Tax-Loss Harvesting Savings Estimator

Model: Geometric Brownian Motion (GBM), the standard continuous-time model for stock prices, same foundation as Black-Scholes.

Each lot's daily price follows: S(t+1) = S(t) × exp((μ - σ²/2)Δt + σ√Δt × Z) where Z ~ N(0,1), μ = expected annual return, σ = annual volatility, Δt = 1/252.

Dollar-cost averaging: Your annual investment is divided into equal lots purchased at evenly-spaced intervals throughout each year. Later purchases have fewer trading days remaining to generate harvestable losses within that year.

Simulation steps (per trial):

1. Each year, new lots enter at regular intervals via dollar-cost averaging.
2. Lots from previous years carry forward with their current price and cost basis.
3. Simulate 252 trading days of price movement for all active lots independently.
4. On each day, check if any lot's price is below its cost basis by more than the harvest threshold.
5. If so, harvest the loss, reset the lot's cost basis to the current price.
6. Each lot can only be harvested once per 31-day wash sale window.
7. Sum all harvested losses for the year, multiply by tax rate = tax savings for that year.

Multi-year dynamics: As lots accumulate over years, there are more harvesting opportunities. However, previously harvested lots have lower cost bases, making them harder to harvest again. New DCA lots enter fresh each year at cost basis.

Simplifications: All lots assumed equal size and independent price paths (no correlation between lots of the same security). Each lot starts at cost basis. Wash sale window simplified to a 31-day cooldown per lot. Does not model cost-basis reduction on repurchase (deferred tax, not eliminated). Long-term vs short-term rate distinction not modeled.

What this tells you: This estimates the gross tax benefit from actively harvesting. The actual long-term benefit is lower because harvesting reduces future cost basis. Think of it as a tax deferral with time-value-of-money benefit, not a permanent tax elimination.