this, we actually eliminate 499 prices in each 5 dollar sub-range and keep only one. The one price we keep in each sub-range is called discrete price.

By using this process of discretization, we drastically reduce the number of prices to deal with. The simplification comes as a consequence of having to treat only small number of discrete price levels. We can also say that we achieve the transition from (almost) continuous spectrum of prices into more favorable discrete domain.

Definition of Depth

Discrete domain of price levels requires that we append our set of definitions and terms with a few additional ones. We are going to introduce small, whole numbers to identify each discrete price level (see figure below). Since we always start from the top of the pyramid, we number the top price level as level zero. Please make a distinction that zero price level is not a price of zero dollars! On the contrary, price level 0 corresponds to the highest price within the range of pyramid prices. Next we move one step down to the first discrete price level and name that level as level 1. Then we go even lower in price and another step down we find the next discrete price level which is level 2. We continue stepping lower in price until we reach bottom of the pyramid.

Discrete price levels and definition of Depth

If you imagine top of the pyramid being at some surface level, then each numbered discrete level has a certain depth relative to the surface (or top). We just defined the term depth. We can reiterate the definition as: Depth, as it relates to discrete price levels, is small, whole number that represents how many steps a certain price level is located beneath the top of the pyramid.

Therefore, each pyramid will have top as a level 0, then many lower discrete levels with depths 1, 2, 3, 4 … until bottom has been reached at depth n. Thus in discrete domain, we can say that pyramid has n discrete price levels or we need to go n steps in order to descend from top to the bottom of the pyramid.

Please observe the direction of depth as being opposite from price. As we move lower from the top of the pyramid, the price decreases but the depth of discrete price levels increases. For our example of discrete price levels, we can show corresponding depths with the following table:

Final observation can be made that while prices have unit of dollar, depth numbers are round numbers with no unit.

Article as a reference

I know this is probably overwhelming amount of definitions, statements and relationships for one article. However, I want you to have all these in one place so you can easily refer back to this article and find the meaning of terms we are going to use. Once you get a little more familiar with these terms, I am sure you will find them logical and self-explanatory.

Assumption is “going long”

At the end of this article I would like to mention one very important assumption: all the term definitions and related statements and conclusions hold true for the case of usual investing practice where investor purchases certain investment vehicle in order to profit from it when its price increases. In investing jargon this is called “going long”.

Won’t consider “shorting” unless explicitly stated

There is also opposite practice from going long in which investor borrows certain investment vehicle in order to profit from it when its price declines. This is called “going short” or “shorting”. Shorting is not that common among amateur investors and investor’s account needs certain provisions in order to allow investor to borrow or short anything. This is one of the reasons we are NOT going to assume shorting unless we explicitly state so. Since shorting is opposite from going long, it also means that we would need to invert the logic for our terms and conclusions. That would probably confuse many of you thus it is another reason NOT to consider shorting and keep it clean and simple.