How It Works

This page explains the models and assumptions behind every number you see in the simulator.

Beta

Beta measures how much a stock tends to move relative to SPY. A beta of 1.5 means the stock historically moves 1.5× as much as SPY on any given day.

We calculate beta using OLS regression on the last 365 calendar days of daily closing prices:

β = cov(ticker returns, SPY returns) / var(SPY returns)

Beta is cached for 24 hours. If live data is unavailable or there are fewer than 20 overlapping trading days, we fall back to hardcoded estimates (e.g. QQQ = 1.15, TLT = −0.30, GLD = −0.05).

Price Change (%)

The SPY Shock slider sets the assumed drop for the overall market. Each asset's price change is then derived as:

Price Change = SPY Shock × β

For example, if SPY drops 10% and a stock has β = 1.5, the estimated drop is 15%. SPY itself always has Price Change = SPY Shock exactly (β = 1.0 by definition). You can override any asset's Price Change manually in the Impact Estimates table.

Vol Change (%)

The VIX Shock slider sets the assumed percentage change in the VIX index. A VIX Shock of +100% means VIX doubles — e.g. from 20 to 40.

Each asset's Vol Change is also scaled by beta:

Vol Change = VIX Shock × β

VIX itself always uses the VIX Shock directly as its Price Change, since it is a volatility index, not a stock. If you hold a VIX option position, you should manually set the Vol Change for VIX in the Impact Estimates table to reflect your assumption. You can override any asset's Vol Change manually in the Impact Estimates table.

Stock P&L

Stock P&L is straightforward — we apply the price change linearly to the position value:

Position Value = Shares × Current Price
P&L = Position Value × Price Change

Negative share counts are supported for short positions, where the P&L direction reverses.

Option P&L — Black-Scholes Reprice

Options are repriced using the Black-Scholes model in 5 steps:

  1. 1
    Solve current IV — We back-solve the implied volatility from the option's current market price using bisection over [0.001, 5.0] with a tolerance of 0.00001.
  2. 2
    Shock the spot price — The underlying's price is multiplied by (1 + Price Change).
  3. 3
    Shock the IV — The solved IV is multiplied by (1 + Vol Change). A +100% Vol Change doubles the IV.
  4. 4
    Reprice with Black-Scholes — We compute a new option price using the shocked spot and shocked IV, with the same strike, time to expiry, and risk-free rate (3.7%).
  5. 5
    Compute P&L — P&L = (New Price − Old Price) × Contracts × 100. Each contract represents 100 shares.

If the underlying price is unavailable or Black-Scholes fails, we fall back to a linear delta approximation: calls gain value when the underlying rises, puts gain when it falls.

NAV & Summary

NAV = Σ(Shares × Price) + Σ(Contracts × Mark × 100) + Cash
Net P&L = Core P&L + Hedge P&L
% Change = Net P&L / NAV

Core P&L is the sum of all non-hedged positions. Hedge P&L is the sum of all positions marked as hedges. Cash is assumed to be unaffected by any scenario.

Limitations & Assumptions

  • All shocks are applied instantaneously — no path dependency or time decay during the shock.
  • Beta is estimated from historical daily returns and may not reflect current market conditions.
  • Black-Scholes assumes log-normal returns and constant volatility — it does not capture volatility skew or jumps.
  • Time to expiry is calculated from today's date. Option P&L does not include theta decay over time.
  • Risk-free rate is fixed at 3.7% (approximate current T-bill rate).
  • Correlations between assets are not modeled — each position is shocked independently.