Exit Strategy for Index Investing (Fixed-Rate Withdrawals)

Monte Carlo simulation of asset paths when withdrawing a fixed rate from index savings.

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 rate (0.01 ~ 100)

Withdrawal interval (1 ~ 365)

days

Simulate assets when you withdraw a fixed rate from index investments. Set the initial assets, withdrawal rate, and withdrawal interval at start. Enter the index's average annual return and risk, then click Calculate. You can also simulate paths with leverage. Use this as a guide 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.

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

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, $C = 1 - r$, where $r$ is the rate. Otherwise, $C = 1$.