The moment of reassessment

MY EDITORIAL ON YOU TUBE

For a few days, I am turning into a different thread of my writing: my investment in the stock market. In winter, I decided to come back into the game of active investment in the stock market, and to use my blog as a tool of self-teaching, in the view of sharpening my game (see, for example: Fathom the outcomes and a few subsequent updates). Those of my readers who have been following this thread know that my basic strategy consists in investing in the stock market, every month, the rent I am collecting from an apartment in town. This is a monthly decision, and, whilst I appreciate a day of quick trade on short positions, every now and then, I generally like that slow, monthly paced cycle of investment.

My updates in this specific thread of thinking and writing have a triple function. Firstly, they make me think what I am doing, and by that virtue they help me sharpen myself as an investor. Secondly, this is educational material for my students, especially in Finance and in Economics. Thirdly, for all the other readers of this blog, it is shared experience, seasoned with some science and mathematical rigour.

The time of collecting another instalment of rent approaches, and I am bracing for a new set of decisions. This time, i.e. in this update, I strongly focus on summarizing my so-far experience, since the end of January. I follow the same principle that sport coaches do: if we want to be more efficient, we need to own our past experience, both our mistakes and our successes. I can tell you: it is hard. Like really. I have already past the point of devising my own analytical tools for financial investment (see for example Partial outcomes from individual tables), and, whilst I am aware of the immense wealth of human invention in this field, it is relatively easy. It is modelled. On the other hand, telling my own story, even a short and selective one, is hard in a different way. It requires taking a step back from my own actions, figuring out a rational way of comprehending them, collecting information and putting it all together. When I was doing it, I discovered that my own behaviour is much more difficult to study than the behaviour of other people in the stock market.

Long story short, I did it. I summarized my own story, in a form interpretable for coining up a strategy for the future. First of all, I summarize the journey, which you can see in Graph 1, below. Over the last 4 months, I invested a total of $3 519,42 in my two investment accounts: the domestic one, which I hold with the PeKaO Bank, for buying and selling stock in the Polish stock market, and the international one, which I hold with the Degiro platform. The details of that strictly financial cash flow are to find in Graph 2, further below. Interestingly, the biggest single cash transfer in this thread of my investment story is the transfer from international account to domestic account, in the first days of April. I described my dilemma of the moment in the update from April 5th, 2020, entitled ‘Which table do I want to play my game on?’. I was panicking about the huge slump in the U.S. stock market, and, in the same time, I was having an eye on the speculative bubble swelling on biotechs in the Polish stock market. The first important observation as for my strategy is therefore the following: my cash flows tend to be regular and systematic, unless I go emotional about the market and then I am able to make sudden twists and turns.

Graph 1

Graph 2

The whole chain of deals I made with the cash I paid in has led me, as for May 27th, 2020, to a capital account worth $4 335,79. Over 4 months, I have added $816.37, or 23.2%, to the cash invested, in a total of 36 deals, 10 of which remain open at the moment of writing those words (see Graph 6, much further below) and 26 are closed. My biggest gains are somehow paired with my biggest losses so far. I lost the most money in the U.S. stock market, when it was all just surfing down over the top of the collapsing wave of COVID-19-related panic. I made the most money on the mounting wave of short-term fascination with biotech businesses in the Polish market, right after. Three companies – Biomed Lublin, Airway Medix, and Mercator Medical – were my vessels to ride that wave. Graph 5, further below, shows the profits and losses I made on each of the 20 stocks, which I have been playing with in those 36 deals I opened. Graph 4 illustrates, in the form of a Pareto curve, the relative importance of the deals I opened by the end of March and the beginning of April. Right after the extraordinary, and, let’s face it, abnormal profits I made by riding crest of that speculative bubble, come the much more normal profits I made on Polish IT companies. The one named 11Bit, a gaming business, brought me the most profit as for now. On the whole, and at the condition of having a good look at the fundamentals, IT businesses seem to be a must in a sensible investment portfolio. Graph 6 shows the profit I am currently making on the open financial positions, with those IT guys, i.e. 11 Bit, Asseco Business Solutions, and Talex, clearly sticking out and up above the lot.   

Graph 3

Graph 4

Graph 5

Graph 6

As I observe the timeline of my cumulative profit (Graph 3), a pattern emerges. Up until the end of March, I had been losing money. I suppose it was the price to pay for learning: the price of my early mistakes. Starting from the beginning of April, my cumulative profit on all deals up to date began to poke its head above the zero line. I began making money: what I had paid for my mistakes started bringing fruit. Question: is it a once-and-for-ever pattern, i.e. have I simply paid my entrance ticket to the game and now I will just ride that wave? It is tempting to believe, and yet it is foolish to rely on. I would rather expect a recurring cycle, likely to take place in moments of turbulence. I need a few weeks (like 8?) to make some reconnaissance in the market around me, and then I can target a wave to ride.  

Interestingly, when I started making money, I also started to make sense of the whole process, in the form of analytical tools (see e.g. Acceptably dumb proof. The method of mean-reversion ). Did I start to make money because I developed more formal an understanding of market trends? It might have been exactly the other way around: I might have gone explicitly analytical as, intuitively, I felt I make money. I am serious. I know myself. I know that when I start thinking recurrently about something, to the point of writing consistently about it, those thoughts manifest something going on at a deeper, subconscious level. It is possible that my writing about mean-reversion in financial analysis was expressing the fact that I was getting acquainted with the really observable variance in stock prices.

I can formulate a tentative description of my own strategy as regards investment. This time, by strategy I mean recurrent behavioural patterns in me rather than a set of goals with a plan. First of all, I am strongly intuitive. It seems that what I consciously think I do is usually one step behind what I really do. Probably a lot of people are like that, and what is interesting is to see that pattern manifest in myself. I intuitively look for relatively short-term opportunities for quick gain, and I jump into the game as soon as I see them. I tend to jump a bit too quickly, though. As I study those 26 closed deals I made since January, sometimes I am like: ‘What? Really? I did THAT? Aston Martin? Virgin Galactic? Seriously? What the hell was I thinking?’.

Even with that propensity to uncontrolled fascination with the prospects of quick gain, I am clearly attached to some specific sectors in my investment. So far, it is IT industry, biotechnology and medicine, as well as renewable energy. I declared such a span of interest in the very beginning (see Back in the game) but, in all honesty, when I was making that declaration, by the end of January, I had no idea how consistent I was going to remain. Looks like I am pretty consistent in my sectoral scope of investment.  

Another pattern I noticed in myself is that I like dividing my portfolio in two categories: the no-brainers, on the one hand, and the waves to ride, on the other hand. I like holding some ETF trackers – this is what I mean by ‘no-brainers’ – sort of having someone else doing some of the thinking for me. Yet, I abhor the idea of investing all my money in one investment fund, and allow other people do to all the thinking for me. I want to stay somehow in the middle, i.e. to hold some balanced investments embodied in structured instruments, such as ETFs, and to do active thinking as for other deals.

Summing (provisionally) up, I make money when I acquire a good understanding of the market environment as for the possible occurrence of sudden slumps and sudden rises. I think it is time for me to develop such understanding now. I made some money on one financial wave (biotechs in Poland), and I want to repeat the experience. I want to spot interesting opportunities in a broader context. Intuitively, I feel that I am entering another phase of searching and learning, similar to the one observable in the left half of Graph 3. An intuition is burgeoning in my brain: the capital market is going into another phase. Why do I think so? Well, the last 4 months were mostly marked by the outbreak of the COVID-19 pandemic and by the resulting lockdowns in most economies. Now, lockdowns are being progressively loosened up and I think they are going to stay loosened up, whatever local, epidemic surges appear. Lockdowns are simply unsustainable on the long run: they are a softened, and overly extended transformation of military protocols applicable in the case of a biological attack. I remember those protocols from high school. I was born and raised in the communist Poland, and at the time, we were being indoctrinated that we are supposed to fight an ever-lasting war for peace. We would even crack jokes, like ‘we will keep fighting for peace even after there is nothing left to be at peace with’. Anyway, at school, we had classes called Preparation for National Defence. In the theoretical part, among other things, we would study the rules to follow in the case of attack with mass-destruction weapons, including bio-attacks. The rules I was being taught were to be played out over days, weeks at the worst, not over months. From a long-range perspective, lockdowns are like an attempt to regulate air traffic with fighter jet planes indicating the available flight corridors: theoretically feasible, maybe even spectacular, yet a tiny little bit unpractical.       

Anyway, lockdowns are becoming the past and the new present requires new business models, new markets, and new public policies. My gut feeling is that a lot is going to change in the coming months and years, technology-wise and business-wise. This is why I think I need to reassess the economic context of my investment in the stock market. I start with reassessing the prospects conveyed by my current portfolio of 10 open positions: 11 Bit Studios, Asseco Business Solutions, Talex, Airway Medix, PBKM, Bioton, SMA Solar, First Solar, Medtronic, and Amundi Asset Management. I want to understand the economic and financial alternative scenarios for this specific portfolio.

By my recent experience, I know that it is important to phrase out my intuitions, in order to utilise them fully. As Frank Knight would probably say, if he was still alive, ‘it is important to know how you think about what you think’. I need to understand what is it exactly that I cover with my intuition when I think about the economic context. In my previous analytical updates, I was very technical, in the sense that I was very much focused on short-term interpretation of stock prices (see for example: Partial outcomes from individual tables ). This time, I want to be more oriented on the long term, and therefore I focus on a different set of metrics. For 9 out of the ten investment positions I hold, I am following the same method (the Amundi ETF tracker is in the category ‘no brainer’).

I want to understand, most of all, what do those companies do with the trust expressed by investors. Are they investing in their future, or are they just riding the waves of capitalism? All those 9 companies have benefited from some amount of trust expressed actively by investors who have acquired and hold their shares. I want to understand how this trust has been used in the view of building a future, and therefore I am focusing on assets in those companies’ balance sheets. I am interested in their assets, because this is where I look for future-oriented decisions. If the given company has more assets than it had at the end of the last reporting period, it means, most of all, that the business is accumulating capital. They are investing into being able to make stuff in the future. Next, I want to know what kind of assets is the most variable in their balance sheets.

An insight into each company’s balance sheet allows me to compare changes observable at this level with their market capitalization, and with stock market indexes which I can take as the closest general context. I consider market indexes as a background, informative about general attitudes in investors. Then, I calculate a simple coefficient, that of elasticity, in those companies’ assets, when denominated over market capitalization, and over the market index I chose. Elasticity is calculated as, respectively: ‘∆(assets) / ∆ (market capitalization)’, and ‘∆(assets) / ∆(market index)’. I want to discover to what extent those companies respond, in their capital base, to the signals they receive from the stock market.

On the top of that I add a long-term analytical tool of the stock price strictly spoken. From the general formula of mean-reverted price (see We really don’t see small change), I extract the component of moving average price, calculated cumulatively over the last 12 months of trade, since May 27th, 2019. For every day of trade between May 27th, 2019 and May 26th, 2020, an average closing price is being calculated, for all the daily closing prices between May 27th 2019 and the given date. This form of moving average is probably one of the simplest forms of artificial intelligence. It is a function which learns a long-term trend as it advances in time, and it answers the question about the probable shape of long-term changes in this specific price, based on past experience.

The remaining part of this update is structured in two parts. At first, I bring up a written account of my observations, as I applied the above-described method to the 9 businesses in my portfolio. Then, a series of tables and graphs is provided, with the source numbers, to use at your pleasure and leisure as analytics. I used market indexes specific to the corresponding markets and sectors. As regards 11 Bit Studios, an IT and gaming company listed in the Warsaw Stock Market, I used three indexes: the WIG-GAMES Index, the WIG-INFO Index, and one more general, the WIG Tech index. The two other Polish IT firms, namely Asseco Business Solutions and Talex are being benchmarked against two of those three indexes, i.e. WIG Info, and WIG Tech. The three companies from the broadly spoken medical and biotech sector –  Airway Medix, PBKM, and Bioton – all three listed in the Warsaw Stock Exchange as well, have been benchmarked against the WIG Pharmaceuticals index. First Solar and Medtronic are both listed in the NASDAQ, and the closest index I can find is NASDAQ Industrial. Finally, the German company SMA Solar is compared with the DAX Performance metric.

As I run those analyses, a first observation pops out: Airway Medix has not published yet any financials for 2019. It is impossible to assess the current balance sheet of that company. I have just read they have postponed until mid-June 2020 the publication of ALL their financials for 2019. This is odd and makes me think of something like a ticking bomb. They must have the hell of a mess in their financials. For the moment, they show an interesting short-term trend in their price, and so I hold this position. Yet, I know I need to stay alert. Maybe I sell shortly.

Generally, like across all those 9 firms, I can notice an interesting pattern: when their assets change, it is almost exclusively about current assets, not the fixed ones. As for their state of possession in terms of productive assets, they all have been staying virtually at the same level over the last year. What changes is most of all cash and financial instruments, and in some cases inventories and receivables (Talex). They build up strategic flexibility without going, yet, into any specific avenue of technology. It looks as if all those businesses were poised, up to something. My own gut feeling, and the theory of business cycles by Joseph Alois Schumpeter, allow expecting a big and imminent technological change.      

