What returns and risks can we expect from the S&P 500 in 10 years?

The average annual return of the US stock market since the 1930s has been 9.5% per annum. The risk, which is measured by mean square/standard deviation (sigma), was 19.5%. That is, according to statistics, in a year we can expect that with a probability of 68% (1 sigma) the market return will be in the range from -10% to 29%. Or there is a 99.7% (3 sigma) probability that the expected return will remain in the 3 sigma range or -49% to +68%.

And if you calculate the same thing, but for a 10-year period. What will be the expected return and risk?

Profitability is calculated simply. (1+0.095)^10=2.48 or 148%.
For risk, you just want to take and multiply 19.5% * 10 years * 3 sigma = 585%. That is, to determine the range of profitability in 10 years, you need to add 585% to 148% (upper limit) and subtract 585% from 148% (lower limit).
But this is an extremely high risk and wrong approach to calculation!

The correct method is actually to multiply 19.5% by the square root of 10. This results in a correct near-maximum range of expected returns in 10 years – -38% to 333%. According to theory, the index will get here with a probability of 99.7%.

When independent distributions are joined together, the variances of each distribution can be successfully added, but their standard deviations cannot be added because the standard deviation is the square root of the variance. Thus, the standard deviation of the long-term probability distribution increases with the square root of time.

If we omit the technical details of the calculation, the graph shows that the lower limit of the range of expected returns increases with increasing duration of the investment period. And by the end of the 13-year period it approaches zero. The return is 0% for 13 years (!), but this is only the lower limit of the range, where the average return is above 200%.

(note: 0% interest yield for 13 years has only occurred once – when buying the market in 1929)

The main conclusion is the following. Regardless of the investment approach you choose – active or passive – the longer the time horizon of your stock investments, the higher the likelihood of achieving a positive return.

Post “Why stocks always go up” Here: https://t.me/TradPhronesis/128

Investing (investing in stocks for a year or more) is a positive sum game. And sooner or later, no matter what crisis happens, the influx of money into the system called the “Share Market” will provide positive returns.

Thanks for “likes!

Visit the telegram channel: https://t.me/TradPhronesis