I am continuing and expanding my so-far line of thinking and writing, into something both more scientific and more educational (we are still in full distance learning mode, at the university). I want to develop on that simple model I have recently presented in the update entitled ‘Acceptably dumb proof. The method of mean-reversion’. I am going to develop and generalize on its cognitive and behavioural implications. By the way, I have just used it (it is April 10th, 15:40 p.m.) to buy a bit into Asseco Business Solutions and to open a position on a company active in stem cells: PBKM. I spotted a moment, when their mean-reversed stock price was passing the 0 point and going up. According to this method, there is very likely to be an upcoming spike, with an opportunity to sell at a profit.
Good. The behavioural context. When I trade in the stock market, with my own money, emotions grow strong. After a few years of pause in investing, I had actually forgotten how strong those emotions can unfold. The first thing which I already know this method has given me is emotional step-back, and the capacity to calm down. This is the mark of a good strategy: it is simple (this model of mine is really simple, as financial forecasts come), thus workable, and it gives that special sort of calm flexibility in decisions.
The capacity to step back from the emotions of the moment, to get some perspective, and make more informed decisions is based on one essential assumption: the distinction between the normal and the alarming. There is a state of things, which I accept as ‘normal’, when I just can do something, but I don’t need to. By opposition, I define a state of things-which-consist-in-me-experiencing-reality, where my perception urges me to take action.
This is about my perception of reality, right? In the stock market, reality is made of numbers, right? I mean, there is much more in trade, there are people, for example, yet the reality which I am most of all supposed to pay attention to is made of numbers: the stock prices. Prices change. This is their normal way of being in the stock market. By the way, some of you might think that stationary a price, in a security, is the best way of being for a long-term investment. Not really. When you try and do some trade, one day, you will see that durably stationary prices can frighten the s**t out of you. It is like a frozen reality: scary. When prices swing, their ebb and flow gives information. When they stop moving, there is no more information. You are in a dark room.
Good, to the numbers that make my reality in the stock market – prices – change constantly and they’d better keep changing. What I observe, thus, is change in prices rather than prices themselves. Mathematically, I observe the values of a function (stock prices), and the values of its derivatives (change in prices, and coefficients calculated thereupon). It is the old intuition of Isaac Newton: what we really perceive is change and difference rather than absolute states of reality.
I define two classes in all the possible types of change I observe in reality. Class #1, the relax-bro type, covers normal change and allows me to sit back and watch what happens next. I can do some action, if I really feel like, yet it is all up to me. Class #2, the c’mon-do-something one, jumps into being when change becomes somehow abnormal, like highly stimulating. There is normal change and abnormal change, then, and I want to define these two states of reality with the toolbox of mathematics. From there on, it is highly subjective. Mathematics provide many ways of defining what’s normal. In my model, I go for a classic: the normal distribution. The normal state of change, seen through the lens of normal distribution, is acceptable oscillation around the expected value of price. The expected value is arithmetical average of prices observed over a given period of time. Seen under this angle, the average price is something like an immediate projection of my past experience: I expect to see, here and now, something aligned with the states of reality I have experienced so far.
The ‘so far’ part is subjective. Do I expect the current change in prices to be somehow in line with what has been happening over the last year, over the last 3 years, or maybe just over the last week? You can see a glimpse of that choice when you go and check stock prices online, with a graph. Most online utilities give you the choice between snapshotting the current day, the last 2 weeks, the last month etc. People have different temporal frames of reference as for what is normal to them. In my personal model, the one I hinted at in ‘Acceptably dumb proof. The method of mean-reversion’, I set my frame of reference at the last month, or, to me more specific, at the last 30 trading days, which actually makes a little more than a calendar month.
Subjectivity is scalable and measurable. I am going to focus on two ramifications of this principle. Firstly, I can make typical change my unit of measurement. Secondly, I can shift between different time frames and see what kind of change it brings in terms of strategic behaviour. Before I walk down these two paths, I am reminding the general mathematical frame of what I am talking about (see picture below).
What happens, mathematically, when I follow the old Newtonian intuition of observing change rather than stationary states of nature? Logically, a given magnitude of change becomes my unit of measurement. In basic statistics, i.e. as long as we stay in the safe realm of Gaussian distributions, standard deviation, i.e. mean expected deviation from the mean expected average, can be such a Sevres-meter of my perception. Let’s keep in mind it is deep in our human perception: there are differences and variations large enough for us to notice, and the remaining part of all the chaos happening in that stuff we call reality passes essentially unnoticed to us.
When standard deviation becomes my gauge, and it serves me to assess whether anything is worth my attention, I can interestingly decompose the basic equation of mean-reversion, as residual difference between the actual value observed (price, in this case) and denominated in its own standard deviation, and the expected average value, denominated in the same way. In other words, mean-reversed price is the residual difference between the locally observed deviation from what I call ‘normal and expected’, and the general variability of what I observe (average divided by standard deviation).
There is a simply and technically useful aspect of that approach. When standard deviation becomes the unit of measurement, I can directly compare the actions I should take on many investment positions, when they are in very different price ranges. Let’s study it on two different cases in my portfolio: Airway Medix, and 11Bit. The former is market-priced at less than PLN 1 per share, the latter is currently around PLN 380. When I mean-reverse their prices, I drive them both to the same scale, like inside the interval -3 ≤ x < 3. The local magnitude of mean reversed prices is directly comparable between the two.
As I talk about comparisons, let’s compare these two – Airway Medix and 11Bit – in different time frames. My basic one is the last 30 trading days, but what if I look differently at time and change? What if I take a shorter view over the timeline, or a longer one? In tables below, I show four alternative temporal perspectives on those two stocks: last 30 days, 7 days, 14 days, and finally the past 6 months of trade.
|Mean-reversed price of Airway Medix|
|Trading day||Window 30 days||Window 7 days||Window 14 days||Window 6 months|
|Mean-reversed price of 11Bit|
|Trading day||Window 30 days||Window 7 days||Window 14 days||Window 6 months|
As I study the two tables above, my first question is: what do I actually see? What the differences between those numbers are actually informative about? Positive numbers tell me that the current price is sort of high as compared to the moving average, and negative say the opposite. As I look at the last days of trade before Easter, 11Bit appears as being kind of moderately positive in the 30-day view, and it means: rather hold than sell, unless you strike a really good deal. A timeframe of 7 days tells me more or less the same. When I set my timeframe at 14 days, it says: definitely look for a good sell, the price is abnormally high. Still, when I take a really long step back and look at the whole thing from the perspective of a 6-month temporal horizon, it says: ‘no, you dumb f**k, don’ even think about selling; if you feel the urge to do something, go and buy some of these’.
You can see empirically that my subjective perception of what is a long time, as opposed to what is just a moment impinges directly on the strategy I am supposed to adopt. It is a deep, general principle of human action. Farmers look at life differently from stock market brokers: their time frames differ.
What if I apply the same logic, i.e. the logic of mean-reversion, to volumes traded, instead of prices? What the mean-reversed volume is informative about? Let’s see. Here below, you can see comparative graphs of Airway Medix with, respectively, stock price and volumes traded daily, both mean-reversed over a window of the last 30 days of trade. You can see that volumes swing much more frequently than prices. It is as if they were two musical tunes: volumes modulated at a faster pace, and prices going at a slower one. Familiar? No? It is rock’n roll. Fast + slower = compound rhythm. The rhythm of life.
How can I generalize into any market? You can go and watch my tutorial in economics, the one about prices and quantities. It connects interestingly: https://youtu.be/S9dkez3BEWw .