| Category | This year | Peak year | Peak | Lifetime total |
|---|---|---|---|---|
| No spending yet. | ||||
| Plan year | Sampled year | Start wealth | Income | Expenses | Withdrawal tax | SPX return | Risk-free | SPX excess | SPX beta | Inflation | SPX real | Portfolio nominal | Portfolio real | End wealth | Home equity | Status |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| No results yet. | ||||||||||||||||
No dynamic policy yet
Set beta mode to Dynamic and run a simulation to inspect the year-by-wealth beta policy.
Optimal SPX beta vs wealth
Beta alternatives
| SPX beta | Run-out risk | Expected terminal wealth | Choice |
|---|---|---|---|
| Run dynamic beta to inspect beta alternatives. | |||
Policy path explorer
Run dynamic beta to inspect a policy path.
| Plan year | Start wealth | Forced beta | Sampled year | SPX return | Inflation | End wealth | Policy beta next | Risk from node |
|---|---|---|---|---|---|---|---|---|
| Run dynamic beta to inspect a policy path. | ||||||||
Historical data
Simulations sample one historical year at a time, with replacement, from the loaded history. Each sampled year supplies an S&P 500 total return, a 3-month T-bill return, and CPI inflation.
Return model
Portfolio nominal return is the T-bill return plus SPX beta times the S&P 500 excess return over T-bills. It is converted to current dollars by dividing by that year's inflation factor.
Dynamic beta
Backward dynamic programming over plan year and wealth, using a zero bucket plus 180 log-spaced buckets from $10K to $1T and betas from 0.0 to 1.5 in 0.1 steps. The solver builds several candidate policies, from minimum run-out risk to maximum expected wealth, with risk-penalty policies in between. The beta for a year is chosen before that year's return is drawn.
Frontier
Each dynamic run also solves the policy with scenario-calibrated risk penalties. Every resulting policy is simulated from your net worth on the same 10,000 extra paths, and the chart plots its expected and median terminal wealth against its run-out risk. Expected wealth is pulled up by a few very good paths; the median is the typical outcome. The run uses the policy with the most median wealth among those whose run-out risk is at most 0.5% or the lowest any policy reaches: below 0.5%, less risk isn't worth giving up wealth for.
How much you need
After each run, 20,000 extra paths of historical years are drawn. For each one, a bisection finds the least starting net worth that survives it under the same policy and cash flows. The share of paths whose threshold is above an amount is the run-out risk at that amount, so the needed net worth for a target risk is a percentile of the thresholds.
Home
An owned home is an asset: its value grows at the plan's real appreciation rate and its equity (value less mortgage) counts toward net worth and terminal wealth. If a path's portfolio would run out, the home is sold that year for its value less 6% selling costs and the mortgage, its costs stop, and rent at 4% of its value starts. Run-out risk means running out even after selling. The beta policy knows about the sale: it is solved first for life after a sale and then for owning, so it can take more stock risk while the home backs the portfolio. Mortgage payments and balances shrink with an assumed 2.5% inflation.
Taxes
Income is entered after tax. Spending that income doesn't cover is withdrawn from the portfolio, and selling costs tax on the gains: covering a shortfall S at the plan's withdrawal tax rate t takes S / (1 − t). The default 15% approximates California taxes on a taxable account where about 60% of each sale is gain. Dividends taxed while invested, account types, and borrowing against the portfolio are not modeled.
Lifestyle builder
The builder prices a described lifestyle as dated annual expenses in today's dollars. Kid costs follow each kid's age: childcare to 4, school 5–17, college 18–21. Local costs (childcare, school, help, everyday living) are priced for SF/NYC and scaled down for cheaper areas. Every line can be overridden or moved to a manual row. Above-inflation cost growth is not modeled; taxes are handled by the plan's withdrawal tax.
Cash flows
Income and expenditures are annual current-dollar flows. Start and end years can be fixed or tied to the plan's current year and year of death. Lifestyle lines use fixed years; one-time costs such as a home purchase are a single-year flow.
Timing
Within each year, returns compound continuously and net cash flow arrives continuously. A path is depleted when current-dollar wealth reaches zero.
Limits
This is a historical bootstrap, not a forecast. It ignores taxes, account types, fees, allocation beyond SPX beta, spending adjustments, serial correlation between years, and valuation-based expected returns.