I don't see how this contradicts my point. If anything, you're providing evidence for it. You'd rather lock-in a loss, to avoid an admittedly small chance of an equal loss. If the opportunity cost seems nil, then so should the risk you're trying to mitigate.
Whether these "losses" are equal depends on when the emergency takes place and where the market is at that time - both unknowable. I would rather give up a small return each year for the confidence that I'm not forced to liquidate positions when it isn't favorable to do so. Half of my emergency fund is in VFSTX and included in my bond allocation. It's not in a savings account, it yields 1.75%, and it also serves to mitigate sequence of returns risk - i can spend it for regular expenses if I don't want to sell equities.
The consideration the OP needs to make is what happens if the market tanks next year and an emergency requiring $10K arises. This is the basic rationale for maintaining an emergency fund. Weigh that against opportunity cost, not projected returns for >10 years.
Seriously, it's just math. I choose 10 years to keep the math easy, but here's the year 2000-current. A historically bad time for stocks. Left side is 100% stocks, right side is a 1% savings account:
Scenario A: We put $100 in our Emergency Fund, and have a $50 emergency in 2008.
Balance during emergency: $26 for stocks, $59 for savings account. A relative difference of $33 in favor of the savings account.
Balance today: $70 for stocks, $64 for savings account. A relative difference of $6 in favor of stocks.
Scenario B: We put $100 in our Emergency Fund, and have no emergencies.
Balance today: $207 for stocks, $117 for savings account. A relative difference of $90 in favor of stocks.
Scenario C: We put $100 in our Emergency Fund, and have a $50 emergency in 2002, and another $50 emergency in 2008.
Balance during 2002 emergency: $13 for stocks, $53 for savings account. A relative difference of $40 in favor of the savings account.
Balance during 2008 emergency: -$34 for stocks, $6 for savings account. A relative difference of $40 in favor of the savings account.
We remove $100 from our portfolio to replenish the Emergency Fund.
Balance today: $118 for stocks, $113 for savings account. A relative difference of $5 in favor of stocks.
"You'd rather lock-in a
50% loss (by going with the savings account in the almost-certain Scenario B), to avoid an admittedly small chance of only
earning 5% (worst-case scenario C with stocks)?"
Even if we only look at the balance during an emergency, the savings account is only up $40. So you're locking in an almost certain loss of $90, so you can avoid the temporary loss of $40? There is no mathematical justification I can see. Only an emotional one.