Now, I am going to exemplify the details of my approach with the 11 Bit Studios. It’s an IT, gaming business, and thus I connect it to three market indexes in the Warsaw Stock Exchange, namely the WIG-GAMES Index, the WIG-INFO Index, and one more general, the WIG Tech index. In Table 1, below, you can see a quick, half-fundamental and half-technical study of 11BIT Studios. Its market capitalisation had shrunk, between the end of 2Q2019 and 1Q2020, yet, currently, its stock price has been growing nicely those last weeks.

Why is that? Let’s look.  The coefficient of market-to-book, i.e. market capitalization divided by the book value of assets, had been decreasing consistently, from the really unsustainable level of 7,17 down to the touch-and-go level of 4,81. It had happened both by a downwards correction in market capitalization (investors collectively said: ‘it is too expensive’), and by ramping up the company’s assets. As I can read in the company’s quarterly reports, the financial strategy they seem to be pursuing, and which manifests in the value of their assets, consists in keeping a baseline reserve of cash around PLN 3 ÷ 3,5 mln, which they periodically pump up to somewhere between PLN 5 million and PLN 6 million, and right after ‘Boom!’, their fixed assets get a pump. It is a sequence I know from observing many tech companies. Over the last few years, tech companies started to behave like banks: they accumulate substantial piles of cash, probably to have flexibility in their investment decisions, and then, suddenly, they acquire some significant, productive assets.

All that development takes place in the context of a capricious market indexes. Yes, they are growing, but the price of growth is increased volatility. The more they grow, the more variance they display. To the extent that anyone can talk about behaviour of a company vis a vis its investors, 11BIT Studios seems to be actively demonstrating that no, they are not an artificially inflated financial balloon, and yes, they intend to invest in future.

Now, you can go to the graphs and tables below.

Table 1 – 11 BIT Studios, selected financial data

30/06/201930/09/201931/12/201930/03/2020
Market cap (PLN mln)908,02902,30914,88823,39
Assets (PLN mln)126,62138,76155,67171,25
Equity (pln mln)100,42106,07119,74136,27
Market cap to assets7,176,505,884,81
WIG Games index18,3418,4518,5515,67
WIG Info Index2 396,242 387,552 834,292 619,12
WIG Tech Index9 965,259 615,8110 898,6610 358,61
Elasticity of assets to market cap(2,12)1,34(0,17)
Elasticity of assets to WIG Games Index110,36169,10(5,41)
Elasticity of assets to WIG Info Index(1,40)0,04(0,07)
Elasticity of assets to WIG Tech index(0,03)0,01(0,03)

Table 2 – Asseco Business Solutions, selected financial data

30/06/201930/09/201931/12/201930/03/2020
Market cap (PLN mln)935,71915,66949,081 035,96
Assets (PLN mln)384,11391,12422,64433,87
Equity (pln mln)272,74288,43316,11331,62
Market cap to assets2,442,342,252,39
WIG Info Index2 396,242 387,552 834,292 619,12
WIG Tech Index9 965,259 615,8110 898,6610 358,61
Elasticity of assets to market cap(0,35)0,940,13
Elasticity of assets to WIG Info Index(0,81)0,07(0,05)
Elasticity of assets to WIG Tech index(0,02)0,02(0,02)

Table 3 – Talex, selected financial data

2020/3M2019/YE2019/9M2019/6M
Market cap (PLN mln)              31,80               38,85               40,80               41,10 
Assets (PLN mln)              81,06               83,34               78,79               81,69 
Equity (pln mln)              54,89               54,59               50,82               51,37 
Market cap to assets                 0,39                  0,47                  0,52                  0,50 
WIG Info Index       2 396,24        2 387,55        2 834,29        2 619,12 
WIG Tech Index       9 965,25        9 615,81     10 898,66     10 358,61 
Elasticity of assets to market cap                 0,32                (2,33)                 9,66 
Elasticity of assets to WIG Info Index               (0,26)               (0,01)               (0,01)
Elasticity of assets to WIG Tech index               (0,01)               (0,00)               (0,01)

Table 4 – Bioton

2020/3M2019/YE2019/9M2019/6M
Market cap (PLN mln)281,63326,28364,06355,48
Assets (PLN mln)890,60881,42914,18907,17
Equity (pln mln)587,84582,00621,10626,59
Market cap to assets0,320,370,400,39
WIG Pharma index3 432,335 197,435 345,735 410,86
Elasticity of assets to market cap(0,21)0,870,82
Elasticity of assets to WIG Pharma index(0,01)0,22(0,11)

Table 5 – PBKM, selected financial data

2020/3M2019/YE2019/9M2019/6M
Market cap (PLN mln)543,06355,68352,27375,00
Assets (PLN mln)n.a.455,59427,00425,20
Equity (pln mln)n.a.188,39181,36179,54
Market cap to assetsn.a.0,780,820,88
WIG Pharma indexn.a.5 197,435 345,735 410,86
Elasticity of assets to market capn.a.8,39(0,08)
Elasticity of assets to WG Pharma indexn.a.(0,19)(0,03)

Table 6 – First Solar

2020/3M2019/YE2019/9M2019/6M
Market cap ($ mln)3 819,015 926,566 143,676 955,98
Assets ($ mln)6 949,147 515,697 054,697 137,81
Equity ($ mln)5 168,625 096,775 182,485 135,12
Market cap to assets0,550,790,870,97
NASDAQ Industrial Index5 785,706 807,706 371,606 559,20
Elasticity of assets to market cap0,27(2,12)0,10
Elasticity of assets to NASDAQ Industrial0,551,060,44

Table 7 – Medtronic

2020/3M2019/YE2019/9M2019/6M
Market cap ($ mln)120 856,18152 041,85145 568,85130 518,78
Assets ($ mln)91 053,0091 268,0089 694,0088 730,00
Equity ($ mln)50 719,0050 497,0050 212,0049 941,00
Market cap to assets1,331,671,621,47
NASDAQ Industrial Index5 785,706 807,706 371,606 559,20
Elasticity of assets to market cap0,010,240,06
Elasticity of assets to NASDAQ Industrial0,213,61(5,14)

Table 8 – SMA Solar

2020/3M2019/YE2019/9M2019/6M
Market cap (€ mln)954,251 199,23902,89887,63
Assets (€ mln)1 031,471 107,321 014,86970,56
Equity (€ mln)415,35416,89411,39406,72
Market cap to assets0,931,080,890,91
DAX Performance Index9 935,8413 249,0112 428,0812 398,80
Elasticity of assets to market cap0,310,312,90
Elasticity of assets to DAX Performance0,020,111,51

Discover Social Sciences is a scientific blog, which I, Krzysztof Wasniewski, individually write and manage. If you enjoy the content I create, you can choose to support my work, with a symbolic $1, or whatever other amount you please, via MY PAYPAL ACCOUNT.  What you will contribute to will be almost exactly what you can read now. I have been blogging since 2017, and I think I have a pretty clearly rounded style.

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What is my take on these four: Bitcoin, Ethereum, Steem, and Golem?

My editorial on You Tube

I am (re)learning investment in the stock market, and I am connecting the two analytical dots I developed on in my recent updates: the method of mean-reversion, and the method of extrapolated return on investment. I know, connecting two dots is not really something I necessarily need my PhD in economics for. Still, practice makes the master. Besides, I want to produce some educational content for my students as regards cryptocurrencies. I have collected some data as regards that topic, and I think it would be interesting to pitch cryptocurrencies against corporate stock, as financial assets, just to show similarities and differences.

As I return to the topic of cryptocurrencies, I am returning to a concept which I have been sniffing around for a long time, essentially since I started blogging via Discover Social Sciences: the concept of complex financial instruments, possibly combining future contracts on a virtual currency, possibly a cryptocurrency, which could boost investment in new technologies.

Finally, I keep returning to the big theoretical question I have been working on for many months now: to what extent and how can artificial intelligence be used to represent the working of collective intelligence in human societies? I have that intuition that financial markets are very largely a tool for tacit coordination in human societies, and I feel that studying financial markets allows understanding how that tacit coordination occurs.

All in all, I am focusing on current developments in the market of cryptocurrencies. I take on four of them: Bitcoin, Ethereum, Steem, and Golem. Here, one educational digression, and I am mostly addressing students: tap into diversity. When you do empirical research, use diversity as a tool, don’t run away from it. You can have the illusion that yielding to the momentary temptation of reducing the scope of observation will make that observation easier. Well, not quite. We, humans, we observe gradients (i.e. cross-categorial differences and change over time) rather than absolute stationary states. No wonder, we descend from hunters-gatherers. Our ancestors had that acute intuition that when you are not really good at spotting and hitting targets which move fast, you have to eat targets that move slowly. Anyway, take my word on it: it will be always easier for you to draw conclusions from comparative observation of a few distinct cases than from observing just one. This is simply how our mind works.

The four cryptocurrencies I chose to observe – Bitcoin, Ethereum, Steem, and Golem – represent different applications of the same root philosophy descending from Satoshi Nakamoto, and they stay in different weight classes, so to say. As for that latter distinction, you can make yourself an idea by glancing at the table below:

Table 1

CryptocurrencyMarket capitalization in USD, as of April 26th, 2019Market capitalization in USD, as of April 26th, 2020Exchange rate against USD, as of April 26th, 2020
Bitcoin (https://bitcoin.org/en/ )93 086 156 556140 903 867 573$7 679,87 
Ethereum (https://ethereum.org/ )16 768 575 99821 839 976 557$197,32 
Steem (https://steem.com/ )111 497 45268 582 369$0,184049
Golem (https://golem.network/)72 130 69441 302 784$0,042144

Before we go further, a resource for you, my readers: all the calculations and source data I used for this update, accessible in an Excel file, UNDER THIS LINK.

As for the distinctive applications, Bitcoin and Ethereum are essentially pure money, i.e. pure financial instruments. Holding Bitcoins or Ethers allows financial liquidity, and the build-up of speculative financial positions. Steem is the cryptocurrency of the creative platform bearing the same name: it serves to pay creators of content, who publish with that platform, to collect exchangeable tokens, the steems. Golem is still different a take on encrypting currency: it serves to trade computational power. You connect your computer (usually server-sized, although you can go lightweight) to the Golem network, and you make a certain amount of your local computational power available to other users of the network. In exchange of that allowance, you receive Golems, which you can use to pay for other users’ computational power when you need some. Golems are a financial instrument serving to balance deficits and surpluses in a complex network of nested, local capacities. Mind you, the same contractual patterns can be applied to balancing any type of capacities, not just computational. You can use it for electric power, hospital beds etc. – anything that is provided by locally nested fixed assets in the presence of varying demand.

Thus, below we go further, a reminder: Bitcoins and Ethers pure money, Steem Payment for Work, Golems Payment for Access to Fixed Assets. A financial market made of those four cryptocurrencies represents something like an economy in miniature: we have the labour market, the market of productive assets, and we have a monetary system. In terms of size (see the table above), this economy is largely and increasingly dominated by money, with labour and productive assets manifesting themselves in small and decreasing quantities. Compared to a living organism, it would be a monstrous shot of hormones spreading inside a tiny physical body, i.e. something like a weasel.

In the following part of this update, I will be referring to the method of mean-reversion, and to that of extrapolated rate of return. I am giving, below, simplified summaries of both, and I invite those among my readers who want to have more details to my earlier updates. More specifically, as regards the method of mean-reversion, you can read: Acceptably dumb proof. The method of mean-reversion , as well as Fast + slower = compound rhythm, the rhythm of life. As for the method of extrapolated rate of return, you can refer to: Partial outcomes from individual tables .

Now, the short version. Mean-reversion, such as I use it now for financial analysis, means that I measure each daily closing price, in the financial market, and each daily volume of trade, as the difference between the actual price (volume), and the moving cumulative average thereof, and then I divide the residual difference by the cumulative moving standard deviation. I take a window in time, which, in what follows, is 1 year, from April 26th, 2019, through April 26th, 2020. For each consecutive day of that timeframe, I calculate the average price, and the average volume, starting from day 1, i.e. from April 26th, 2019. I do the same for standard deviation, i.e. with each consecutive day, I count standard deviation in price and standard deviation in volume, since April 26th, 2019.

Long story short, it goes like…

May 10th, 2019 Average (April 26th, 2019 –> May 10th, 2019), same for standard deviation

May 20th, 2019 Average (April 26th, 2019 –> May 20th, 2019), same for standard deviation

… etc.

Mean-reversion allows comparing trends in pricing and volumes for financial instruments operating at very different magnitudes thereof. As you could see from the introductory table, those 4 cryptocurrencies really operate at different levels of pricing and volumes traded. Direct comparison is possible, because I standardize each variable (price or volume) with its own average value and its own standard deviation.

The method of extrapolated return is a strongly reductionist prediction of future return on investment, where I assume that financial markets are essentially cyclical, and my future return is most likely to be an extrapolation of the past returns. I take the same window in time, i.e. from April 26th, 2019, through April 26th, 2020. I assume that I bought the given coin (i.e. one of the four studied here) on the last day, i.e. on April 26th, 2020. For each daily closing price, I go: [Price(Day t) – Price(April 26th. 2020)] / Price(April 26th. 2020). In other words, each daily closing price is considered as if it was bound to happen again in the year to come, i.e. from April 26th, 2020 to April 26th, 2021. Over the period, April 26th, 2019 – April 26th, 2020, I count the days when the closing price was higher than that of April 26th, 2020. The number of those ‘positive’ days, divided by the total of 366 trading days (they don’t stop trading on weekends, in the cryptocurrencies business), gives me the probability that I can get positive return on investment in the year to come. In other words, I calculate a very simple, past experience-based probability that buying the given coin on April 26th, 2020 will give me any profit at all over the next 366 trading days.

