The emergency fund covers stochastic shocks. Known lumps — payments predictable in both amount and date but irregular in cadence — are a separate liquidity problem with a separate solution. The mechanism is the sinking fund: for each upcoming lump, buy a US Treasury bill (or short Treasury note) whose maturity falls a week before the payment date. The principal earns state-tax-exempt yield (section “Consider Taxation”) from the day you fund it through the week before the bill is due, then matures into cash exactly when you need it. No market timing, no liquidity surprise, no commingling with the emergency tier.
The argument against checking-account pre-funding is arithmetic. A California household that keeps a $300,000 perpetual tax reserve sitting in checking is leaving roughly $300,000 2.5% $7,500 a year of after-tax yield on the table — recoverable for the price of opening a TreasuryDirect account or laddering through the brokerage. Scale that across quarterly taxes, annual insurance premiums, semi-annual tuition, and contingent capital calls, and the recovered yield runs into five figures a year for a typical high-income household.