I've posted on this before, but I see no reason to keep 'emergency money' in a low interest, 'dollar certain' account. The key is liquidity and access. If you set up for electronic transfers with your broker or fund manager, transfers are fast and easy. Many funds allow check writing for checks >$500 or whatever. Sign up.
I do keep a couple months expenses in my checking/savings account, just for simplicity, and if I had some 'oopps' moment, the money is right there.
Sure maybe the fund will be down a smidgen when you need to draw on it. That's life, but if you are investing at all that means you count on the long term appreciation of assets. So why treat this money differently? Your emergency is unlikely to be exactly $4,000.01, there just is no 'magic' to a dollar-certain figure. With the added growth, that fund will be bigger and able to handle bigger emergencies. Keep it growing.
OK, this assumes you have investments to begin with. If that $4,000 is a large part of your liquid net worth, I cans see not wanting to 'risk' any of it. But beyond that, I think of it as one big pile of money, investment/safety-wise. I don't know if your "only have" comment referred to this account, or total portfolio.