I start presenting the results of that analysis with the Bitcoin, the big, fat, patient-zero beast in the world of cryptocurrencies. In the graph below, you can see the basic logic of extrapolated return on investment, which, in the case of Bitcoin, yields a 69,7% probability of positive return in the year to come.

In the next graph, you can see the representation of mean-reverted prices and quantities traded, in the Bitcoin market. What is particularly interesting here is the shape of the curve informative about mean-reverted volume. What we can see here is consistent activity. That curve looks a bit like the inside of an alligator’s mouth: a regular dentition made of relatively evenly spaced spikes. This is a behavioural piece of data. It says that the price of Bitcoin is shaped by regular, consistent trade, all year long. This is like a busy market place, and busy market places usually yield a consistent equilibrium price. 

The next in line is Ethereum. As you can see in the next graph, below, the method of extrapolated return yields a probability of any positive return whatsoever, for the year to come, around 36,9%. Not only is that probability lower than the one calculated for the Bitcoin, but also the story told by the graph is different. Partial moral of the fairy tale: cryptocurrencies differ in their ways. Talking about ‘investing in cryptocurrencies’ in general is like talking about investing in the stock market: these are very broad categories. Still, of you pitch those probabilities for the Bitcoin and for the Ethereum against what can be expected in the stock market (see to: Partial outcomes from individual tables), cryptocurrencies look really interesting.

The next graph, further below, representing mean-reversion in price and volume of Ethereum, tells a story similar to that of the Bitcoin, yet just similar. As strange as it seems, the COVID crisis, since January 2020, seems to have brought a new breeze into that house. There had been a sudden spike in activity (volumes traded) in the beginning of 2020, and that spike in activity led to a slump in price. It is a bit as if a lot of investors suddenly went: ‘What? Those old Ethers in my portfolio? Still there? Unbelievable? I need to get rid of them. Jeeves! Please, be as kind and give those old Ethers to poor investors from the village.’. Another provisional lesson: spikes in activity, in any financial market, can lead both to appreciation of a financial instrument, and to its depreciation. This is why big corporations, and stockbrokers working for them, employ the services of market moderators, i.e. various financial underwriters who keep trading in the given stock, sort of back and forth, just to keep the thing liquid enough to make the price predictable. 

Now, we go into the world of niche cryptocurrencies: the Steem and the Golem. I present their four graphs (Extrapolated return *2, Mean-reversion *2) further below, and now a few general observations about those two. Their mean-reverted volumes are like nothing even remotely similar to the dentition of an alligator. An alligator like that couldn’t survive. Both present something like a series of earthquakes, of growing magnitudes, with the greatest spike in activity in the beginning of 2020. Interesting: it looks as if the COVID crisis had suddenly changed something for these two. When combined with the graphs of extrapolated return, mean-reverted prices and quantities tell us a story of two cryptocurrencies which, back in the day, attracted a lot of attention, and started to have sort of a career, but then it all went flat, and even negative. This is the difference between something that aspires to be money (Steem, Golem), and something that really is money (Bitcoin, Ethereum). The difference is in the predictably speculative patterns of behaviour in market participants. John Maynard Keynes used to stress the fact that real money has always two functions: it serves as a means of payment, and it is being used as a speculative asset to save for later. Without the latter part, i.e. without the propensity to save substantial balances for later, a wannabe money has no chance to become real money.   

Now, I am trying to sharpen my thinking in terms of practical investment. Supposing that I invest in cryptocurrencies (which I do not do yet, although I am thinking about it), what is my take on these four: Bitcoin, Ethereum, Steem, and Golem? Which one should I choose, or how should I mix them in my investment portfolio?

The Bitcoin seems to be the most attractive as investment, on the whole. Still, it is so expensive that I would essentially have to sell out all the stock I have now, just in order to buy even a small number of Bitcoins. The remaining three – Ethereum, Steem and Golem – fall into different categories. Ethereum is regular crypto-money, whilst Steem and Golem are niche currencies. In finance, it is a bit like in exploratory travel: if I want to go down a side road, I’d better be prepared for the unexpected. In the case of Steem and Golem, the unexpected consists in me not knowing how they play out as pure investment. To the extent of my knowledge, these two are working horses, i.e. they give liquidity to real markets of something: Steem in the sector of online creation, Golem in the market of networked computational power. Between those two, I know a bit about online creation (I am a blogger), and I can honestly admit I don’t know s**t about the market of networked computation. The sensible strategy for me would be to engage into the Steem platform as a creator, take my time to gain experience, see how those Steems play out in real life as a currency, and then try to build an investment position in them.

Thus, as regards investment strictly I would leave Steem and Golem aside and go for Ethereum. In terms of extrapolated rate of return, Ethereum offers me chances of positive outcomes comparable to what I can expect from the stock of PBKM, which I already hold, higher chances of positive return than other stock I hold now, and lower chances than, for example, the stock of First Solar or Medtronic (as for these considerations, you can consult Partial outcomes from individual tables ).   

OK, so let’s suppose I stay with the portfolio I already hold –11Bit, Airway Medix , Asseco Business Solutions, Bioton, Mercator Medical, PBKM – and I consider diversifying into Ethereum, First Solar , and Medtronic. What can I expect? As I look at the graphs (once again, I invite you to have a look at Partial outcomes from individual tables ), Ethereum, Medtronic and First Solar offer pretty solid prospects in the sense that I don’t have to watch them every day. All the rest looks pretty wobbly: depending on how the whole market plays out, they can become good investments or bad ones. In order to become good investments, those remaining stocks would need to break their individual patterns expressed in the graphs of extrapolated return and engage into new types of market games.

I can see that with the investment portfolio I currently hold, I am exposed to a lot of risk resulting from price volatility, which, in turn, seems to be based on very uneven market activity (i.e. volumes traded) in those stocks. Their respective histories of mean-reverted volumes look very uneven. What I think I need now are investment positions with less risk and more solidity. Ethereum, First Solar , and Medtronic seem to be offering that, and yet I am still a bit wary about coming back (with my money) to the U.S. stock market. I wrapped up my investments there, like one month ago, because I had the impression that I cannot exactly understand the rules of the game. Still, the US dollar seems to be a good investment in itself. If I take my next portion of investment, scheduled for the next week, i.e. the rent I will collect, transferring it partly to the U.S. market and partly to the Ethereum platform will expose just some 15% of my overall portfolio to the kind of risks I don’t necessarily understand yet. In exchange, I would have additional gains from investing into the US dollar, and additional fun with investing into the Ethereum.

Good. When I started my investment games by the end of January, 2020 (see Back in the game), I had great plans and a lot of doubts. Since then, I received a few nasty punches into my financial face, and yet I think I am getting the hang of it. One month ago, I managed to surf nicely the crest of the speculative bubble on biotech companies in the Polish stock market (see A day of trade. Learning short positions), and, in the same time, I had to admit a short-term defeat in the U.S. stock market. I yielded to some panic, and it made me make some mistakes. Now, I know that panic manifests in me both as an urge to act immediately, and as an irrational passivity. Investment is the art of controlling my emotions, as I see.

All I all, I have built an investment portfolio which seems to be taking care of itself quite nicely, at least in short perspective (it has earnt $238 over the last two days, Monday and Tuesday), and I have coined up my first analytical tools, i.e. mean-reversion and extrapolation of returns. I have also learnt that analytical tools, in finance, serve precisely the purpose I just mentioned: self-control.

Partial outcomes from individual tables

My editorial on You Tube

It is time to return to my investment strategy, and to the gradual shaping thereof, which I undertook in the beginning of February, this year (see Back in the game). Every month, as I collect the rent from the apartment I own and rent out, downtown, I invest that rent in the stock market. The date of collecting the next one approaches (it is in 10 days from now), and it is time for me to sharpen myself again for the next step in investment.

By the same occasion, I want to go scientific, and I want to connect the dots between my own strategy, and my research on collective intelligence. The expression ‘shaping my own investment strategy’ comes in two shades. I can understand it as the process of defining what I want, for one, or, on the other hand, as describing, with a maximum of objectivity, what I actually do. That second approach to strategy, a behavioural one, is sort of a phantom I have been pursuing for more than 10 years now. The central idea is that before having goals, I have values, i.e. I pursue a certain category of valuable outcomes and I optimize my actions regarding those outcomes. This is an approach in the lines of ethics: I value certain things more than others. Once I learn how to orient my actions value-wise, I can set more precise goals on the scale of those values.

I have been using a simple neural network to represent that mechanism at the level of collective intelligence, and I now, I am trying to apply the same logic at the level of my own existence, and inside that existence I can phenomenologically delineate the portion called ‘investment strategy in the stock market’. I feel like one of those early inventors, in the 18th or 19th century, testing a new idea on myself. Fortunately, testing ideas on oneself is much safer than testing drugs or machines. That thing, at least, is not going to kill me, whatever the outcome of experimentation. Depends on the exact kind of idea, though.

What meaningful can I say about my behaviour? I feel like saying something meaningful, like a big fat bottom line under my experience. My current experience is similar to very nearly everybody else’s experience: the pandemic, the lockdown, and everything that goes with it. I noticed something interesting about myself in this situation. As I spend week after week at home, more and more frequently I tend to ask myself those existential questions, in the lines of: “What is my purpose in life?”.  The frame of mind that I experience in the background of those questions is precisely that of the needle in my personal compass swinging undecidedly. Of course, asking myself this type of questions is a good thing, from time to time, when I need to retriangulate my personal map in the surrounding territory of reality. Still, if I ask those questions more and more frequently, there is probably something changing in my interaction with reality, as if with the time passing under lockdown I were drifting further and further away from some kind of firm pegs delineating my personal path.

Here they are, then, two of my behavioural variables, apparently staying in mutually negative correlation: the lower the intensity of social stimulation (variable #1), the greater the propensity to cognitive social repositioning (variable #2). This is what monks and hermits do, essentially: they cut themselves from social stimulation, so as to get really serious about cognitive social repositioning. With any luck, if I go far enough down this path, I reposition myself socially quite deeply, i.e. I become convinced that other people have to pay my bills so as I can experience the state of unity with the Divine, but I can even become convinced that I really am in a state of unity with the Divine. Of course, the state of unity lasts only until I need to pay my bills by myself again.

Good. I need to reinstate some social stimulation in my life. I stimulate myself with numbers, which is typical for economists. I take my investment portfolio such as it is now, plus some interesting outliers, and I do what I have already done once, i.e. I am being mean in reverse, pardon, mean-reverting the prices, and I develop on this general idea. This time, I apply the general line of logic to a metric which is absolutely central to any investment: THE RATE OF RETURN ON INVESTMENT. The general formula thereof is: RR = [profit] / [investment]. I am going to use this general equation, together with very basic calculation of probability, in order to build a PREDICTION BASED ENTIRELY ON AN EXTRAPOLATION OF PAST EVENTS. This is a technique of making forecasts, where we make forecasts composed of two layers. The baseline layer is precisely made of extrapolated past, and it is modified with hypotheses as for what new can happen in the future.

The general formula for calculating any rate of return on investment is: RR = [profit] / [investment]. In the stock market, with a given number of shares held in portfolio, and assumed constant, both profit and investment can be reduced to prices only. Therefore, we modify the equation of return into: RR = [closing price – opening price] / [opening price]. We can consider any price observed in the market, for the given stock, as an instance of closing price bringing some kind of return on a constant opening price. In other words, the closing price of any given trading day can be considered as a case of positive or negative return on my opening price. This is a case of Ockham’s razor, thus quite reductionist an approach. I ask myself what the probability is – given the known facts from the past – that my investment position brings me any kind of positive return vs. the probability of having a negative one. I don’t even care how much positive gain could I have or how deep is a local loss. I am interested in just the probability, i.e. in the sheer frequency of occurrence as regards those two states of nature: gain or loss.

In the graph below, I am illustrating this method with the case of Bioton, one of the companies whose stock I currently hold in my portfolio. I chose a complex, line-bar graph, so as to show graphically the distinction between the incidence of loss (i.e. negative return) vs that of gain. My opening price is the one I paid for 600 shares of Bioton on April 6th, 2020, i.e. PLN 5,01 per share. I cover one year of trading history, thus 247 sessions. In that temporal framework, Bioton had 12 days when it went above my opening price, and, sadly enough, 235 sessions closed with a price below my opening. That gives me probabilities that play out as follows: P(positive return) = 12/247 = 4,9% and P(negative return) = 235/247 = 95,1%. Brutal and sobering, as I see it. The partial moral of the fairy tale is that should the past project itself perfectly in the future, this if all the stuff that happens is truly cyclical, I should wait patiently, yet vigilantly, to spot that narrow window in the reality of stock trade, when I can sell my Bioton with a positive return on investment.      

Now, I am going to tell a different story, the story of First Solar, a company which I used to have an investment position in. As I said, I used to, and I do not have any position anymore in that stock. I sold it in the beginning of April, when I was a bit scared of uncertainty in the U.S. stock market, and I saw a window of opportunity in the swelling speculative bubble on biotech companies in Poland. As I do not have any stock of First Solar, I do not have any real opening price. Still, I can play a game with myself, the game of ‘as if…’. I calculate my return as if I had bought First Solar last Friday, April 24th. I take the closing price from Friday, April 24th, 2020, and I put it in the same calculation as my opening price. The resulting story is being told in the graph below. This is mostly positive a story. In strictly mathematical terms, over the last year, there had been 222 sessions, out of a total of 247, when the price of First Solar went over the closing price of Friday, April 24th, 2020. That gives P(positive return) = 222/247 = 89,9%, whilst P(negative return) = 10,1%.

