Steve Mayo Legend  Posts: 414 Joined: 10/11/2012 Location: Austin, TX  User Profile | Hi Steve, I hear you! The 2008 one-day drop was 6 sigma -- that's only supposed to happen once every 1.4 million years in a normal distribution! (The 1987 crash was 21 sigma drop. The biggest gain was 11 sigma in Oct-2008) In reality, a 6 Sigma drop occurs about once every 6 years (a 6 sigma one-day gain occurs about every 20 years) so the market clearly doesn't follow a normal bell-curve distribution, at least at the two tails. One hopeful thought: you are undoubtedly counting TRADES not mark-to-market end-of-day equity which is what that equation presumes. :-) PS: Someone asked me to explain the statistical jargon better. Sigma basically means standard deviation. The average daily return on the S&P is around 0.03% and the standard deviation of that return (a measure of variability) is 0.98% (read: a lot of volatility for very little average return). A 6-sigma loss would be a day when the market loses 0.03 - (6 x 0.98) = 5.85%. Do the compound return calculation on that 003% gain and you get the 8% average return (slope of the equity line) of the market over the long haul (assuming no change in market characteristic!) -- if you can stomach the fluctuations in the short term. In comparison, the ARM4-Margin port has an MONTHLY average return of 5 with an SD of 8.87 (I haven't calculated it on daily) meaning that 95% of the time (in theory, at least), the monthly return should be between +/- 2 Sigma or -13% and +23%. That's over a 7-year period...it can be much different in a shorter timeframe, of course. | |
