Index Investing Exit Strategy (Fixed-Amount Withdrawals)

Monte Carlo simulation of assets with constant withdrawals from index investments.

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

Initial assets (1 ~ 1,000,000,000)

dollars

Withdrawal amount (1 ~ 1,000,000,000)

dollars

Withdrawal interval (1 ~ 365)

days

Simulate asset paths with constant withdrawals from index investments. Set initial assets, withdrawal amount, and interval at the start. Enter the index's average annual return and risk, then click Calculate. You can also simulate paths with leverage. Use this as a reference when planning your exit strategy.

Monte Carlo Simulation Formula

We simulate the return $S_t$ from time $t-1$ to $t$ using the formula below.

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

Here, $\mu$ is the average annual return, $\sigma$ is the risk, and $L$ is the leverage. $\epsilon$ is a random variable with mean 0 and standard deviation 1, normally distributed. $C$ adjusts for withdrawals. If $t$ is a withdrawal time, $C$ equals the withdrawal amount. Otherwise, $C = 0$.