The provisional moral of this specific fairy tale is that with First Solar, I can sort of sleep in all tranquillity. Should the past project itself in the future, most of trading days is likely to close with a positive return on investment, had I opened on First Solar on Friday, April 24th, 2020.  

Now, I generalize this way of thinking over my entire current portfolio of investment positions, and I pitch what I have against what I could possibly have. I split the latter category in two subsets: the outliers I already have some experience with, i.e. the stock I used to hold in the past and sold it, accompanied by two companies I am just having an eye on: Medtronic (see Chitchatting about kings, wars and medical ventilators: project tutorial in Finance), and Tesla. Yes, that Tesla. I present the results in the table below. Linked names of companies in the first column of the table send to their respective ‘investor relations’ sites, whilst I placed other graphs of return, similar to the two already presented, under the links provided in the last column.      

Company (investment position)Probability of negative returnProbability of positive returnLink to the graph of return  
  My current portfolio
11BitP(negative) = 209/247 = 84,6%P(positive) = 15,4%11Bit: Graph of return  
Airway Medix (243 sessions)P(negative) = 173/243 = 71,2%P(positive) = 70/243 = 28,8%Airway Medix: Graph of return  
Asseco Business SolutionsP(negative) = 221/247 = 89,5%P(positive) = 10,5%Asseco Business Solutions: Graph of return  
BiotonP(negative) = 235/247 = 95,1%P(positive) = 12/247 = 4,9%Bioton: Graph of return  
Mercator MedicalP(negative) = 235/247 = 95,1%P(positive) = 12/247 = 4,9%Mercator: graph of return  
PBKMP(negative) = 138/243 = 56,8%P(positive) = 105/243 = 43,2%  PBKM: Graph of return
  Interesting outliers from the past
Biomaxima (218 sessions)P(negative) = 215/218 = 98,6%P(positive) = 3/218 = 1,4%Biomaxima: Graph of return  
Biomed LublinP(negative) = 239/246 = 97,2%P(positive) = 7/246 = 2,8%Biomed Lublin: graph of return  
OAT (Onco Arendi Therapeutics)P(negative) = 205/245 = 83,7%P(positive) = 40/245 = 16,3%OAT: Graph of return  
Incyte CorporationP(negative) = 251/251 = 100%P(positive) = 0/251 = 0%Incyte: Graph of return  
First SolarP(negative) = 10,1%P(positive) = 222/247 = 89,9%First Solar: Graph of return  
  Completely new interesting outliers
TeslaP(negative) = 226/251 = 90%P(positive) = 25/251 = 10%Tesla: Graph of return  
MedtronicP(negative) = 50/250 = 20%P(positive) = 200/250 = 80%  Medtronic: Graph of return

As I browse through that table, I can see that extrapolating the past return on investment, i.e. simulating the recurrence of some cycle in the stock market, sheds a completely new light on both the investment positions I have open now, and those I think about opening soon. Graphs of return, which you can see under those links in the last column on the right, in the table, tell very disparate stories. My current portfolio seems to be made mostly of companies, which the whole COVID-19 crisis has shaken from a really deep sleep. The virus played the role of that charming prince, who kisses the sleeping beauty and then the REAL story begins. This is something I sort of feel, in my fingertips, but I have hard times to phrase it out: the coronavirus story seems to have awoken some kind of deep undertow in business. Businesses which seemed half mummified suddenly come to life, whilst others suddenly plunge. This is Schumpeterian technological change, if anybody asked me.

In mathematical terms, what I have just done and presented reflects the very classical theory of probability, coming from Abraham de Moivre’s ‘The doctrine of chances: or, A method of calculating the probabilities of events in play’, published in 1756. This is probability used for playing games, when I assume that I know the rules thereof. Indeed, when I extrapolate the past and use that extrapolation as my basic piece of knowledge, I assume that past events have taught me everything I need to understand the present. I used exactly the same approach as Abraham De Moivre did. I assumed that each investment position I open is a distinct gambling table, where a singular game is being played. My overall outcome from investment is the sum total of partial outcomes from individual tables (see Which table do I want to play my game on?).   

Chitchatting about kings, wars and medical ventilators: project tutorial in Finance

My editorial on You Tube

I continue with educational stuff, so as to help my students with their graduation projects. This time, I take on finance, and on the projects that my students are to prepare in the curriculum of ‘Foundations of Finance’. The general substance of those projects consists in designing a financial instrument. I know that many students struggle already at the stage of reading that sentence with understanding: they don’t really grasp the concept of designing a financial instrument. Thus, I want to sort of briefly retake it from the beginning.

The first step in this cursory revision is to explain what I mean by ‘financial instrument’. Within the framework of that basic course of finance, I want my students to develop intellectual distinction between 5 essential types of financial instruments: equity-based securities, debt-based securities, bank-based currencies, virtual currencies (inclusive of cryptocurrencies), and insurance contracts. I am going to (re)explain the meaning of those terms. I focus on those basic types because they are what we, humans, simply do, and have been doing for centuries. Those types of financial instruments have been present in our culture for a long time, and, according to my own scientific views, they manifest collective intelligence in human societies: they are standardized parcels of information, able to provoke certain types of behaviour in some categories of recipients. In other words, those financial instruments work similarly to a hormone. Someone drops them in the middle of the (social) ocean. Someone else, completely unknown and unrelated picks them up, and their content changes the acquirer’s behaviour. 

When we talk about securities, both equity-based and debt-based, the general idea is that of securing claims, and then making those secured claims tradable. Look up the general definition of security, e.g. on Investopedia. If you want, in your project, to design a security, the starting point is to define the assets it gives claim on. Equity-based securities give direct, unconditional claims on the assets held by a business (or by any other type of social entity incorporated in a business-like way, with an explicit balance sheet), as well as conditional, indirect claims on the dividend paid out of future net income generated with those assets. Debt-based securities give direct, unconditional claim on the future cash flows, generated by the assets of the given business. The basic idea of tradable securities is that all those types of claims come with a risk, and the providers of capital can reduce their overall risk by slicing the capital they give into small tradable portions, each accompanied by a small portion of adjacent risk. Partitioning big risks and big claims into small parcels is the first mechanism of reducing risk. The possibility to trade those small parcels freely, i.e. to buy them, hold them for however long pleases, and then sell them, is the second risk-reducing device.

The entire concept of securities aims, precisely, at reducing financial risks connected to investing big amounts of capital into business structures, and thus at making that investment more attractive and easier. Historically, it literally has been working like that. Over centuries, whenever people with money were somehow reluctant to connect with people having bold ideas, securities usually solved the problem. You were a rich merchant, like in the 17th century-France, and your king asked you to lend him money for the next war he wanted to fight. You would answer: ‘Of course, my Lord, I would gladly provide you with the necessary financial means, yet I have a tiny little doubt. What if you lose that war, my Lord? Who’s going to pay me back?’. Such an answer could lead into two separate avenues: decapitation or securitization of debt. The former was somehow less interesting financially, but the latter was a real solution: you lend to the King, in exchange he hands you his royal bonds (debt-based securities), and you can further sell those bonds to whoever is interested in betting on the results of war.      

Thus, start with a simple business concept, e.g. something of current interest, such as a factory of medical ventilators. You have a capital base, i.e. some assets, and you finance them with equity and liabilities. Classical. You can skip the business planning part by going to the investors relations site of any company you know, taking their last financial report and simply simulating a situation when those guys want to increase their capital base, i.e. add to their assets. I mentioned medical ventilators, so you could go and check Medtronic’s investors relations site (http://investorrelations.medtronic.com/ ), and pick their latest quarterly financials. They have assets worth $92 822 mln, financed with $51 953 mln in equity and $40 869 in debt. Imagine they see big business looming on the horizon, and they want to accumulate $10 000 mln more in assets. They can do it either through additional borrowing, or through the issuance of new shares in the stock market.

You can go through the reports of Medtronic as well as through their corporate governance rules, and start by taking your own stance at the basic question: if Medtronic intends to accrue their assets by $10 000 mln, would you advise them to collect that capital by equity, or by debt, or maybe to split it somehow between the two. Try to justify your answer in a meaningful way.

If you go for equity-based securities (shares in equity), keep asking questions such as: what should be the nominal value (AKA face value) of those shares? How does it compare with the nominal value of shares already outstanding with this company? What dividend can shareholders expect, based on past experience? How are those new shares expected to behave in the stock market, once again based on the past experience?

If your choice is to bring capital through the issuance of debt-based securities, go for answering the following: what should be the interest rate on those corporate bonds? What should be their maturity time (i.e. for how long should they stay in the market of debt before Medtronic buys them back)? Should they be convertible into something else, like in the shares in equity, or in some next generation of bonds? Once again, try to answer those questions as if I were just a moderately educated hominid, i.e. as if I needed to have things explained simply, step by step.

See? Chitchatting, talking about kings, wars and medical ventilators, we have already covered the basics of preparing a project on equity-based securities, as well as on the debt-based ones.

If you want to go somehow further down those two avenues, you can check two of my blog updates from the last academic year: Finding the right spot in that flow: educational about equity-based securities , and  Unconditional claim, remember? Educational about debt-based securities.

Now, we talk about money, i.e. about a hypothetical situation when my students design a new currency in the framework of their project. Money is strange, to the extent that technically it should not have any intrinsic value of itself, as a pure means of exchange, and yet any currency can be deemed mature and established once its users start hoarding it a little bit, thus when they start associating with it some sort of intrinsic value. Presently, with the development of cryptocurrencies, we distinguish them from bank-based or central-unit-based currencies. In what follows immediately, I am focusing on the latter category, before passing to the former.

So, what is a bank-based currency, AKA central-unit-based currency? A financial institution, e.g. a bank, issues a certain number of monetary units (AKA monetary titles), which are basically used just as a means of exchange. The bank guarantees the nominal value of that currency, which, in itself, does not embody any claim on anything. This is an important difference between money and securities: securities secure claims, money doesn’t. Money just assures liquidity, understood as the capacity to enter into exchange transactions.   

When designing a new currency, step #1 consists in identifying a market with liquidity problems, e.g. we have 5 developing countries, which do business with each other: they trade goods and services, business entities from each of those countries invest in the remaining four etc. Those 5 countries have closed or semi-closed monetary systems, i.e. their national currencies either are not exchangeable at all against any other currency, or there are severe limitations on such exchange (e.g. you need a special authorization from some government agency). Why do those countries have closed monetary systems? Because their governments are afraid that if they make it open, thus when they allow free exchange against foreign currencies, the actual exchange rate will be so volatile, and so prone to speculative attacks (yes, there are bloody big sharks in those international financial waters) that the domestic financial system will be direly destabilized. Why any national currency should be so drastically volatile? It happens when this currency is not really exchanged a lot against other currencies, i.e. when exchange is sort of occasional and happens in really big bundles. There is not enough accumulated transactional experience. Long story short, we have national currencies which are closed because of the possible volatility and are so prone to volatility because they are closed systems. Yes, I know it sounds stupid. Yet, once you see that mechanism at work, you immediately understand. In the communist Poland, we had a closed monetary system, with our national currency, the zloty, technically being not exchangeable at all against anything else. As a result, whenever such exchange actually took place, e.g. against the US dollar, you needed to be a wizard, or a prime minister, to predict more or less accurately the applicable exchange rate.

Those 5 countries have two options. For one, they can use a third-country, strong currency as a local means of exchange, i.e. their governments, and their national business entities can agree that whenever they do business transnationally, they use a reference currency to settle their mutual obligations. The second option consists in creating an international currency, specifically designed for settling business accounts between those countries. This is how the ECU, the grandpa of the euro, was born, back in the day. The ECU was a business currency – you couldn’t have it in your wallet, you just could settle your international accounts with it – and then, as banks got used to it, the ECU progressively morphed into the euro. What you need for such a currency is a financial institution, or a contractually established network thereof, who guarantee the nominal value of that business currency.

If our 5 countries go for the second option, the financial institution(s) who step in as guarantors if the newly established currency need to bring to the table something more than just mutual trust. They need to assign, in their balance sheets, specific financial assets which back the aggregate nominal value of the new currency put in circulation. Those assets can consist of, for example, a reserve basket of other currencies. Once again, it sounds crazy, i.e. money being guaranteed with money, but this is how it works.

Therefore, step #2 in designing a new, bank-based currency, requires giving some aggregate numbers. What is the aggregate value of transactions served by the new currency? Let’s go, just as an example, for $100 billion a year. How long will each unit of the new currency spend on an individual bank account? In a perfectly liquid market, each unit of currency is used as soon as it has been received, thus it just has one night to sleep on a bank account, and back to work, bro’. In such a situation, that average time on one account is 1 day. Therefore, in order to cover $100 billion in transactions, we need [$100 / 365 days in the year] = $0,2739726 billion = $274 million in currency. If people tend to build speculative positions in that currency, i.e. they tend to save some of it for later, the average time spent on an individual account by the average unit of that new money could stretch up to 2 weeks = 14 days. In such case, the amount of currency we need to finance $100 billion in transactions is calculated as [$100 / (365/14)] = [$100 * 14 / 365] = $3,8356 billion.

