Depth of basic oscillation is one step
Earlier in this category, we introduced Basic Price Oscillation and defined exact actions that are to be performed along the price path. Price change that corresponds to the basic price oscillation spans exactly one price step. In other words, price starts from one discreet price level and falls one step lower to the next adjacent discreet level before it rises up again. We can say that price moves one step into the depth. While performing this oscillation, price never falls more than one step and thus the oscillation is considered basic.
Depth of deeper oscillation is two steps or more
Although basic price oscillation happens quite often in reality, it is only a special case of a deeper price oscillation where price experiences larger swing that spans two or more steps. Price drops deeper than within the basic price oscillation and moves two or more steps into the depth.
Please note that since price and the way it moves is out of our control, we can obtain the equivalent result by reducing the step size of the pyramid. Therefore, the same absolute price move can span more than one step if the step is smaller. Thus for the same price swing, instead of basic price oscillation, we may be acting according to deeper price oscillation.
Interesting fact about deeper price oscillation is that the rules of pyramidal trades kick in. Since price moves at least two steps in depth, then at least two buy trades occur. Similarly, at least two sell trades occur as the price moves back up. I would like to point out that we still haven’t defined the term offset and thus we have equal number of buy and sell trades for a given symmetrical price oscillation. When we introduce offset in selling, levels at which sells occur will shift accordingly.
Since there are two or more trades in each direction, they have certain relationship. Naturally, the relationship is pyramidal. Pyramidal trades imply ever increasing buy amounts as the price drops lower and ever increasing sell amounts as the price rises higher. An example of deeper price oscillation that spans four steps is shown in Figure 1.
Fig 1. Deeper Price Oscillation
We can observe that blue rectangle widths increase as we buy into larger weakness and red rectangle widths increase as we sell into larger strength. But, let’s break apart deeper price oscillation and look closer at each portion thereof.
Downward price movement (buying)
We have already mentioned earlier that in Pyramid Investing we exclusively buy price weakness. Considering the price is at the top when oscillation begins (depth = 0), price expresses ever larger weakness with each new discreet price level reached on the way down. The idea is to buy into weakness. Also as the price tanks, the size of price weakness relative to the top is getting larger. The larger the price weakness, the larger our commitment to buy the underlying stock. Buying weakness is always difficult and feeling of fear is usually in our way. However, buying weakness is the most proper action we can do. Courage of buying weakness is always handsomely rewarded.
Fig. 2. Downward price movement - Price decline
Figure 2 shows the down slope of deeper price oscillation. Blue rectangles represent buy trades. Width of each blue rectangle represents the amount of shares bought at corresponding discreet price level. Number of additional shares bought at each depth is shown next to the rectangle. Of course, the numbers shown here are just as an example and the actual amounts bought get determined by particular pyramid in use. Also, larger font size is used for larger amounts to visually emphasize importance of pyramidal buys. Rectangles are framed into a pyramid for clearer distinction and easier shape discrimination.
Price bottoming and turning direction
At some point that is unknown to us, price bottoms and turns around. It then proceeds in an upward direction. Take a look at the Figure 3 and observe some important details related to the price bottoming.
Fig. 3. Price bottoming and turning direction
As the price was moving down, we already made our last buy. Soon after, price bottomed. Turning point is only slightly lower then the price of our last buy and certainly less lower than the step size. Otherwise we would have bought the next lower discreet price level. Since price turned around, that level was never reached. We can pretty much say that we bought the exact bottom, especially when our pyramid applies small step size.
Price turned around and quickly reached discreet price level of our last buy. An important rule can be reiterated here: Trade at certain price level disqualifies that price level at least until next trade occurs at some other price level. This may sound complicated but it only means no action is performed at the level we already made purchase at. On the other hand, if we would to sell at this level, it would only mean zero profit and incurred trade commissions, which of course doesn’t make any sense for us to do.
Therefore, we patiently wait for the price to move one step higher. Again, no offset is used and thus one step higher is all the move price needs to make before we make a sell. That is our first sell. Please note that the amount of first sell is significantly smaller than the amount of last buy.
