Mutual Fund Price

This is a very basic question, I'm surprised I haven't thought of it before. The market price of a mutual fund, is it determined by the demand of those wanting to buy it (as is a stock)? Or is determined
by the cost of the individual stocks within it (some sort of mathematical additon/division/formula reflecting the actual value of the stocks in the fund)?
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That's the case for a "closed-end mutual fund". The CEF has a fixed number of shares outstanding and the market forces of supply and demand keeps the sum value of all those shares somewhere in the area of the value of the underlying portfolio, but not exactly at it - which is why they trade at a discount or premium.

"open ended mutual funds" (what most folks mean when they refer to a mutual fund) go through a calculation every night - figuring out the value of the portfolio and dividing by the number of shares outstanding to come up with a "NAV" ("Net Asset Value") per share. After they do that, any share purchases and sales from that day are processed at that NAV price. Suppose there are a million shares outstanding and the portfolio is worth $80million dollars. The NAV is now $80/sh. Now, suppose that Bob sent in a check for $8000 and Sam conctacted the fund and asked for a redemption of 50 shares. The fund goes and creates 100 new shares out of thin air for Bob (and the $8000 gets incorporated into the portfolio). Then the fund takes back those 50 shares that Sam redeemed and sends Sam his $4000. Now, the portfolio is worth $80,004,000 and there are 1,000,050 shares outstanding. All the open-ended funds go through this computation, sale and redemption process every night and the number of shares outstanding changes every day. That way, open-ended funds always "trade" (they don't really trade) at NAV.
Closed end funds also compute a NAV every day, but since they don't issue or redeem shares nightly, whatever the NAV is when it trades (in the secondary market), it trades at whatever folks are willing to trade at, sometimes more and most often for less than NAV.
[Some quirks to all that which are ignored above: multiple share classes, extraction of management fees and trading costs, possible sales loads front-end, ongoing, or back-end, the IPO of a CEF, etc. etc. But that's the very simple version]
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Excellently concise answer by Bread.
Just wanted to point out to Iarwain that even in open ended funds the portfolio value is determined by the underlying stocks held in the fund. The value of those stocks is controlled by demand.
So one could say that ALL mutual fund pricing is controlled by investor demand, but not necessarily directly.
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