As in the case of Bitcoin's hard fork Bitcoin Cash, what determines the value of the forked currency?
Say before the fork I had X BTC; then now after the fork I have X BTC and X BCH. What does affect the value of my X BTC? What does affect the value of my X BCH? What does determine the market caps of both currencies? Is it a group of big backers that come to an agreement on shifting their assets to the forked currency? Can you think of it (in the bigger picture) as: post_fork_BTC_market_cap = pre_fork_BTC_market_cap - initial_BCH_market_cap? Or otherwise the forked currency's market cap is "imported" from a combination of different market caps?
Note: I used Bitcoin and Bitcoin Cash as an example, without loss of generality.
Another approach that comes to my mind is to think of it as an ICO funding. Let's say that there is currently a circulating supply of 800,000 FOO (Foocoin), and now I'm creating a fork of Foocoin called Barcoin (BAR). I funded 200,000 FOO for this purpose at an exchange rate of 1 FOO = 500 BAR, so the initial circulating supply of Barcoin is 800,000 + 200,000 * 500 BAR = 100,800,000 BAR, so that eventually each one of the funders has lost some value, while each one of the FOO holders has gained some value in the form of an "airdrop".
For example someone who had ~2000 FOO now also has ~2000 BAR that equal to ~4 FOO; this is without correlation to the market cap of FOO. But if this person funded Barcoin using Foocoin, then it is resulted in less profit out of the fork. But then nobody will fund this project unless it's completely necessary from the person's viewpoint.
Is it something like this?