Upward price movement (selling)
After the price bottomed, it began ascending. We have already mentioned earlier that in Pyramid Investing we exclusively sell price strength. Considering the price was at the bottom, price expresses ever larger strength with each new discreet price level reached on the way up. The idea is to sell into strength. Also as the price soars, the size of price strength relative to the bottom is getting larger. The larger the price strength, the larger our determination to sell the underlying stock. Selling strength is always difficult and feeling of greed is usually in our way. However, selling strength is an important professional action that we have to undertake.
Fig. 4. Upward price movement - Price ascent
Figure 4 shows the up slope of deeper price oscillation. Red rectangles represent sell trades. Width of each red rectangle represents the amount of shares sold at corresponding discreet price level. Number of additional shares sold at each level is shown next to the rectangle. Also, larger font size is used for larger amounts to visually emphasize importance of pyramidal sells. Rectangles are framed into a pyramid for clearer distinction and easier shape discrimination.
Symmetry
Taking a distant view of deeper price oscillation, we can observe certain symmetry between actions that occur along the downward and upward price moves. Take a look at Figure 5 and observe that buy and sell pyramids are exactly the same, except inverted (or flipped). Conclusion is: Only one pyramid is enough to determine both buying and selling.
Fig. 5. Symmetry of buy and sell pyramids
Vertical symmetry is a consequence of equidistant buys and sells as the price moves down and up. All buys and sells are exactly one step apart. Horizontal symmetry is a consequence of no intended accumulation of shares upon executed deeper price oscillation. In other words, if we add up all the amounts of shares purchased it is exactly the same as the amount of all shares sold. In our example, we buy 10+20+30+40=100 shares. Then we sell 10+20+30+40=100 shares. After completion of price oscillation, we are left with zero shares (and whole bunch of profits).
The approach of symmetry works perfectly in a sideways market. However, during trending markets we intentionally introduce asymmetry. We will address ways to create asymmetry in future articles. Profit considerations comprise topic for itself and that will be addressed in future articles as well.
Hourglass
Now, let’s broaden our Pyramid Investing terminology with some new terms. But before, let’s rearrange our buy and sell rectangles so they are center symmetrical. In addition, let’s move the sell pyramid on top of buy pyramid (see Figure 6). Now we lost the price association part, however the shape obtained resembles hourglass. Therefore, when we want to point out the nature of changing amounts of buys and sells as we trade in and out of certain stock, we tend to refer to hourglass. We even derived the verb “hourglassing” that stands for process of acquiring and disposing shares in an hourglass way.
Fig. 6. Hourglassing or Pyramiding
Take a look at the address bar in your web browser – you will see a little hourglass icon 
Another term that is equivalent to hourglassing is “pyramiding”. We tend to say: Pyramiding in and out of position. Pyramiding refers to buying and selling shares in a pyramidal way or following principles of Pyramid Investing.
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I might be getting ahead of things a little, but I would be interested in how you deal with volatility that triggers sells on some levels but not all and then heads back down.
For example, lets say we have 10 levels. Price weakness triggers our buy orders on 6 levels. Price strength then triggers sells on 3 levels, but then price weakness goes down through the same levels and further.
Do you rebuy at those levels you have already sold? And for how much?
It seems that these pyramids could get very complex on a wide ranging stock.
Thanks in advance.
Simon,
What you are referring to is called Dynamics of Pyramid Investing. At this time, dynamics hasn’t been discussed here yet. With a little help of some spreadsheets (I use Excel), it is possible to manage buy and sell orders quite successfully and not only for one but for many pyramids at the same time. I do it on a daily basis and I don’t find it difficult. There are certain rules that one needs to follow in order not to get lost though. Rules are logical and easy to implement. I plan on describing the whole process in detail so please bear with me as I put out related articles.
To follow up on your questions:
a) Price weakness triggered buy orders on depths 1 thru 6. Let’s assume you bought 10, 20, 30, 40, 50 and 60 shares respectively at each depth.
b) Price strength triggered sell orders on depths 5, 4 and 3. So you were selling in an hourglass way (assuming no offset):
- Depth 5, sell 10 shares
- Depth 4, sell 20 shares and
- Depth 3, sell 30 shares
c) Price weakness expresses itself again, so your buys look like this (again, no offset):
- Depth 4, buy 10 shares
- Depth 5, buy 20 shares
- Depth 6, buy 30 shares
Now comes the trick: b) and c) comprise one complete (inverted) oscillation. Therefore, associated buys and sells cancel each other out. At the end of c) you own the same amount of shares as you did at the end of a). Of course, you made profits during b). On a continued weakness, you basically proceed with a). So your further buys look like this:
- Depth 7, buy 70 shares
- Depth 8, buy 80 shares
- Depth 9, buy 90 shares…
Hopefully, this gives you glimpse into Pyramid Investing dynamics. Let me know if you have any other examples that may not be clear how to deal with.
