Index Investment Return

This page performs a Monte Carlo simulation of index investment returns. The x-axis represents the number of years, and the y-axis shows the change in index return over time.

Average Annual Return (0.01 ~ 50)

Risk (0.01 ~ 50)

Leverage (0.01 ~ 5)

Maximum Number of Years (1 ~ 50)

years

Number of Patterns (1 ~ 50)

patterns

Please enter the average annual return and risk of the index you are interested in. Press the calculate button. You can also simulate returns with leverage.

Monte Carlo Simulation Formula

Return $S_t$ from time $t-1$ to $t$ is simulated using the following formula.

$$ S_t = S_{t-1} \exp { \left( \left( L \mu - 0.5 L^2 \mu ^2 \right) \delta t + \epsilon \sqrt{ \delta t } L \sigma \right) } $$

where $\mu$ is the average annual return, $\sigma$ is the risk, and $L$ is the leverage. $\epsilon$ is a normally distributed random variable with mean 0 and standard deviation 1.