Why do we need an emergency fund beyond one month if we have a brokerage account?
I’ve always had a hard time psychologically keeping a large cash emergency fund beyond about one month of expenses. It feels difficult to accept earning ~3% in a money market fund when historically the S&P 500 has returned closer to ~10% annually over the long run.
So I’m trying to understand why it’s commonly recommended to keep 6–12 months of expenses in cash before investing heavily.
For example, in my taxable brokerage account I hold a large amount of SPY accumulated over time. If an emergency happens, why wouldn’t it make more sense to simply sell some shares when needed? The cash settles within a couple of days. Even if I pay 15% long-term capital gains tax, the after-tax expected return still seems much better than parking a large amount in cash for years.
I do understand the sequence-of-returns risk, meaning the market could be down exactly when I need the money. But historically, the S&P 500 has been positive more often than negative over multi-year periods. Because of that, keeping a full year of expenses permanently out of the market sometimes feels irrational to me, especially if that money may sit unused for many years.
Am I underestimating some major risk here? Can someone walk through the math or probabilities and explain why a large emergency fund is still considered optimal despite the long-term return difference?