The emergency fund is the one part of your finances where return is irrelevant. Its function is availability: being intact, reachable within 24 hours, and independent of what the market is doing on the day the boiler breaks or a contract ends.
The usual benchmark is three to six months of expenses, but what actually determines it is the stability of your income. A salaried couple with two incomes can live with three months; a freelancer with one main client should be thinking about nine or twelve.
Its biggest benefit shows up in no spreadsheet: it is what allows the rest of the portfolio to behave like a long-term portfolio. Without a buffer, a $2,000 repair becomes a forced sale or a 20% debt, and that is where money is genuinely lost.