@Tom73 Thanks, Tom. I will look at the video, o/s atm, and will not be back for a bit. From the description you give, I have no issues with the data outcomes and have disclosed data from my benchmark universe on SM, showing skewing, as I call it, or non-normal distributions. we can also see that skewing increases with the level of stock uncertainty and unpredictability. the question that this outcome raises with me speaks directly to why i do what i do, and i described in detail in my "40-year" post. to summarise, is randomness controllable? is there a framework that consistently outperforms at the more volatile end of the spectrum? i would say no. none that i have seen, and my 5 years on SM if anything, confirms that view.

ok this is a big topic, but i think as you reduce the risk, you get better control and more consistent returns without sacrificing a lot in absolute returns. if there is a framework for consistent returns at high levels of volatility im all ears. the closest i can come to is buying cheap options. ( i dont mean exchange-traded options, lol, but the "things could happen and they are not priced in" type of options in various stocks). Trading the hype cycle? That is quite a large philosophical jump btw from where i am.

To use a cricketing analogy, im more of a Denis Lillee/ Glen McGrath line and length, with the view that consistency will pay off more than a Jeff Thomo who had much more speed but less direction. Maintaining control (consistent returns) at higher levels of randomness, I've got an issue with. but maybe that's me.

one of my pet subjects. thnaks

TLDR: Know if the game you are playing has outcomes based on Normal (Bell curve) or Power Law (Pareto) distributions otherwise you will not understand the risk/reward you are dealing with (eg Long-Term Capital Management).

Video that kicked it of by Veritasium:

You've (Likely) Been Playing The Game of Life Wrong (38:20 for the key point)

I watched this video (love their work generally) and it catalysed many concepts or thoughts I have on investing, risk and markets. The main insight was understanding what a Power Law was and how it differed from a Normal distribution, which crystalised my understanding around Parato’s 80/20 law that I have known for 30 years.

This paper Power Laws in the Stock Market (Chapter 2), provides similar information but is more market focused (and dryer).

Normal Vs Power Law distributions

Normal distribution characterised by many independent and random events centred around the average with thin tails. Where random factors are generally additive you get a Normal distribution.

Power Law distributions are characterised by a few large events that skew averages with fat tails allowing for huge outliers. Where random factors are generally factorial (multiplicative) you get a Log Normal distribution (the Log of the outcomes make a bell curve) which is a Power Law distribution.

How to tell the difference: If there is a significant difference between mean and median (eg income distributions), then that would indicate a Power Law rather than a Normal distribution (where low probability but extreme outcomes distort the mean). The 80/20 Pareto distribution is a Power Law distribution, so if outcomes exhibit this pattern then it’s likely to be a Power Law distribution.

Self-Organising Criticality

Criticality is a point in a system where events switch from a more Normal to a Power Law distribution as disproportionately larger outcomes start to occur (a linier relationship between cause and effect breaks down). Some systems (eg the stock market) will move to a point of criticality naturally (eg price rising to a bubble). Until the point of criticality, the impact of events are often small/minor and similar is scale (Normal), but at the point of criticality disproportionally larger or major events can occur that are far outside of the range of normal events (once in a decade crash at criticality Vs regular volatility) but the events can be the same as before the point of criticality. Self-Organising Criticality Systems have Power Law distribution outcomes (unsure if their relationship is a universal law, ie both are true or neither).

Predicting the cause and timing of a critical event remains difficult/impossible because there is nothing distinctive about the triggers from less impactful events (trigger for a crash is likely the same as for normal volatility), but awareness of reaching criticality or even the existence of it’s possibility should be factored in when looking at risk or volatility. The Sandpile model exemplifies Self Organising Criticality, showing small events can lead to large outcomes via a cascading effect once criticality is reached.

Investing Distributions

Compound returns follow a Power Law as a relative change in one quantity results in a proportional relative change in another, it is multiplicative rather than additive. This is only evident over longer time periods, over a month or year the distributions are more Normal. Over 5, 10 and 20 years the Power Law distribution shows as compounding is allowed to work it’s magic. Read: Power Laws in the Stock Market - A Wealth of Common Sense, which the graphs below are from.

The return on any one company in the market ranges from -100% to in theory an infinite positive return (long investments have a limited downside and unlimited upside), so it has a long tail of outcomes. This is not a Normal Distribution centered around an average and mean, rather the mean is well above the median as large outliers which are very low probability have a very high impact on the mean.

Market Return Probabilities:

Some Lessons & Application:

·        Trading Vs Investing: If you are doing short term trading, then Normal distributions are to be expected with a similar mean and median. If you are investing long term, then Power Law distributions are to be expected, mean will exceed the median and you expose yourself to outsized returns. This explains why investing returns can blow trading returns out of the water over the long term.

·        Diversification: Increases the chance of catching the outlier results which dominate returns for the market and a portfolio. The more position the more your expected return moves from the median to the mean (all other things being equal), which is a positive move where the market reflects a power law. Explains the advantage broad Indexes (mean result) have over concentrated portfolio managers (median result) on a straight probability basis.

·        Risk Vs Reward: VC’s take a very high-risk investment approach spreading their bets over a large number of small bets knowing that they just need a very small number of bets to pay off to get a good return, because of the outsized returns available. The portfolio construction needs to reflect the expected outcome distribution.

·        Let your winners run: Given most of the return in the market or a portfolio is the result of a small number of exceptional outcomes, the worst thing you can do is sell your winners after a small gain and even trimming your winners for portfolio balance can be a significant drag. There are limits and it is investor goal dependent, but the lesson is, hold your winners as long as you can, a bit of discomfort may be worth it to take advantage of the Power Law in effect.

·        Standard Deviation (SD)/Risk Measures: The SD for a Power Law distribution are erratic and can be infinite, so SD is irrelevant for data sets that exhibit Power Law distributions. So using SD or risk measurements based on SD for listed companies is useless in anything other than assessing short term risk/volatility. This is an issue for CAPM and Black-Scholes option pricing – both used extensively by the finance industry.

·        Black-Scholes: Options pricing is based on Normal distributions and based on a history that is either dominated by a Power Law event or excludes them. Hence Black-Scholes is misleading and the error increases the longer the duration of the Option. So long dated options exhibit a high degree of miss-pricing. My personal use of Options has lead me to use longer dated (1 year+) out of experience that volatility increases significantly more long term than is priced in (ie I get better results from long term options), I now have a better understanding of why.

·        Taleb – The Black Swan: If I could sum this in the context of this topic, he says people think in Normal Distributions (Bell Curves/MediocriStan) and what are called Black Swans are in fact expected, if they recognised that Power Law’s (ExtremaStan) are in place, so using history to predict the future breaks down at what are points of Criticality. I finally read this as a result of this matter. Part 3 focuses on Power Laws.

Like I said at the top – no revolution on what most investors understand from experience and wide reading and probably already known by many, but for me it made the WHY more real and provides a mathematical/statistical framework I can use (mostly conceptually) to vet information, date and make decisions.

PS: I just listened to MF Money pod and @Strawman mentioned the video on that, so have a watch.