Ok, I think I get it. As price strength takes us through Depth 3, we sell the allocated number of shares. We then only take further action when price goes through a different Depth, either 2 (sell again) or 4 (buy again). And if we buy again, we do so as if starting at the top of the pyramid.
In this way, we are always accumulating shares on price weakness and selling on strength, regardless of whether price trends or is rangebound. So it would be possible to trade our way out of a position, without price needing to make new highs, yes?
This was the bit that was troubling me initially, because there is no guarantee that price will regain it’s old highs and it seemed that you could end up with capital tied up for a very long time waiting for it to do so.
I am very impressed with your system and look forward to the next installment. I would be very interested in seeing your spreadsheet when you explain the Dynamics.
Thanks for the quick reply.
One way to look at Pyramid Investing is to see it as a number of bets:
When you sell something you previously bought, it means you won the bet. The profit realized is your reward for winning the bet. By selling, you actually bet at the same time that the price will fall. If it falls, your reward is that you didn’t lose anything since you haven’t been invested during that price drop.
There is a general truth that the lower the price, the higher the probability it is going to rise. In other words, the lower the price, the less chance it will drop further more. We exploit this fact by increasing our bets as the price goes down. Therefore, we buy in a pyramidal way. Similar holds for selling except the logic is inverted. But we also sell in a pyramidal way.
Capital you dedicate to Pyramid Investing is not only divided into number of different pyramids, each pyramid divides it further into number of chunks of different sizes. Since nobody knows where the price will go and we don’t even want to speculate on that topic, we simply place small chunks of our capital at different price levels. Each chunk is our bet.
By definition, we have many chunks and once we place a bet, we don’t touch it until it wins. Pyramid Investing is transparent to time. We win when the price reaches certain level. That may happen shortly after we placed the bet or many years later. It is important that whenever you place a bet with a certain chunk of money, you accept that it may take forever before it wins. I am sure you would be pleasantly surprised how many of your bets win quicker than expected. However some get stuck. If you are not comfortable with every single bet you place for it to get stuck, it means you are placing too big of a bets.
Therefore, you are not going to trade your way out of position before the top of the pyramid has been reached. If you think that is unlikely, you need to start lower. If you don’t want to involve any thinking, that is why you buy in a pyramidal way. Pyramids have many wonderful features and I will be discussing those in due course of time. There are ways to handle different stocks and markets. You can shape pyramids based on how bullish or bearish you are. You can be a successful player regardless of the market you are in.
I understand that it will take time for the pyramid to complete and you are right that the pyramid doesn’t complete until the top, as you never sell the last shares until the top.
What I meant (but didn’t explain very well) was trading yourself out of drawdown, rather than your position.
Say for example you have 20 Depths, you buy down through 15 of them. At the moment you are facing quite a big drawdown. Then price rises and falls but never goes higher than say Depth 5. You are not out of your position, but the more you buy and sell across the various lower depths, the lower your overall average price will become. So eventually you would show a profit without the pyramid ever completing.
In this way, pyramiding becomes relatively risk-free as long as you have the capital to cover all the depths and the time to allow volatility to bring down your average price.
The only risk is for the price to go to zero, or you run out of time.
I am very excited by what you have shown me, and am backtesting the basic principles that you have shown so far.
I appreciate that you are doing this for free and that it takes a lot of effort, but I have so many questions. Is there anywhere I can get more information, as I do not want to take up all your time with my questions?
Many thanks.
From your comments, I see you have advanced understanding of principles that are heavily utilized in Pyramid Investing. I appreciate your comments very much and I think everyone benefits from them. Feel free to ask questions thru my E-mail as well if those don’t seem to fit any of articles published at the time. I’ll take care that relevant content gets posted in blog’s Questions and Answers category.
