Index Investing Exit Strategy (Fixed-Rate Drawdown Stats)

Monte Carlo simulation of asset paths with fixed-rate 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 simulations (10 ~ 1000)

runs

Withdrawal rate (0.01 ~ 100)

Withdrawal interval (1 ~ 365)

days

You can simulate paths with fixed-rate withdrawals from index assets. We set the initial asset at the start to 1. Set the withdrawal rate and the withdrawal interval. Enter the index's average annual return and risk, then click Calculate. You can also simulate paths with leverage.

From the Monte Carlo runs, we plot yearly statistics. $prob$ is the probability that assets fall below the initial level. We also plot the mode $mode$ and the median $median$. We plot the 95% CI bounds $lower$ and $upper$.

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.

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

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, $C = 1$.