There is a catch. I talk about introducing a new currency, but I keep denominating in US dollars, whence the next question and the next step, step #3, in a project devoted to this topic. The real economic value of our money depends on what we do with that money, and not really on what we call it. One of the things we do with an international currency is to exchange it against national currencies. In this case, we are talking about 5 essentially closed national currencies. For the sake of convenience, let’s call them: Ducat A, Ducat B, Ducat C, Ducat D, and Ducat E. Once again for sheer convenience we label the new currency ‘Wanderer’. So far, our 5 countries have been using the US dollar for international settlements, whence my calculations denominated therein. The issue of exchange rate of the Wanderer against the US dollar, as well as against our 5 national Ducats, is a behavioural one. Yes, behavioural: it is about human behaviour.

We have businesspeople doing international business in USD, and we want to convince them to switch to the Wanderer. What arguments can we use? There are two: exchange rate per se, and exchange rate risk. Whoever is a national of our 5 countries, needs to exchange their national Ducat against the US dollar and the other way around. As neither of the Ducats is freely convertible, exchange with the dollar takes place, most probably, in the form of big, bulk transactions, like once a month, mediated by the central banks of our 5 countries. Those bulk transactions yield an average exchange rate, and an average variance around that average.

We want to put in place an alternative scheme, where the national Ducats (A, B, C, D, E) are exchanged in real time against the Wanderer, and then the Wanderer gets exchanged against the US dollar. The purpose is to make the exchange {Ducat Wanderer USD} more attractive, average-rate-wise or variance-in-rate-wise, than the incumbent {Ducat Individual, National Central Bank USD} one. Some of you might think it is not realistically possible, yet it really is. If 5 central banks of developing countries gang up together to buy and sell US dollars, they can probably achieve a better price, and less volatile a price, as compared to what each of them separately could have. There is even an additional trick, and this is like really a trick: central banks of our 5 countries could hold some of their financial reserves in US dollars, more specifically the part devoted to backing the Wanderer. That’s the trick that our central bank in Poland, the National Central Bank of Poland, uses all the time. We are in the European Union, but we do not belong to the European Monetary Union, and yet we do a lot of business with partners in the eurozone. The National Bank of Poland holds important financial reserves in euros, and thus gives itself a better grip on the exchange rate between the Polish zloty and the euro.

Summing up the case of graduation projects focused on designing a new bank-based currency, here are, rephrased once again, the basic logical steps. Start with identifying a market with liquidity problems, such as closed monetary systems or very volatile national currencies. This is usually an international market made of developing countries. Imagine a situation, when the central banks of the countries in question place some of their financial reserves in a strong currency, e.g. the US dollar, or the Euro, and then the same central banks introduce a currency for international settlements in that closed group of countries. Keep in mind that the whole group of countries will need an amount of currency calculated as: [Aggregate value of international transactions done in a year * [Average number of days that one user holds one unit of currency / 365].  

The whole scheme consists, at the end of the day, in obtaining a better and less volatile exchange rate of individual national currencies against the BIG ONES (e.g. the US dollar) through aggregating their exchange transactions in the financial market.       

That would be all in this tutorial. I have covered three types of financial instruments that my students can possibly design for their graduation: equity-based securities, debt-based securities, and bank-based currencies. In the coming weeks I will try to write something smart on designing cryptocurrencies and insurance contracts. Till then, you can additionally read entry March, 26th, 2019 – More and more money just in case. Educational about money and monetary systems – and entry March 31st, 2019 – The painful occurrence of sometimes. Educational about insurance and financial risk.

Cut some slack. Project tutorial for International Management at the Frycz University.

My editorial on You Tube

I am focusing, for a few days starting from today, on delivering educational content. In the framework of 4 courses I teach, this semester, at the Andrzej Frycz Modrzewski Krakow University, three – Foundations of Finance, International Management, and International Trade – require preparing graduation projects. I am presenting guidelines for those projects, and I start with the way I advise for preparing a project in International Management, Summer-Spring 2020.

When my students prepare a project in management, I keep repeating the truth: neither I, the teacher, nor you, my students, are professional managers. We are looking at the world of management from outside. This is a harsh truth to swallow: I teach something I have almost no practical experience with. What kind of skills can I, the teacher, bring to the table, in such case? I have skills in patterning and modelling social structures. That could be the reason why I do social sciences, and this is the bacon I can feed my students in any kind of management course. Thus, when you do management with me, in class, we are all throwing our limited knowledge at real situations and try to understand our own cognitive limitations. From that angle, the course of management aims at learning how much you don’t know, and what you need to learn about the situations we are talking about.   

In the course of International Management, the general frame for your graduation projects is to figure out an organisational solution to problems, which manifest themselves as officially acknowledged risk factors, explicitly discussed in annual reports of the companies, whose cases we discuss in class. That general approach unfolds in a few distinct steps. You read the annual report of, for example, General Electric, which you have already worked with in the first online class this semester. You take any risk factor named in that report. That risk factor means that something specific can happen, which will harm GE’s business. What exactly is that specific, adverse event? Try to imagine very realistically what kind of real situation can it be. When you do that, you will probably figure out 4 types of situations.

Firstly, someone recurrently makes small mistakes, over and over again. Those small mistakes pile up, and they sort of capitalize on each other. If today I neglect checking something important, tomorrow that negligence is likely to bring some adverse effects, and when I repeat it, i.e. when I skip that important check once again, adverse effects combine. When I neglect to check, whether the salary system for salespeople in my business is working well, those people get more and more pissed every month. Their frustration accumulates, and they react more and more nervously to even small imperfections in the wage system.

Secondly, someone can make one, big, catastrophic mistake, e.g. signing a big, really bad contract, which, in turn, will expose our business to a whole series of adverse outcomes, or, for example, a person will take revenge on the top management by transmitting the details of some in-house technology to a competitor. Please, note that mistakes can fluidly transform, or coexist with opportunistic behaviour. What is seen as a mistake from outside can be the manifestation of wrongful intentions on the part of the person who makes that mistake.

A big, catastrophic event can take place as ‘force majeure’, e.g. a hurricane, or a pandemic such as the present COVID-19 one, and this is the third type of risk factor. Finally, the external structure of our market can change in an unfavourable direction, and this usually takes place on an adverse change in prices, e.g. the present slump in the prices of crude oil, which is a good thing for some businesses, and a very bad one for others. That fourth type of risk is usually called ‘financial risk’.

Thus, whatever bad happens to a business, the roots of that adverse event usually fall into one of those four categories: repeated, small human mistakes, occasional big mistake, external disaster, or unfavourable external change in the prices of something. Now, think how you can make an organisation resilient to those risks. What kind of people would you need, in order to shield the business against those risks? What kind of jobs should those people do? How can you pay them? What kind of internal control you need? What kind of organisational structure will work better, in terms of resilience? Do you need, for a given business, a solid, relatively slow functional structure with a lot of internal controls, exhaustive documentation etc., or, maybe, what you need is an agile, very horizontal structure, with task-teams focused on projects rather than functional divisions with distinct competences? Which organisational pattern which shield you better against small, bitchy mistakes or frauds? Which is going to play out better when it comes to preventing a disaster-like bad decision?

In that case of General Electric, I asked my students to study the risk of making bad investments or unfavourable dispositions (reminder: disposition, in this context, means selling and entire business or an important portion of strategic assets from a business), thus the risk named as ‘Portfolio strategy execution’. We focused on the healthcare segment of GE’s business (i.e. technologies for healthcare and biotech), and I gave my students (it was in the beginning of March) a task which looks prophetic now. I asked them to imagine that GE wants to sell (i.e. divest from) the entire healthcare segment of their business. Right now, hardly anyone in their right mind would get rid of technological assets in healthcare. Still, in the beginning of march, the s**t we currently have was just outlining itself.

Anyway, we focus on the healthcare segment in the general portfolio of General Electric. In the discussion of ‘Portfolio strategy execution’, in the GE’s annual report for 2019, you can read the following passage: “Our success depends on achieving our strategic and financial objectives, including through dispositions. We are pursuing a variety of dispositions, including the planned sale of our BioPharma business within our Healthcare segment and exiting our remaining equity ownership position in Baker Hughes. The proceeds that we expect to receive from such actions are an important source of cash flow for the Company as part of our strategic and financial planning”. Let’s break it down into adverse events, and then I can take a risk (!) at trying to lead my students from risk factors to organisational solutions that can shield against those risks.

The first sentence of that passage says: “Our success depends on achieving our strategic and financial objectives, including through dispositions”. It roughly means that the top management of GE sees the entire portfolio of businesses, all segments combined, as a hand of cards in a poker game. You probably know that in poker you can ask the croupier to exchange one or more of the cards from your hand against cards from the deck. When you go for such an exchange, you expect that the cards you get from the croupier will make a better match to the remaining ones, which you still keep in hand. You are a top manager with GE, and you decide to sell (i.e. to dispose of) an entire business, in order to generate a cash inflow, which, in turn, will serve you to buy (i.e. invest in) another entire business.

Your basic challenge in such a situation is limited, imperfect information. You know, how the business you intend to sell is playing out with all the rest in your hand, and you have some expectations as for how another business – which you intend to buy – could work with the same rest in your hand. From the cognitive point of view, you are trading actual, hard-facts-based knowledge of a presently owned business, against much foggier expectations as for future possible gains from another business. You are exchanging some known s**t against some unknown s**t, with the unknown being somehow tempting you with potentially higher rewards.

Let’s translate this situation into the four basic types of risk: repeated, small human mistakes, occasional big mistake, external disaster, or unfavourable external change in the prices of something. Someone, further down the corporate hierarchy, could have been making small recurrent mistakes, or could have been perpetrating small recurrent frauds, which could have brought the healthcare business you intend to dispose of to a situation of suboptimal performance. You think the business you want to sell is worth X $ million in terms of expected net income, but in fact it could bring much more, like 2*X $ million, if you eliminate the risk factor of recurrent, small human mistakes. How can an organization shield itself against this type of risk? The most obvious answer is that if you currently control, in a rational way, operational performance in the given business, you can have a pretty good idea of what that business is capable of. If you don’t have such a controlling system, you could be selling a business with a lot of potential, and you would be selling because you cannot see that potential.

Conclusion #1: if you have in place a rational system of KPIs (Key Performance Indicators), in each business you have in your portfolio, you can make much more informed decisions as for selling (disposing of) each such business. Topic #1, which my students can develop in their projects, and which arises from that partial conclusion, could go as follows: ‘Study the entire portfolio of businesses in General Electric. Look for any piece of information you can find about it. How can you know that each of those businesses is currently working at 100%? What system of performance measurement you would like to see in place, so as to be well informed? At the end of the day, what information would you need to be sure that the decision of selling a business is really well-founded?

Let’s move further. The next sentence, in the same passage says: ‘We are pursuing a variety of dispositions, including the planned sale of our BioPharma business within our Healthcare segment and exiting our remaining equity ownership position in Baker Hughes’. A variety of dispositions means that GE is selling, or, potentially, can be selling at any given moment, many businesses at once. You can lose your balance in the midst of variety. You can do something relatively well, at the expense of doing something else much less efficiently that what you expect from yourself. Let’s try to find ways of preventing it.

When you perform many similar actions in parallel, you would like to carry out each of those actions with a maximum of efficiency. You study, you practice some sport, and you engage in business, and you would like to deliver your A game in each of these fields. There are some basic techniques you can use to assess whether you can find efficient balance at all, and whether your actions are balanced at a given moment. One of those techniques consist in assessing your resources. If, pursuing that existential example, you study, you do sport and you do business, a basic personal resource is time and human energy (i.e. the chemical energy you need in order to generate neurotransmitters, which, in turn, your nervous system needs to have all the major angles covered). Question: do you have enough time to cover studies, sport and business? It is a harsh question. The answer might be no, I haven’t. The even harsher implication of that answer is the necessity to cut something out. I focus on exams, and I give up my performance in an important sports event, or I focus on business and take a sabbatical at the university. Another answer could be yes, I have enough time, but I need to cut some slack. I need to give up on some pleasures (e.g. watching Netflix, or partying), and that will give me 2 extra hours a day for packing all my priorities in it.      

We can translate it back into the context of General Electric. When ‘We are pursuing a variety of dispositions’, we can ask: ‘Do we have enough organisational resources to pursue that entire variety of dispositions efficiently? Do we have enough people, enough computational power in our digital systems, enough good relations (or good enough relations!) with external entities so as to handle all that variety as it is?’. The answer can be yes, we have, or no, we haven’t. In the former case, the immediately following question is: ‘Do we have those resources organized optimally? Does every person involved know what they are supposed to do? Etc.’. In the latter situation, when we conclude that we cannot possibly cover all the angles with the resources we have, we follow up by asking ourselves: ‘What do we do? Do we hire additional human resources, or/and engage additional technology into the process of managing as wide a variety of dispositions as we are currently handling, or, maybe, it is a better idea to reduce variety? Maybe we can postpone some of those dispositions and focus more efficiently on the remaining deals? Does it all have to be carried out right now? Maybe we can make a timeline over the 2 years to come?’. By the way, in unstable market conditions, such as every business is facing now, with the COVID-19 pandemic and its consequences, it might pay off to slow down our decision-making, to observe and learn more before taking strategic decisions.

