You have $100k. Put all of it in the stock market. The stock market drops by 40%, your investment is worth $60k and you withdraw $20k. The market goes back to 100% and now you have $67k in your portfolio.

If the market dropped by 80% your portfolio would be gone entirely. Meanwhile if you had enough emergency funds you would have kept everything.

The worse the emergency, the higher the ROI of the emergency fund. Since there is no upper bound for how bad an emergency can be the theoretical ROI of an emergency fund is also unbounded.

In this comment the definition of an emergency is a stock market drop combined with unexpected unemployment.