Idea of Pyramid Investing is not new. However, I am not aware of any resource that explains into any great detail how to go about Pyramid Investing. I have myself meticulously developed every aspect of Pyramid Investing concept except the idea itself. I worked it out from scratch and now I have well-rounded package that I apply in my own account. I am proud of the concept and I am open to share every single detail about it through this blog. There is only one caveat – as a reader of this blog, you will need patience while I post articles at my own pace. Patience is a crucial trait of every serious pyramid investor so I don’t expect that to be a problem.
Trading yourself out of drawdown, as you put it, is an excellent observation and highly applicable to Pyramid Investing. Pyramid Investing makes profits thanks to volatility. At the same time, those profits reduce your position average cost. The objective is to reduce the average cost to zero, at which time you would be solely dealing with “market’s money”. Prolonged volatility around some lower level of your pyramid would eventually bring your average cost down to that level and you would be having no drawdown anymore. The amount of time needed for that to happen depends on frequency and magnitude of volatility as well as the depth the volatility occurs around. We have no control of any of these factors. However, proper pyramid shaping can increase profits and mitigate the wait.
I advocate applying exclusively pyramids that go to zero. At the moment you make your first pyramidal buy, you should have enough cash to cover the whole pyramid. That is the ultimate low risk approach you can take. Then you have peace of mind that no amount of weakness would come as a surprise. There is some price to be paid for such an approach on the reward side, but the whole point is to stay in the game regardless of price making possible or impossible moves.
Basing your pyramids on gold and certain commodities alleviates the risk of underlying vehicle going off the board. So you can robotically execute your pyramids thru any and all meltdowns with a smile on your face as opposed to being forced to liquidate in terror.
As far as backtesting, I have some rather primitive but very straightforward ways to show the profitability of pyramids for different scenarios. I think this is yet another great advantage of Pyramid Investing that it doesn’t require sophisticated algorithms executed on historical data to prove the viability of the concept, although such an approach certainly wouldn’t hurt especially for unbelieving Thomases.
Thanks again. I agree that the pyramid must go down to zero, although this does often mean that the bulk of your capital is on the sidelines.
I have been playing around with different widths of levels and would be interested in your thoughts on this.
You have talked already about how the width of the levels increases as you buy more shares per $ the further down the pyramid price goes. So let’s say I have $10k and 10 depths, then I invest 10% ($1k) at each level but get more shares each time.
But let’s say I use a different scale and invest a bigger proportion of my capital at each level, for example:
Depth 1 – 5%
Depth 2 – 5%
Depth 3 – 8%
Depth 4 – 8%
Depth 5 – 10%
Depth 6 – 10%
Depth 7 – 12%
Depth 8 – 12%
Depth 9 – 15%
Depth 10 – 15%
So this way the width of each level gets wider in both shares and dollar terms. When I test this, it brings much bigger profits, but only when price goes down to the lower levels. And of course there is no guarantee that this will happen.
I think this system would be better used in a bear market, as it limits the drawdown at the top of the pyramid and gets more capital invested at the bottom, which a bear market is likely to reach. But in a bull market, it is unlikely to go down more than 3-4 levels so it would be better to go with the original system of investing the same proportion of capital on each level (or perhaps scaling your capital the other way round?).
You did say that there were different ways to shape the pyramid depending on how bullish or bearish you are, so I will be interested to see how you have done that.
Your remark that caught my eye was: “…the bulk of your capital is on the sidelines”. I think this deserves some commenting on my part. This is exactly what differentiates consistent market winners from others – market winners ALWAYS have plenty of capital on the sidelines. They are prepared for every price weakness including those “impossible” ones. On the other hand, others who cannot control their greed tend to be fully invested based on their analyses and beliefs which get shattered and proved wrong more often than not. In the best case scenario, they fail to be buyers on significant weakness. In the worst case, they get liquidated at the bottom and wiped out from market arena. Pyramids tame your emotions and let you allocate capital in a professional manner. Success is achieved in great part because there IS bulk of the capital on the sidelines and not despite of it. Those who refuse to accept this fact play with the fire and consistently get burnt.
I think you are on the right track with your analysis. You are hitting some very important aspects of Pyramid Investing and your observations are correct.
