This tool implements a Monte-Carlo-Estimation based on randomized/empiric ETF (e.g. MSCI World) growth rates to estimate the profit given a monthly saving rate and an investment horizon.
Have you ever ask how much money you can earn through a monthly saving rate after a specified time? - This algorithm is an easy-to-understand-approach to estimate possible returns and compare it to a naive intrest-based investment.
Basically, the capital is build through a monthly saving rate. Profits of an investment rely on anual fluctuations of a choosen stock share. The development of the economy can be considered as a random process. The corresponding random variable is anually drawn from a distribution. The current implementations supports two approaches:
- An uniform distribution between a lower expected value of economic growth (hyperparameter) and an upper value of economic growth. The latter one is computed by an expected anual growth rate (further hyperparameter).
- A empiric Weibull-distribution is computed based on transformed historic data of the economy.
The anual drawing of the growth rate as a random variable renders the observed return at the investment horizon a random variable itself. Rather than analytically estimate the expected return, a Monte-Carlo-Estimation is suggested. In simple words, the returns based on drawings of the the growth rates are computed various times and corresponding statistics are provided. This outcomes can be compared to a intrest-based investment for compromise.
Figure (1) illustrates a single investment simulation. The initial capital was 1000.0 € with a monthly saving rate of 100.0 €. Further hyperparameter can be found in the main.py file. The left subplot illustrates the investment over time compared to a basline approach. The right subplot depicts the anual growth rate that was drawn during simulation.
Figure (2) summarizes the returns, if the random process of figure (1) is realized 10000 times. The left plot contains the actual value of the investment and the right figure states the relative profit referenced to the intrest-based investment.