Inputs
$
Initial portfolio value at Year 0.
$
Returns Source
Comma-separated annual returns in percent. Presets are illustrative only; for authoritative data, paste the actual historical series you prefer.
Lognormal interprets inputs as target arithmetic mean and stdev of R and solves parameters of ln(1+R) accordingly.
Sequence & Monte Carlo
Floor
Cap
Results & Chart
Final (nominal): $—
Final (real): $—
Lines: base random, ascending, descending, median.
Shaded bands: configurable percentiles from Monte Carlo distribution at each year.
Example Data Table (Base Scenario)
| Year | Return % | Cashflow | End Balance | End Balance (Real) |
|---|
Tip: Click Run Simulation, then export the table below.
Formulas Used
Let Bt be beginning balance in year t, annual net cashflow Ct (positive = contribution, negative = withdrawal), nominal return rt, annual fee f (as decimal), and CPI inflation π.
- Net return after fees: r't = rt − f (approx). Alternatively, (1+rt)(1−f)−1.
- Cashflow timing:
- Beginning: Bt ← Bt + Ct, then grow by (1 + r't).
- End: Grow first, then EndBalance ← Bt(1+r't) + Ct.
- Inflation-indexed cashflows: Ct = C0(1+π)t if indexing enabled; else Ct = C0.
- Real balances: Btreal = Bt / (1+π)t.
- Monte Carlo bands derived from simulated path distribution at each t.
- Lognormal option: if X=1+R ~ LogNormal(m,s²), parameters from target arithmetic mean μ and stdev σ are s² = ln( σ² / (1+μ)² + 1 ), m = ln(1+μ) − s²/2.
How to Use
- Enter a starting balance, horizon in years, and annual cashflow (positive to add, negative to withdraw).
- Choose cashflow timing and whether to index cashflows to inflation.
- Use a preset to populate the custom returns box or paste your own series; or switch to statistical mode to draw from Normal or Lognormal.
- Set fees, inflation, Monte Carlo runs, cap/floor, and a seed for reproducibility.
- Click Run Simulation. Compare base random, ascending, descending, and median lines; enable extra percentile bands as desired.
- Review the table, then export to CSV or PDF.
FAQs
It’s the risk that the order of annual returns changes outcomes when you’re adding to or withdrawing from a portfolio. Identical averages can lead to very different balances.
During withdrawals, poor early returns can permanently impair the portfolio. During contributions, strong early returns help more. Context matters.
They are illustrative sequences to demonstrate timing effects. For authoritative analysis, paste historical total returns from your preferred source into the custom box.
When you want to forbid returns below −100% and better approximate multiplicative compounding. Inputs are target arithmetic mean and stdev of R; parameters of ln(1+R) are solved internally.
They provide additional confidence intervals such as 10–90% or 40–60%, letting you visualize uncertainty at different levels around the median path.
Yes. A per‑year cap/floor is applied to each simulated return after fees, which helps avoid unrealistic extremes in Normal mode.
Set a fixed random seed. Changing only the seed reshuffles Monte Carlo paths while preserving all other settings.