Conclusion #2: in a given context of external market conditions, the organization we actually have in place has a given capacity to process information and to make strategic change on the grounds of that information. If we want to pursue more operations in parallel than our organizational resources actually allow to, we risk losing our bearings in the midst of variety. There are two alternative ways out of that predicament. On the one hand, we can cut on the variety of our operations and/or our strategic decisions so as to focus on the amount we can really handle. On the other hand, we can expand our organizational resources so as to pursue efficiently the entire variety of actions that presents itself to us.

Thus, a possible topic #2 emerges for my students in International Management. Once again, go over the business of General Electric. Try to understand very practically, what do they mean by ‘pursuing a variety of dispositions’. Variety means what exactly? Now, what organizational resources (people, information, business relations etc.) does GE need so as to carry out efficiently one single disposition? Expand by assuming that you run an investment fund, with participations in many high-tech businesses. Every few months, you need to decide whether each of those businesses is worth holding in your portfolio, or maybe it would be better to sell it. What organizational resources do you need to manage such decisions efficiently? How many people would you need to hire, in such an investment fund? What kind of duties would those people have to carry out, and what skillset you would expect in them?               

A flow I can ride, rather than a storm I should fear

My editorial on You Tube

I am in an intellectually playful frame of mind, and I decide to play with Keynes and probability. It makes like 4 weeks that I mess around with the theory of probability, and yesterday my students told me they have a problem with Keynes. I mean, not with Sir John Maynard Keynes as a person, but more sort of with what he wrote. I decided to connect those two dots. Before John Maynard Keynes wrote his ‘General Theory of Employment, Interest, and Money’, in 1935, he wrote a few other books, and among them was ‘A Treatise on Probability’ (1921).

I am deeply convinced that mathematics expresses our cognitive take on that otherwise little known, chaotic stuff we call reality, fault of a better label. I am going to compare John Maynard Keynes’s approaches to, respectively, probability and economics, so as to find connections. I start with the beginning of Chapter I, entitled ‘The Meaning of Probability’, in Keynes’s Treatise on Probability,   

Part of our knowledge we obtain direct; and part by argument. The Theory of Probability is concerned with that part which we obtain by argument, and it treats of the different degrees in which the results so obtained are conclusive or inconclusive. In most branches of academic logic, such as the theory of the syllogism or the geometry of ideal space, all the arguments aim at demonstrative certainty. They claim to be conclusive. But many other arguments are rational and claim some weight without pretending to be certain. In Metaphysics, in Science, and in Conduct, most of the arguments, upon which we habitually base our rational beliefs, are admitted to be inconclusive in a greater or less degree. Thus for a philosophical treatment of these branches of knowledge, the study of probability is required. […] The Theory of Probability is logical, therefore, because it is concerned with the degree of belief which it is rational to entertain in given conditions, and not merely with the actual beliefs of particular individuals, which may or may not be rational. Given the body of direct knowledge which constitutes our ultimate premises, this theory tells us what further rational beliefs, certain or probable, can be derived by valid argument from our direct knowledge. This involves purely logical relations between the propositions which embody our direct knowledge and the propositions about which we seek indirect knowledge. […] Writers on Probability have generally dealt with what they term the “happening” of “events.” In the problems which they first studied this did not involve much departure from common usage. But these expressions are now used in a way which is vague and ambiguous; and it will be more than a verbal improvement to discuss the truth and the probability of propositions instead of the occurrence and the probability of events’.

See? Something interesting. I think most of us connect the concept of probability to that experiment which we used to perform at high school: toss a coin 100 times, see how many times you have tails, and how many occurrences of heads you had etc. Tossing a coin is empirical: we make very little assumptions and we just observe. How is it possible, then, for anybody to even hypothesise that probability is a science of propositions rather than hard facts?

Now, here is the thing with John Maynard Keynes (and I address this passage to all those of my students who struggle with understanding what the hell did John Maynard mean): John Maynard Keynes had a unique ability to sell his ideas, and his ideas came from his experience. Whatever general principles you can read in Keynes’s writings, and however irrefutable he suggests these principles are, John Maynard tells us the same kind of story that everybody tells: the story of his own existence. He just tells it in so elegantly sleek a way that most people just feel disarmed and conquered. Yet, convincing is not the same as true. Even the most persuasive theorists – and John Maynard Keynes could persuade the s**t out of most common mortals – can be wrong. How can they be wrong? Well, when I fail to own my own story, i.e. when I am just too afraid of looking the chaos of life straight in the eyes (which is elegantly called ‘cognitive bias’), then I tell just the nice little story which I would like to hear, in order to calm down my own fear.      

Let’s try to understand John Maynard Keynes’s story of existence, which leads to seeing probabilities as a type of logic rather than data. I browse through his ‘Treatise on Probability’. I’m patient. I know he will give himself away sooner or later. Everybody does. Well, let’s say that according to my experience of conversations with dead people via their writings, each of them ends up by telling me, through his very writing, what kind of existential story made him tell the elegantly packaged theoretical story in the title of the book. Gotcha’, Sir Keynes! Part I – Fundamental Ideas – Chapter III, ‘The Measurement of Probabilities’, page 22 in the PDF I am linking to: ‘If we pass from the opinions of theorists to the experience of practical men, it might perhaps be held that a presumption in favour of the numerical valuation of all probabilities can be based on the practice of underwriters and the willingness of Lloyd’s to insure against practically any risk. Underwriters are actually willing, it might be urged, to name a numerical measure in every case, and to back their opinion with money. But this practice shows no more than that many probabilities are greater or less than some numerical measure, not that they themselves are numerically definite. It is sufficient for the underwriter if the premium he names exceeds the probable risk. But, apart from this, I doubt whether in extreme cases the process of thought, through which he goes before naming a premium, is wholly rational and determinate; or that two equally intelligent brokers acting on the same evidence would always arrive at the same result. In the case, for instance, of insurances effected before a Budget, the figures quoted must be partly arbitrary. There is in them an element of caprice, and the broker’s state of mind, when he quotes a figure, is like a bookmaker’s when he names odds. Whilst he may be able to make sure of a profit, on the principles of the bookmaker, yet the individual figures that make up the book are, within certain limits, arbitrary. He may be almost certain, that is to say, that there will not be new taxes on more than one of the articles tea, sugar, and whisky; there may be an opinion abroad, reasonable or unreasonable, that the likelihood is in the order—whisky, tea, sugar; and he may, therefore be able to effect insurances for equal amounts in each at 30 per cent, 40 per cent, and 45 per cent. He has thus made sure of a profit of 15 per cent, however absurd and arbitrary his quotations may be’.  

See? Told you he’s got a REAL story to tell, Sir Keynes. You just need to follow him home and see whom he’s hanging with. He is actually hanging with financial brokers and insurers. He observes them and concludes there is no way of predicting the exact probability of complex occurrences they essentially bet money on. There is some deeply intuitive mental process taking place in their minds, which makes them guess correctly if insuring a ship full of cotton, for reimbursable damages worth X amount of money, in exchange of an insurance premium worth Y money.

The story that John Maynard Keynes tells is through his ‘Treatise on Probability’ is the story of the wild, exuberant capitalism of the early 1920ies, right after World War I, and after the epidemic of Spanish flu. It was a frame of mind that pushed people to run towards a mirage of wealth, and they would run towards it so frantically, because they wanted to run away from memories of horrible things. Sometimes we assume that what’s can possibly catch us from behind is so frightening that whatever we can run towards is worth running forward. In such a world, probability is a hasty evaluation of odds, with no time left for elaborate calculations. There are so many opportunities to catch, and so much fear to run away from that I don’t waste my time to think what an event actually is. It is just the ‘have I placed my bets right?’ thing. I think I understand it, as I recently experienced very much the same (see A day of trade. Learning short positions).

The very same existential story, just more seasoned and marinated in the oils of older age, can be seen in John Maynard Keynes’s ‘General Theory of Employment, Interest, and Money’. I read the ‘Preface’, dated December 13th, 1935, where the last paragraph says: ‘The composition of this book has been for the author a long struggle of escape, and so must the reading of it be for most readers if the author’s assault upon them is to be successful,—a struggle of escape from habitual modes of thought and expression. The ideas which are here expressed so laboriously are extremely simple and should be obvious. The difficulty lies, not in the new ideas, but in escaping from the old ones, which ramify, for those brought up as most of us have been, into every corner of our minds’. The same line of logic is present in country-specific prefaces that follow, i.e. to national translations of ‘General Theory’ published in Germany, France, and Japan.

In 1935, John Maynard Keynes had lived the exuberance of the 1920ies and the sobering cruelty of the 1930ies. He felt like telling a completely new story, yet the established theory, that of classical economics, would resist. How can you overcome resistance of such type? One of the strategies we can use is to take the old concepts and just present them in a new way, and I think this is very largely what John Maynard Keynes did. He took the well-known ideas, such as aggregate output, average wage etc., and made a desperate effort to reframe them. In the preface to the French edition of ‘General Theory’, there is a passage which, I believe, sums up some 50%, if not more, of all the general theorizing to be found in this book. It goes: ‘I believe that economics everywhere up to recent times has been dominated, much more than has been understood, by the doctrines associated with the name of J.-B. Say. It is true that his ‘law of markets’ has been long abandoned by most economists; but they have not extricated themselves from his basic assumptions and particularly from his fallacy that demand is created by supply. Say was implicitly assuming that the economic system was always operating up to its full capacity, so that a new activity was always in substitution for, and never in addition to, some other activity. Nearly all subsequent economic theory has depended on, in the sense that it has required, this same assumption. Yet a theory so based is clearly incompetent to tackle the problems of unemployment and of the trade cycle. Perhaps I can best express to French readers what I claim for this book by saying that in the theory of production it is a final break-away from the doctrines of J.- B. Say and that in the theory of interest it is a return to the doctrines of Montesquieu’.

Good. Sir Keynes assumes that it is a delicate thing to keep the economic system in balance. Why? Well, Sir Keynes knows it because he had lived it. That preface to the French edition of ‘General Theory’ is dated February 20th, 1939. We are all the way through the Great Depression, Hitler has already overtaken Austria and Czechoslovakia, and the United States are in the New Deal. Things don’t balance themselves by themselves, it is true. Yet, against this general assumption of equilibrium-is-something-precarious, the development which follows, in ‘General Theory’ goes exactly in the opposite direction. John Maynard Keynes builds a perfect world of equations, where Savings equal Investment, Investment equals Amortization, and generally things are equal to many other things. Having claimed the precarity of economic equilibrium, Sir Keynes paints one in bright pink.

I think that Keynes tried to express radically new ideas with old concepts, whence the confusion. He wanted to communicate the clearly underrated power of change vs that of homeostasis, yet he kept thinking in terms of, precisely, homeostasis between absolute aggregates, e.g. the sum of all proceedings anyone can have from a given amount of business is equal to the value conveyed by the same amount of business (this is my own, completely unauthorized summary of the principle, which Keynes called ‘effective demand’).  

The ‘General Theory of Employment, Interest, and Money’ was somehow competing for the interest of readers with another theory, phrased out practically at the same moment, namely the theory of business cycles by Joseph Alois Schumpeter. I perceive the difference between the respective takes by Keynes and Schumpeter, on the general turbulence of existence, in the acknowledgment of chaos and complexity. Keynes says: ‘Look, folks. This, I mean that whole stuff around, is bloody uncertain and volatile. Still, the good news is that I can wrap it up, just for you, in an elegant theory with nice equations, and then you will have a very ordered picture of chaos’. Joseph Alois Schumpeter retorts: ‘Not quite. What we perceive as chaos is simply complex change, too complex for being grasped once and for all. There is a cycle of change, and we are part of the cycle. We are in the cycle, not the other way around (i.e. cycle is not in us). What we can understand, and even exploit, is the change in itself’.

Where do I stand in all that? I am definitely more Schumpeterian than Keynesian. I prefer dishevelled reality to any nicely ordered and essentially false picture thereof. Yes, existence is change, and any impression of permanence is temporary. My recent intellectual wrestling with stochastic processes (see We really don’t see small change) showed me that even when I use quite elaborate analytical tools, such as mean-reversion, I keep stumbling upon my purely subjective partition of perceivable reality into the normal order, and the alarming chaos (see The kind of puzzle that Karl Friedrich was after).

A vision of game comes to my mind. This is me vs universe. Looks familiar? Right you are. That’s exactly the kind of game each of us plays throughout time. I make a move, and I wait for the universe to make its own. I have a problem: I don’t really know what kind of phenomenon I can account as move made by the universe. I need to guess: has the universe already made its move, in that game with me, or not yet? If I answer ‘yes’, I react. I assume that what has just happened is informative about the way my existence works. If, on the other hand, I guess that the universe has not figured yet any plausible way to put me at check, I wait and observe. Which is better, day after day: assuming that the universe made its move or sitting and waiting? I can very strongly feel this dilemma in my learning of investment in the stock market. Something happened. Prices have changed. Should I react immediately, or should I wait?

I provisionally claim that it depends. The universe moves at an uneven speed. By ‘provisionally’ I mean I claim it until I die, and then someone else will take on claiming the same, just as provisionally. Yet, all that existential instability acknowledged, there are rhythms I can follow. As regards my investment, I discovered that the most sensible rhythm to follow beats on the passive side of my investment portfolio. Every month, I collect the rent from an apartment, downtown, and I invest that rent in the stock market. I discovered that when I orchestrate my own thinking into that monthly rhythm of inflow in equity, it sort of works nicely. I collect the rent around the 5th day of each month, and for like one week beforehand, I do my homework about the market. When the rent comes, I have a scenario in mind, usually with a few question marks, i.e. with uncertainty to deal with. I play my investment game for 1 – 3 days, with occasional adjustments, and this is my move. Then I let the universe (the stock market in this case) make its own move over the next 3 – 4 weeks, and I repeat the same cycle over and over again.

