A cash emergency fund is there to help you weather financial storms, that's its sole purpose.

I have a six figure US stock position and I'm not going to change anything I do as long as I remain employed. Save for retirement/long term in the stock market, save for big ticket items in cash (I have a new car fund, for example). If I lose my job I'll have to stop contributions until I get another job. If I remain unemployed longer term I'd have to tighten my belt on frivolous purchases.