Since the 1930s, the average return on the US stock market has been 9.5% per annum. The risk, measured by root mean square / standard deviation (sigma), was 19.6%. Therefore, according to statistics, the 1 year forecast with 1 sigma probability (68%) is that the market profitability will fall within the range of -10% to 29%. The 3 sigma (99.7%) probability expected return will remain in the -49% to + 68% range. Now let’s count the expected returns and risks for the 10 year period the same way. And if you count the same thing, but for a 10 year period. The yield can simply be calculated as (1 + 0.095) ^ 10 = 2.48 or 148%. For risk, it seems that all you have to do is multiply the annual 19.5% * 10 years * 3 sigma = 585%. That is, to determine the range of returns in 10 years, you need to add 585% (upper limit) to 148% and subtract 585% (lower limit) from 148%. However, is this how we should really calculate our risks? No. The correct method is to multiply 19.5% by the square root of 10. This leads to the correct near-maximum range of expected returns in 10 years, from -38% to 333%. Theoretically, the index will stay within those limits with a probability of 99.7%. When you put these independent calculations together, the variances of each distribution can be successfully added up to one another. However, their standard deviations cannot be added up. The standard deviation is the square root of variance. Thus, the standard deviation of the long-term probability distribution increases as a proportion to the square root of time. If we omit the technical details of the calculation, the graph shows that the lower expected profitability range increases with the investment period duration. By the end of the 13-year period, it is approaching zero. The return is 0% over 13 years, but this is only the lower end of the range, whereas the average return is above 200%. Let me remind you that there were only 2 times when the yield was 0% within a 13 year period since 1928. Let me wrap this up. Regardless of whether you choose an active or a passive approach to investing, the longer your time horizon, the more likely you will get a positive return. Investing is a positive-sum game. Sooner or later, whatever the crisis, the stock market money flow will eventually generate a positive return.
I know you can forecast future probability of which way the markets could possibly trade, but what if things were to change significantly in the next week and carry on for a period of time, how long would those significant changes have to hold, for the numbers you represented to change dramatically??
This question has no easy answer because probability calculations are always based on past data. If you take one part of that data and change it, by duration or weight, you get different results. The longer the timeframe of calculation, the fewer influences it has because it gets broader with time. The harder fluctuation of the data, the bigger the chance it does influence longer-term probability. So any data point has a tipping point where it influences the end results.
"Since the 1930s, the average return on the US stock market has been 9.5% per annum. ... Regardless of whether you choose an active or a passive approach to investing, the longer your time horizon, the more likely you will get a positive return. Investing is a positive-sum game." If this defined by using the Dow and its (just like all other indices) survivorship bias than of course it will be a long term positive-sum game by definition.