I make a short move, and I let the universe making a long move. Is it a sensible strategy? From my point of view, there are two reasons for answering ‘yes’ to that question. First of all, it works in purely financial terms. I have learnt to wait patiently for an abnormally good opportunity to make profits. When I go too fast, like every day is a decision day, I usually get entangled in a game of my own illusions, and I lose money on transactions which I don’t quite understand. When I take my time, pace myself, and define a precise window for going hunting, usually something appears in that window, and I can make good money. Second of all, it is something I have sort of learnt generally and existentially: chaos is there, and I am there, and a good way to be alongside the chaos is to find a rhythm. When I follow my beat, chaos becomes a flow I can ride, rather than a storm I should fear.

The kind of puzzle that Karl Friedrich was after

My editorial on You Tube

Over the last few updates, I have been indulging in the mathematical logic of Gaussian process, eating it with the spoon of mean-reversion. My so-far experience with using the logic of Gaussian process is that of my personal strategy as regards investment in the stock market, and especially as regards those short, periodical episodes of reshuffling in my investment portfolio, when I am exposed to, and I frequently yield to the gambling-like temptation of short trade (see Acceptably dumb proof. The method of mean-reversion , Fast + slower = compound rhythm, the rhythm of life, and We really don’t see small change ). Gambling-like is the key concept here. I engage into quick trade, and I feel that special flow, peculiar to gambling behaviour, and yet I want that flow to weave around a rational strategy, very much in the spirit of Abraham de Moivre’s ‘The doctrine of chances: or, A method of calculating the probabilities of events in play’, published in 1756. A bit of gambling, yes, but informed gambling.  

I am trying to understand why a neural network based on mean-reversed prices as input consistently underestimates the real price, and why the whole method of mean-reversion fails with super-stable prices, such as those of cobalt or uranium (see We really don’t see small change).

I like understanding things. I like understanding the deep logic of the things I do and the methods I use. Here comes the object of my deep intellectual dive, the normal distribution. In the two pictures below, you can see the initial outline of the problem.

How does a function, namely that of normal distribution, assist my process of decision making? Of course, the first-order answer is simple: ‘it gives you numbers, bro’, and when you see those numbers you essentially know what to do’. Good, great, but I want to understand HOW EXACTLY those numbers, thus the function I use, match with my thinking and my action.

Good. I have a function, i.e. that of normal distribution, and for some reason that function works. It works geometrically. The whole mathematical expression serves to create a fraction. If you look carefully at the equation, you will understand that with given mean value μ and standard deviation σ, there is no way this function can go above 1. It is always a fraction. A fraction can be seen from different angles. Firstly, it is a portion of something, like a / b, where a < b. There is a bigger something, the denominator of the fraction, σ[(2π)0,5] = σ* 2,506628275. (elevation to power 0,5 replaces the sign of square root, which I cannot reproduce exactly from the keyboard, as a font).  Secondly, as we talk about denominators, a fraction is a change in units of measurement. Instead of measuring reality in units of 1 – the smallest prime number – we measure reality in units of whatever we put in the denominator of the fraction. Thirdly, a fraction is a proportion between two sides of a rectangle, namely the proportion between the shorter side and the longer side.

Good, so what this function of normal distribution represents is a portion cut of a bigger something equal to σ[(2π)0,5], and that something is my unit of measurement, and, in the same time, it is the longer side of a rectangle. The expression σ[(2π)0,5] is something like one dimension of my world, whilst the whole equation of normal distribution, i.e. the value of that function, makes the other dimension. Is the Gaussian world a rectangular world? I need to know. I start talking to dead people. Usually helps. This time, my interlocutor is Karl Friedrich Gauss, in his General Investigations of Curved Surfaces, presented to the Royal Society, October 8th, 1827.

What many people ignore today is that what we call a Gaussian curve is the outcome of a mathematical problem, which, initially, had virtually nothing to do with probability. What Karl Friedrich Gauss (almost) solved was the problem of geodetic measurements, i.e. the distinction between the bird’s flight distance, and the actual length of the same distance on the rugged and uneven surface of the Earth. I know, when we go through mountains, it is sometimes uphill, sometimes downhill, and, on average, it is flat. Still, when you have to build a railroad through the same mountains, the actual length (spell: cost) of rails to put on the ground is much greater than what would be needed for building the same railroad in the plain. That’s the type of puzzle that Karl Friedrich was after.

Someone could say there is no puzzle. You want to know how long a rail do you need to go over a mountain, you send surveyors and they measure it. Splendid. Yet, civil engineering involves some kind of interference with the landscape. I can come up with the idea of putting my railroad alongside like the half-height of the mountain (instead of going right over its top), or maybe we could sort of shave off the top, couldn’t we, civilised people whom we are? Yes, those ideas are all valid, and I can have a lot of them. Sending surveyors each time I come up with a new concept can become terribly time- and money-consuming. What I could do with is a method of approximating each of those alternative distances on a curved surface, a method which finds good compromise between exactitude and simplicity.

Gauss assumed that when we convert the observation of anything curved – rugged land, or the orbit of a planet – into linear equations, we lose information. The challenge is to lose as little an amount thereof as possible. And here the story starts. Below, you will find a short quote from Gauss: the first paragraph of the introduction.   

1.

Investigations, in which the directions of various straight lines in space are to be considered, attain a high degree of clearness and simplicity if we employ, as an auxiliary, a sphere of unit radius described about an arbitrary centre, and suppose the different points of the sphere to represent the directions of straight lines parallel to the radii ending at these points. As the position of every point in space is determined by three coordinates, that is to say, the distances of the point from three mutually perpendicular fixed planes, it is necessary to consider, first of all, the directions of the axes perpendicular to these planes. The points on the sphere, which represent these directions, we shall denote by (1), (2), (3). The distance of any one of these points from either of the other two will be a quadrant; and we shall suppose that the directions of the axes are those in which the corresponding coordinates increase.’

Before I go further, a disclaimer is due. What follows is my own development on Karl Friedrich Gauss’s ideas, not an exact summary on his thoughts. If you want to go to the source, go to the source, i.e. to Gauss’s original writings.

In this introductory paragraph, reality is a sphere. Question: what geometrical shape does my perception of reality have? Do I perceive reality as a flat surface, as a sphere (as it is the case with Karl Friedrich Gauss), or maybe is it a cone, or a cube? How can I know what is the geometrical shape of my perception? Good. I feel my synapses firing a bit faster. There is nothing like an apparently absurd, mindf**king question to kick my brain into higher gear. If I want to know what shape of reality I am perceiving, it is essentially about distance.

I approach the thing scientifically, and I start by positing hypotheses. My perceived reality is just a point, i.e. everything could be happening together, without any perceived dimension to it. Sort of a super small and stationary life. I could stretch into a segment, and thus giving my existence at least one dimension to move along, and yet within some limits. If I allow the unknown and the unpredictable into my reality, I can perceive it in the form of a continuous, endless, straight line. Sometimes, my existence can be like a bundle of separate paths, each endowed with its own indefiniteness and its own expanse: this is reality made of a few straight lines in front of me, crossing or parallel to each other. Of course, I can stop messing around with discontinuities and I can generalise those few straight lines into a continuous plane. This could make me ambitious, and I could I come to the conclusion that flat is boring. Then I bend the plane into a sphere, and, finally things get really interesting and I assume that what I initially thought is a sphere is actually a space, i.e. a Russian doll made of a lot of spheres with different radiuses, packed one into the other.

I am pretty sure that anything else can be made out of those seven cases. If, for example, my perceived reality is a tetrahedron (i.e. any of the Egyptian pyramids after having taken flight, as any spaceship should, from time to time; just kidding), it is a reality made of semi-planes delimited by segments, thus the offspring of a really tumultuous relationship between a segment and a plane etc.

Let’s take any two points in my universe. Why two and not just one? ‘Cause it’s more fun, in the first place, and then, because of an old, almost forgotten technique called triangulation. I did it in the boy scout times, long before Internet and commercial use of Global Positioning System. You are in the middle of nowhere, and you have just a very faint idea of where exactly that nowhere is, and yet you have a map of it. On the map of nowhere, you find points which you are sort of spotting in the vicinity. That mountain on your 11:00 o’clock looks almost exactly like the mountain (i.e. the dense congregation of concentric contour lines) on the map. That radio tower on your 01:00 o’clock looks like the one marked on the map etc. Having just two points, i.e. the mountain and the radio tower, you can already find your position. You need a flat surface to put your map on, a compass (or elementary orientation by the position of the sun), a pencil and a ruler (or anything with a straight, smooth, hard edge). You position your map conformingly to the geographical directions, i.e. the top edge of the map should be perpendicular to the East-West axis (or, in other words, the top edge of the map should be facing North). You position the ruler on the map so as it marks an imaginary line from the mountain in the real landscape to the mountain on the map. You draw that straight line with the pencil. I do the same for the radio tower, i.e. I draw, on the map, a line connecting the real radio tower I can see to the radio tower on the map. Those lines cross on the map, and the crossing point is my most likely position.

Most likely is different from exact. By my own experience of having applied triangulation in real outdoors (back in the day, before Google Maps, and almost right after Gutenberg printed his first Bible), I know that triangulating with two points is sort of tricky. If my map is really precise (low scale, like military grade), and if it is my lucky day, two points yield a reliable positioning. Still, what used to happen more frequently, were doubtful situations. Is the mountain I can see on the horizon the mountain I think it is on the map? Sometimes it is, sometimes not quite. The more points I triangulate my position on, the closer I come to my exact location. If I have like 5 points or more, triangulating on them can even compensate slight inexactitude in the North-positioning of my map.   

The partial moral of the fairy tale is that representing my reality as a sphere around me comes with some advantages: I can find my place in that reality (the landscape) by using just an imperfect representation thereof (the map), and some thinking (the pencil, the ruler, and the compass).  I perceive my reality as a sphere, and I assume, following the intuitions of William James, expressed in his ‘Essays in Radical Empiricism’ that “there is only one primal stuff or material in the world, a stuff of which everything is composed, and if we call that stuff ‘pure experience,’ then knowing can easily be explained as a particular sort of relation towards one another into which portions of pure experience may enter. The relation itself is a part of pure experience; one of its ‘terms’ becomes the subject or bearer of the knowledge, the knower,[…] the other becomes the object known.” (Excerpt From: William James. “Essays in Radical Empiricism”. Apple Books).

Good. I’m lost. I can have two alternative shapes of my perceptual world: it can be a flat rectangle, or a sphere, and I keep in mind that both shapes are essentially my representations, i.e. my relations with the primal stuff of what’s really going on. The rectangle serves me to measure the likelihood of something happening, and the unit of likelihood is σ[(2π)0,5]. The sphere, on the other hand, has an interesting property: being in the centre of the sphere is radically different from being anywhere else. When I am in the centre, all points on the sphere are equidistant from me. Whatever happens is always at the same distance from my position: everything is equiprobable. On the other hand, when my current position is somewhere else than the centre of the sphere, points on the sphere are at different distances from me.

Now, things become a bit complicated geometrically, yet they remain logical. Imagine that your world is essentially spherical, and that you have two complementary, perceptual representations thereof, thus two types of maps, and they are both spherical as well. One of those maps locates you in its centre: it is a map of all the phenomena which you perceive as equidistant from you, thus equiprobable as for their possible occurrence. C’mon, you know, we all have that thing: anything can happen, and we don’t even bother which exact thing happens in the first place. This is a state of mind which can be a bit disquieting – it is essentially chaos acknowledged – yet, once you get the hang of it, it becomes interesting. The second spherical map locates you away from its centre, and automatically makes real phenomena different in their distance from you, i.e. in their likelihood of happening. That second map is more structured than the first one. Whilst the first is chaos, the second is order.

The next step is to assume that I can have many imperfectly overlapping chaoses in an otherwise ordered reality. I can squeeze, into an overarching, ordered representation of reality, many local, chaotic representations thereof. Then, I can just slice through the big and ordered representation of reality, following one of its secant planes. I can obtain something that I try to represent graphically in the picture below. Each point under the curve of normal distribution can correspond to the centre of a local sphere, with points on that sphere being equidistant from the centre. This is a local chaos. I can fit indefinitely many local chaoses of different size under the curve of normal distribution. The sphere in the middle, the one that touches the very belly of the Gaussian curve, roughly corresponds to what is called ‘standard normal distribution’, with mean μ = 0, and standard deviation σ =1. This is my central chaos, if you want, and it can have indefinitely many siblings, i.e. other local chaoses, located further towards the tails of the Gaussian curve.

An interesting proportion emerges between the sphere in the middle (my central chaos), and all the other spheres I can squeeze under the curve of normal distribution. That central chaos groups all the phenomena, which are one standard deviation away from me; remember: σ =1. All the points on the curve correspond to indefinitely many intersections between indefinitely many smaller spheres (smaller local chaoses), and the likelihood of each of those intersections happening is always a fraction of σ[(2π)0,5] = σ* 2,506628275. The normal curve, with its inherent proportions, represents the combination of all the possible local chaoses in my complex representation of reality.    

