Was it chance that drove Apple shares from a $1 in late 2004 to over a $120 by 2021. Perhaps probability had a lot to do with the demise of Nokia’s share of the mobile phone market. Many forget that it was actually the Finnish company that pioneered both the first smart and camera phone. In fact chance had nothing to do with either of these outcomes. Why then are potential probabilities explained through a framework of probabilistic chance? As investors, we need to distinguish between determinism [i.e. what actually caused this thing to move] and probability or chance. The latter is steeped in heavy assumptions and theory. Determinism is the meat on the bones. Determinism only works however if we know everything.

Do we have every angle covered? Of course we do not. Therefore, we are forced to confront the black-box of financial markets by analyzing the constituent parts and the end-results. The transition probabilities provide the insights we need. The skillful work is constructing models clever enough to capture this information. This all sounds rather pedestrian until you realize that your model inputs [data] suffers from several subjectivities including bias, noise, speculation, triviality, naked deception and wild anticipation. Human behavior, witnessed primarily through the competing forces of greed and nature do more to drive the fluctuations of asset prices than any tangible market phenomenon.

The proverbial coin-toss is used extensively to describe one of the central theories of probability – the law of large numbers [LOLN]. The LOLN proves statistically that a random experiment performed repeatedly produces an average number that converges to an expected value. The key word here is “repeatedly”.  How many times to we repeat the exercise. Is it one hundred times, a thousand times or perhaps ten thousand times? The significance of the result is dependent upon the number of coin tosses or market observations from an asset pricing perspective. The key point here is clear; a large number of observations or coin tosses is required to provide the average value. Therefore randomness operates within a variety of different state spaces and can exits across short to medium and longer-term periods with varying outcomes.

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