This is an example from the book "Fooled by Randomness":
(...)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 10% volatility (or uncertainty) per annum translates into a 93% probability of success in any given year. But seen at a narrow time scale, this translates into a mere 50.02% probability of success over any given second.
Table 3.1 Probability of success at different scales
Scale Probability 1 year 93% 1 quarter 77% 1 month 67% 1 day 54% 1 hour 51.3% 1 minute 50.17% 1 second 50.02%
How do I calculate the probability of success at different scales (Table 3.1)? E.g. where does 77% for a quarter come from?