My latest system, which i am currently trading live, averages 40% a year in backtesting. The largest drawdown was 13%. The standard deviation of yearly returns is 20%. This would indicate the yearly return range as -20% to +100%, based on 3 standard deviations from the average. However in the backtest the yearly range was +6% to +88%. There were no negative years as the back test was less than 20 years long. If I were to trade for long enough i am sure this system would produce a negative year at some point. An average year (40%),12 months, taken from the backtest: +0.4% +6.6% +1.1% -3.6% +8.1% +6.7% +9.0% -0.4% +5.0% +1.7% -2.8% +7.8% A very poor year (6%): -1.3 +0.7 +1.7 +6.1 +2.2 +2.0 +2.3 -3.9 +3.2 +4.3 -5.7 -5.2 A much better than average year (69%): +8.3 +3.0 +16.8 +7.6 +4.5 +1.2 -3.6 +11.4 +0.6 +4.8 +7.3 +6.9 Monthly returns typically range between -8% and +20%, with about 70% of months being profitable. Drawdowns can last over 6 months. So over the next 12 months, how much can i expect to make? The answer, based on the above statistics, is anywhere between -20% to +100%. I have a 50% chance of making over 40% but also a 50% chance of making less than 40%. (The above returns are based on 1% risk sizing, if I risk 2% per trade, all those figures above would double, and if i risk 0.5% then halved. I have also ignored compounding and used a simple yearly return in the above figures)
I get the impression that you assume the bell curve of results to be symmetrical. It could be helpful to investigate the skewness of the histogram of annual results. That might explain the difference between the estimated worst case of -20% and the observed worse case of +6%. Same for the maxima 100% versus 88%.
No. Not only did you ignore compounding, but more importantly, you ignored "I.I.D." conditions -- which is to say, your eventual returns will depend on the sequence of events, because the individual events in your trading account's calendar are most certainly linked to the events which preceded them. Ouchie! The bell curve was built without memory; the market definitely knows where it was yesterday, cuz it's where today started. Yo.
It is the 2008 period which skews the returns at the top end Without 2008 the yearly returns would be much more symmetrical. So the back test period includes an upside outlier, 2008, but perhaps it didn't include a downside outlier. Therefore i am assuming a negative year might happen, e.g. -10% and that would balance out 2008. A down year is certainly possible. The longest drawdown in the backtest was 8 months so i think a 12+ month drawdown (i.e. a down year) is not impossible.
The key question is what drives price fluctuations and therefore identifying key factors that determine prices is the first step before testing performances ... Merely backtesting time series data is not going to work.
Also, of course, distribution of market returns is not stationary, what makes you believe the patterns you trade on are? Depends on how you came up with your trading system, how many degrees of freedom/parameters, data snooping, ..
Yes. I have a trading method/model. This comes from market observations. Then i back test the method to get an idea which parameter values work well, being very careful not to over fit. Back testing also provides an idea of the stats, win %, range and stdev of daily/monthly/yearly returns. I am just trying to get a ballpark for the stats on the system. Perhaps the system edge will degrade going forward but then again perhaps it will hold up well for the next 10 years. If it degrades the hope is it will degrade slowly over time and not just stop working one day with zero profit expectation from that day onwards.
Having only about 20 data points (annual results) might be insufficient to say something meaningful about the statistics. The amount of observations might be too small for this. You could try to break it up in monthly or quarterly results and see whether you get more meaningful statistical information.