by On the scaling property of randomness I thought hard and long on how to explain with as little mathematics as possible the difference between noise and meaning, and how to show why the time scale is important in judging an historical event. The Monte Carlo simulator can provide us with such an intuition. We will start with an example borrowed from the investment world … Let us manufacture a happily retired dentist, living in a pleasant sunny town. We know a priori that he is an excellent investor, and that he will be expected to earn a return of 15% in excess of Treasury bills, with a 10% error rate per annum (what we call volatility). It means that out of 100 sample paths, we expect close to 68 of them to fall within a band of plus and minus 10% around the 15% excess return, i.e. between 5% and 25% (to be technical; the bell-shaped normal distribution has 68% of all observations falling between —1 and 1 standard deviations). It also means that 95 sample paths would fall between —5% and 35% … A 15 % return with a 1 0 % volatility (or uncertainty) per annum translates into a 93% probability of making money in any given year. But seen at a narrow time scale, this translates into a mere 50.02% probability of making money over any given second.
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Lars Pålsson Syll considers the following as important: Economics
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On the scaling property of randomness
I thought hard and long on how to explain with as little mathematics as possible the difference between noise and meaning, and how to show why the time scale is important in judging an historical event. The Monte Carlo simulator can provide us with such an intuition. We will start with an example borrowed from the investment world …
Let us manufacture a happily retired dentist, living in a pleasant sunny town. We know a priori that he is an excellent investor, and that he will be expected to earn a return of 15% in excess of Treasury bills, with a 10% error rate per annum (what we call volatility). It means that out of 100 sample paths, we expect close to 68 of them to fall within a band of plus and minus 10% around the 15% excess return, i.e. between 5% and 25% (to be technical; the bell-shaped normal distribution has 68% of all observations falling between —1 and 1 standard deviations). It also means that 95 sample paths would fall between —5% and 35% …
A 15 % return with a 1 0 % volatility (or uncertainty) per annum translates into a 93% probability of making money in any given year. But seen at a narrow time scale, this translates into a mere 50.02% probability of making money over any given second. Over the very narrow time increment, the observation will reveal close to nothing …
This scaling property of randomness is generally misunderstood, even by professionals. I have seen Ph.D.s argue over a performance observed in a narrow time scale (meaningless by any standard) …
The same methodology can explain why the news (the high scale) is full of noise and why history (the low scale) is largely stripped of it (though fraught with interpretation problems).