Beta alternatives
| Optimal SPX beta | Estimated depletion risk | Expected terminal wealth | Optimal choice |
|---|---|---|---|
| Run dynamic beta to inspect beta alternatives. | |||
Optimal SPX beta vs current wealth
Policy path explorer
Run dynamic beta to inspect a policy path.
| Plan year | Start wealth | Forced beta | Sampled year | SPX return | Inflation | End wealth | Optimal SPX beta next | Risk from node |
|---|---|---|---|---|---|---|---|---|
| Run dynamic beta to inspect a policy path. | ||||||||
| Plan year | Sampled year | Start wealth | Income | Expenses | SPX return | Risk-free | SPX excess | SPX beta used | Inflation | SPX real return | Portfolio nominal return | Portfolio real return | End wealth | Status |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| No results yet. | ||||||||||||||
Historical Data
Fixed-beta and dynamic-beta simulations sample one historical year at a time from 1950-2025. Dynamic beta chooses each year's beta before that year's return is drawn.
Return Model
Portfolio nominal return is the sampled T-bill return plus SPX beta times the sampled S&P 500 excess return over T-bills, then converted into current dollars by dividing by that year's inflation factor. Dynamic beta chooses from 0.0 to 1.5 in 0.1 steps.
Dynamic Beta
Dynamic mode builds a backward dynamic-programming policy over plan year and current wealth. It uses a zero bucket plus 180 log-spaced positive wealth buckets from $10,000 to $1 trillion, picks the beta with the lowest estimated depletion probability, then breaks ties by highest expected terminal wealth. The Dynamic Beta Frontier tab can run a separate scenario-calibrated risk-penalty sweep by expected terminal wealth and run-out probability. Inspect Beta Policy shows per-beta alternatives, a visible wealth bucket plot through $1 billion, and a forced-beta path explorer.
Cash Flows
Income and expenditure amounts are treated as annual current-dollar flows. Start and end years can be fixed or tied to the plan's current year and expected year of death.
Timing
Within each simulated year, returns compound continuously and net cash flow is spread continuously through the year. Depletion occurs when current-dollar wealth reaches zero or below.
Charts
The depletion-year chart shows probability across all simulations. The overview charts show expected current-dollar wealth, average SPX beta, and downsampled paths for hover inspection. Dynamic-beta runs expose the scenario-level beta alternatives, visible wealth buckets, and recommended beta by year in Inspect Beta Policy.
Limits
The model is a historical bootstrap, not a forecast. It does not model taxes, account types, asset allocation beyond SPX beta, fees, changing spending behavior, sequence constraints, or valuation-based expected returns.