Good, so when I use the logic of mean-reversion to study stock prices and elaborating a strategy of investment, thus when I denominate the differences between those prices and their moving averages in units of standard deviation, it is as if I assumed that standard deviation makes σ =1. In other words, I am in the sphere of central chaos, and I discriminate stock prices into three categories, depending on the mean-reversed price. Those in the interval -1 ≤ mean-reversed price ≤ 1 are in my central chaos, which is essentially the ‘hold stock’ chaos. Those, which bear a mean-reversed price < -1, are in the peripheral chaos of the ‘buy’ strategy. Conversely, those with mean-reversed price > 1 are in another peripheral chaos, that of ‘sell’ strategy.

Now, I am trying to understand why a neural network based on mean-reversed prices as input consistently underestimates the real price, and why the whole method of mean-reversion fails with super-stable prices, such as those of cobalt or uranium (see We really don’t see small change). When prices are super-stable, thus when the moving standard deviation is σ = 0, mean-reversion, with its denomination in standard deviations, yields the ‘Division by zero!’ error, which is the mathematical equivalent of ‘WTF?’. When σ = 0, my central chaos (the central sphere under the curve) shrinks a point, devoid of any radius. Interesting. Things that change below the level of my perception deprive me of my central sphere of chaos. I am left just with the possible outliers (peripheral chaoses) without a ruler to measure them.

As regards the estimated output of my neural network (I mean, not the one in my head, the one I programmed) being consistently below real prices, I understand it as a proclivity of said network to overestimate the relative importance of peripheral chaoses in the [x < -1] [buy] zone, and, on the other hand, to underestimate peripheral chaoses existing in the [x > 1] [sell] zone. My neural network is sort of myopic to peripheral chaoses located far above (or to the right of, if you prefer) the center of my central chaos. If, as I deeply believe, the logic of mean-reversion represents an important cognitive structure in my mind, said mind tends to sort of leave one gate unguarded. In the case of price estimation, it is the gate of ‘sell’ opportunities, which, in turn, leads me to buy and hold whatever I invest in, rather than exchanging it back into money (which is the exact economic content of what we call ‘selling’).         

Interesting. When I use the normal distribution to study stock prices, one tail of the distribution – the one with abnormally high values – is sort of neglected to the benefit of the other tail, that with low values. It looks like the normal distribution is not really normal, but biased.

We really don’t see small change

My editorial on You Tube

Whatever kind of story I am telling, it is, at the end of the day, my own story, the story of my existence: this is hermeneutic philosophy, which I fully espouse intellectually. What’s my story, then? My essential story, I mean, the one which I weave, barely perceptibly, into the fabric of my narration about anything?

I think this is a story of change and learning. I change, my life changes, and I learn. Yes, I think that change is the most general denominator in my existence. You would say that it is the story of us all. Yes, indeed it is. We change, things change, and we learn. I think I was nine, when I got scarlet fever, AKA scarlatina. Nasty stuff: I spent almost two months with a fever around 39 degrees Celsius (= 102 Fahrenheit), on huge doses of Erythromycin (which is nasty stuff in itself). I remember doctors just sighing and alluding, in conversations with my parents, that we are sailing further and further into the hardly charted at all seas of maybe-it-is-going-to-work medicine. I had cardiac damage, and most probably some brain damage. I am not quite sure of that last one: in 1977, in the communist Poland, it was not like you can go and have your kid’s brain CT scanned just like that. Still, after that scarlet fever, I started to stutter (which had been haunting me until quite recently) and I started having learning problems at school. School fixed itself after like 3 years, stuttering took another 38 years or so (still have some echo of that in me), and here I am, having consumed and hopefully owned that particular avenue of change.

I am (mildly) obsessed about the connection between the collective intelligence of human societies. Not just human, as a matter of fact; viruses become kind of trendy, recently. I am going to develop on the concept of mean-reversed price precisely in that spirit, i.e. the link between us, humans, being collectively smart, and the ways to use artificial intelligence so as to discover how exactly collectively smart we are. In my previous two updates, I outlined the logic of mean-reversed price as analytical tool for nailing down a workable strategy of investment in the stock market. See ‘Acceptably dumb proof. The method of mean-reversion’ (earlier, April 9th, 2020), and ‘Fast + slower = compound rhythm, the rhythm of life’ (later, April 11th, 2020). Now, I go out of the stock market, and about into commodities. I want to check my intuitions in a different transactional context, and I want my writing to be useful for students in the courses of International Trade, International Management, and Macroeconomics.

Here is a perfectly normal world, where the entire social activity is centred on making (mining, growing) and trading 4 commodities: pork meat (lean hogs), uranium, coffee, and cobalt. Perfectly normal, I say. We raise pigs, and eat them, we make a lot of nuclear bombs, and a lot of electronics, and, obviously, doing all those things requires big amounts of coffee. In that perfectly normal world, the logic of ‘Price * Quantity’ still holds (see: https://youtu.be/S9dkez3BEWw ): we, humans, do all kinds of crazy and wonderful things, doing those things makes us generate an aggregate amount Q of economic utility, we go about that utility in recurrently patterned deals of exchange (AKA transactions), and observing transactional prices in, respectively, pork meat (lean hogs), uranium, coffee, and cobalt, can be possibly informative about how’s life going for us. Here is the link to download the Excel file with prices: https://discoversocialsciences.com/wp-content/uploads/2020/04/Uranium_Cobalt_Coffee_Lean-Hogs.xlsx .

I learn by accumulating knowledge, which allows, in the first place, distinguishing the normal from the alarming. I go Gaussian about it, and thus I build my expectations as moving average of past prices, and I denominate my perception in units of just as moving a standard deviation. Once again, I am in the world of mean-reversion.

I allow different temporal perspectives in my learning, and I introduce one more fundamental distinction, namely between learning with full memory, and learning with imperfect recall. The ways of calculating mean-reverted prices, which I showed in ‘Acceptably dumb proof. The method of mean-reversion’, and ‘Fast + slower = compound rhythm, the rhythm of life’, are marked with imperfect recall. I remember over a limited window in time: 30 days, 7 days etc. If my window is 30 days, on the 32nd day I forget whatever I remembered from day 1; on day 33, it is day 2 that I forget etc. Economic sciences convey substantial evidence that most markets, and most societies, as a matter of fact, shake off their memories every now and then. Yes, it seems that we like forgetting collectively.

Still, I want to have an alternative of not forgetting, and I introduce slightly different a method of calculating mean-reverted price: my temporal window stretches as far into the past as my data reaches back. My ‘lag’ in the equation grows every day. On day 15, I mean-revert the actually observed price with an average of prices 14 days back, and a standard deviation with the same window. On day 20, I reach back 19 days; on day 300, it is 299 days into the past etc. I call it mean-reversed cumulative.   

Once again, what mathematically is called mean-reversion is a typical pattern of our human cognition. We learn in order to slow down learning. Now, let’s see if it really works in all cases. I encourage you to go and retrieve the Excel file with those prices of : pork meat (lean hogs), uranium, coffee, and cobalt (link HERE), and practice calculating the mean-reversed prices. You will notice something interesting: sometimes it does not work at all. If you do the operation in Excel, it will yield the ‘DIV/0!’ error, which means that you are trying to divide by zero, which just doesn’t do in decent mathematics. The denominator we are dividing by is standard deviation, and when the phenomena observed are rrreaallly stationary, their standard deviation is equal to zero. In human cognition, it corresponds to a situation when the observable gradient of change is too subtle to be perceived and processed. We need perceivable change in order to learn. No change, no experience to put in your belt, sorry bro’. In this perfectly normal world, where we focus our activity on lean hogs, uranium, cobalt and coffee, such impossible situation happens a lot with uranium and cobalt, whilst taking place much less frequently with pork meat and coffee. In the reality we are currently experiencing, there are phenomena variable enough to offer our brain some material for trying to look clever, and there are others, like undertows of what’s happening, too stationary to be noticed.

The capacity to perceive change depends on the time frame of change. Those ‘WTF!? Division by zero!’ situations happen more frequently with shorter temporal windows. When I compute my moving average and moving standard deviation over a period of 7 days, and I observe the prices of cobalt, ‘DIV/0!’ happens like half of the time. When I stretch my temporal reference up to 30 days, many of those embarrassing absences of judgement disappear, and when I just go for cumulative moving average (and standard deviation), it happens just once, on day one, and then Bob’s my uncle: I always have some change to learn from.

If you have ever wondered why we have memories of various temporal reach, this might be an interesting avenue to walk down in order to find some answers. When our brain suddenly pulls out into consciousness some old stuff from back when I was twelve, it probably needs to compare data, to find some standard deviation as base of new learning.

Now, I put the same data into a simple neural network, a multi-layer perceptron. My question is: what kind of learning can an intelligent structure make out of observing reality the Newtonian way, with a focus on change?  In layer 1, I put three neurons. Each of them computes a different mean-reversion of the actual price: cumulative (from the beginning of time), the 30-day-based one, and the short one, with just 7 days of reference. In layer 2, another set of 3 neurons standardizes the mean-reversed observations on a scale from 0 to 1. In layer 3, I put one neuron, which assigns random coefficients to standardized observations, each random coefficient ranging between 0 and 1. This neuron experiments. It is the ‘what-happens-if-I-change-my-priorities?’ experimentation. In layer 4, three neurons activate, each based on a different function of neural activation: there is one sigmoid-based, another one working with hyperbolic tangent, and the third one made with ArcSinH, or hyperbolic arcsine. I add that third one because it has the interesting property not to require any standardization of raw data. Sigmoid and hyperbolic tangent are like refined intellectuals, who do not accept any input without a cappuccino as accompaniment. Hyperbolic arcsine is like a child, who just accepts what happens for what it is. In layer 5 of my network, three neurons calculate the error that each of those neural activations make in estimating the output, i.e. the actual price as recorded in the market. Layer 6 contains one neuron, which selects the least error among those coming from layer 5 and feeds it forward to the next round of experimentation.       

If I want my neural network to work, I need to get rid of the ‘DIV/0!’ cases and replace them by some arbitrary value. If at least one observation yields ‘DIV/0!’, the neural network goes on strike and yields the same, i.e. structural error of dividing by zero. Looks like intelligent structures do it all the time: I cannot see change, so I pretend that nothing happened. If I don’t pretend that, I face so strong a cognitive dissonance that I just go to intellectual sleep. Openly admitting that some important information has slipped out of our attention is one of the hardest things to do, cognitively. It is always safer to assume that we know everything we need to know.

Perception of actual empirical values, such as typical neural networks are based on, are maybe more natural and less human. There are less filters. Perception based on mean-reverted values i.e. rooted in change rather than absolute states, is more human-like.

Below, you can see visualisations of prices, respectively in coffee and in cobalt. Each of those markets is shown under two angles. Actual prices, i.e. market closures on each trading day over the last year (blue lines on each graph) are put back to back with prices estimated through the neural network which I have just described (orange line).

Two observations sort of jump to the eye (or maybe it is just my eye?). Prices simulated by the piece of AI are consistently lower that the actual ones, for one. An intelligent structure based on the very human cognitive mechanism of habitual perception and assessment (mean-reversion) consistently underestimates the real magnitude of the phenomenon under scrutiny. Secondly, that underestimation is much more pronounced in the case of cobalt than regarding coffee.

As you might remember from your own calculations, which I encouraged you to perform with those prices, mean-reverted prices of cobalt are much more prone to the ‘DIV/0!’ error, fault of sufficient variance, than the prices of coffee. Cognitively, it means that habitual perception (i.e. based on mean-reversion) tends to underestimate the magnitude of mostly those phenomena, which offer really low variance to our direct perception. We really don’t see small change. This is why we need scales of measurement. We need a scale of temperature, and the corresponding measurements, to assess the local kinetic energy of particles. In our perception, the difference between 35 degrees Celsius and 37 degrees Celsius is not a big deal when it comes to the ambient exterior, but it makes a difference when applied to body temperature.

As you might remember, had you followed ‘Acceptably dumb proof. The method of mean-reversion’ and ‘Fast + slower = compound rhythm, the rhythm of life’, I am developing a strategic tool for investing in the stock market, on the grounds of mean-reversion. What I can already see is that approached from this angle, my strategy could be a shade conservative, consistently downplaying the likelihood of sudden spikes in price, susceptible to offer me big rewards. Have to work on this one.

Fast + slower = compound rhythm, the rhythm of life

My editorial on You Tube

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 dayWindow 30 daysWindow 7 daysWindow 14 daysWindow 6 months
01.04.20202,361,542,180,22
02.04.20201,921,001,630,02
03.04.20203,702,032,752,23
06.04.20203,771,952,663,62
07.04.20201,970,601,241,64
08.04.20201,440,020,791,06
09.04.20202,170,861,392,41
10.04.20201,750,371,022,02
 Mean-reversed price of 11Bit
Trading dayWindow 30 daysWindow 7 daysWindow 14 daysWindow 6 months
01.04.2020(0,47)0,490,62         (0,90)
02.04.2020(0,42)0,300,57         (0,90)
03.04.2020(0,31)0,730,90         (0,82)
06.04.20200,522,513,01           0,06 
07.04.2020(0,23)(0,10)0,25         (0,83)
08.04.2020(0,04)0,210,61         (0,68)
09.04.20200,411,021,46         (0,31)
10.04.20200,440,791,27         (0,30)

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 .