Your focus is on the amount of dollars committed to certain price levels. Although, there is nothing wrong with that approach, for the sake of simplicity I focus on number of shares. As a consequence the analysis becomes linear and easy to discretize. Your approach involves dealing with exponential functions. Bottom line is that either approach is similarly profitable.
Major obstacle for most of us to properly act in the market is EXPECTATION of price movement (let alone some investor’s “knowledge”). It is very hard, but one needs to accept inability to know in what direction and how much price will move. After you accept you don’t really know anything about future price moves, you are ready to shape your pyramids properly. It is good idea to have differently shaped pyramids designed to capture different price moves. This helps balance your emotions and prevents you from acting irrationally in the market. Being bullish or bearish has little to do with the shape of pyramids – it has a lot to do with determining the top of the pyramids: bullish equals higher top, bearish equals lower top. Bottom is always at zero.
As far as the shape goes, it is determined by base and increment. Larger base and smaller increment makes more aggressive approach suitable for shallow oscillations. Smaller base and especially larger increment make conservative, long-term pyramids that are to capture large price swings. Those pyramids are very very profitable.
That is some good advice Sasa. I look forward to the next installment.
Thanks for your time so far.
Sasa, Thanks so much for your very useful system. I wish I had known about it years ago. Is this correct: I buy 100 shares of ? corp. @ $17. It goes to $15 and I buy 125 shares. It goes back to $17, I sell 100 shares. It goes to $19, I sell 125 shares and I am out, or it goes back to $15 and I buy 100 shares. Thanks for your help. rb
Your example is correct. However you need to understand the bigger picture and be prepared for all possibilities.
First, let’s analyze your pyramid. You can also see the line of my thinking during the process of shaping pyramids. All parameters can be inferred from the example you gave above, i.e.:
1) Top = $19
2) Step = $2
3) Base = 100sh
4) Increment = 25sh
5) Offset = 0
Top is $19, which is Depth = 0. First buy occurs at Depth =1 or $17. This is all fine.
Your Step is $2, which is little more than 10% of the Top. While theoretically there is nothing wrong with 10% Step, it is practically little large. Depending what you are trading, Step should be between 1% and 5%. 1% would correspond to stable and not much volatile instruments (bullion for example). 5% would correspond to very volatile stocks (gold juniors for example). Of course, there is no right or wrong step size. This is all eyeballing, and you normally develop a good feel after trading few different instruments over some time. Too large of a step makes very slow trading. It may be months between two trades. However, profits are great. You may miss a lot of small ups and downs. Depending on your temperament and desire not to be involved in the market very often, 10% step may be just fine.
Base of 100sh means you will trade $1,000 – $2,000 at a time. That is a decent chunk that may tolerate higher commissions. Commissions are realistic factor that usually prohibit profitable trading of very small chunks (let’s say $10 or less).
Increment of $25 is good (quarter of your Base). That makes for nice pyramid that is probably in the golden middle between aggressive skyscraper and a conservative, wide pyramid.
The article above doesn’t address Offset. Offset of zero is a school example. In real world, better efficiency is achieved with Offset of one or two. That means you delay selling and skip one or two steps. It also holds for subsequent delay in buying.
Very important thing that you need to understand is that price may NOT bottom at $15. You certainly don’t want to stop buying if price craters to $10 or $5. In other words, pay attention to the cost of your pyramid. In your case, it is $13,200 all the way to zero (actually $1). You need to have as much capital set aside in one way or another before you commit to trading this pyramid. That is the big picture. You don’t want to be guessing where the bottom may be. You have to be prepared for every possibility. That includes the possibility of losing all your $13,200, should the stock goes bankrupt. At least the ultimate loss is limited.
Sasa, Thanks for your response. I understand the total potential cost of a pyramid, but didn’t realize that the steps should be up to 5%. That will help in further pyramid setups. The system makes one much more disciplined, taking emotion out of the equation. rb
Smaller step size means extracting profits from smaller price moves. That comes at the price of costlier pyramid and more dollars wasted on trading commissions. There is always an optimum and micro steps are not necessarily good. Smaller steps mean smaller trading chunks thus low commission becomes extremely important. You can also dedicate huge amount of capital so your trading chunks get to be significant even with small step size. However the point is to increase percentual return of the pyramid (measured against the total amount of capital dedicated) and not absolute dollar amount. Thus the practical optimum step size between 1% and 5%.