Assume that you initially invested $1,000,000 in the portfolio and that the distribution of the annual rate of return of the portfolio is normal. What is the distribution of the return of the portfolio 20 years after its formation?

If the rate of return is normal distributed for the portfolio, the 20-year distribution will be influenced by a number of external factors like changes in the market and economic conditions. In this case, statistics can be used to determine what proportion of outcomes will fall into certain ranges based on an anticipated mean return rate over time. As an example, let’s assume that a 20-year rate of return of 8% is expected. Then 68% (or all possible outcomes) should fall within a range of 6.2% to 9,8%. This would be a range of 1 standard deviations above and below expected average rate, which means that the majority of investments in this portfolio will have rates similar to each other.

In addition, further extremes outside 2 standard deviations from the mean are also possible but much less likely – only 5% being expected to yield rates lower than 4.4%, while another 5% exceeding 11.6%. However these figures do not necessarily indicate success or failure as there are numerous variables at play when it comes to investing including individual risk tolerance and long-term goals which could ultimately make some higher risk/higher reward ventures more attractive than more consistent returns depending on one’s situation.

Ultimately though, understanding how different portfolios may perform over time is essential for making informed decisions when it comes to investing – especially when dealing with large sums like $1 million dollars. Investors who keep track of trends and establish reasonable expectations on the basis of past performance can reduce their risk while potentially still achieving competitive returns.