I think about what kind of emergencies could happen to me, and how do I handle each? My E Fund isn't one pile of cash. It's spread across a few accounts.
For one, we have an HSA. The first $2000 of which is cash, the remaining balance is invested. But all of it is for medical emergencies. We pay routine co-pays out of cash flow, and will reimburse ourselves out of the HSA in retirement, treating it like an IRA. But if we had a sudden medical event that eclipsed our ability to use cash flow, we're covered.
Then there is the "stuff happens" fund. This is for the new tires, transmissions, felled trees, bail money (jk) kind of unplanned expenses that only in retrospect are actually irregular life expenses and not genuine emergencies.
We have a HELOC that we would tap for big housing emergencies. I bought my first house the year Andrew hit Florida. I remember news reports about how the homeowners with HELOCs were able to get work started a whole lot sooner than those who had to wait for insurance or FEMA money. So when I could, I protected myself the same way. Now that we have income property, this has proved quite useful. Hurricane Sandy hit my state very hard. I know of a few homeowners who had their insurance money within days, and others who are still waiting. They couldn't use their EF to rebuild because they needed it to rent somewhere else.
Lastly, there is my spouse's IRA. Much of it is cash equivalent. His risk tolerance is different from mine. Our total portfolio is balanced, but his is at least 50% cash. If we had to, we'd draw that down.
Besides natural disasters and medical events, we faced the other likely need for an EF. Job loss.
I had a job loss in 2008 that was unexpected and lasted 13 months. Unemployment benefits covered the mortgage and health insurance, but nothing else. Faced with uncertainty about how long the 2008 market implosion would last, we wanted to ensure our savings and investments lasted as long as possible. I'd thought I was frugal before, but this experience caused me to rethink and challenge assumptions, to see just how little we could live on. Broken appliances didn't get replaced out of the shit happens fund, because we needed that money to eat. 8 years later with a very full economic recovery, we still have not replaced the microwave or dishwasher. No problem. Easy to live without. The other thing we learned was that buying in bulk revealed itself to be a folly for our situation. Do I take money out of the market, at the bottom, to invest it in rice, chicken parts or toilet paper that I won't use for weeks or months? On a small scale, this is trading equities for commodities. Commodities, in the case of perishable foods, that cost money (running a freezer) to own.
Having been an adult thru a few extended market downturns, including the one that took my job, I see what's wrong with thinking index funds will always go up, up, up. They don't. The worst position to be in is to face several unexpected expenses all at once in a market bottom, where not only is the value down, you've also wiped out your own recovery potential.
Finally, and most importantly, my most valuable emergency resource is personal relationships. Friends and extended family members who'll know when i've faced an emergency and help with a chainsaw, shop vac, cash advance, meal or shoulder to cry on. It's not all about the money.