How is value forked? If a blockchain is forked, is it's value also forked? Isn't that a doubling of value overall?
: pre-fork BTC is worth USD 4000,- BCH forks off and is evaluated at USD 1000,-,
What do you mean it is evaluated? who evaluates it? I mean if anything splits it's value is halved. Are you saying at the instant of spliting, the value is halved and then corrects itself based on what people decide to do with either of the coins? or is the value of the new coin zero and then builds up based on how many people ....... did what?
A fork is just the creation of a new altcoin. It is only called a fork because the altcoin happens to share some historical data, but that doesn't change the fact that it is an entirely new thing.
As such, the forked coin obtains value in the same way that any altcoin gains value (from the willingness of individuals to pay for it).
Asking if "at the instant of spliting, the value is halved and then corrects itself" or if "the value of the new coin zero and then builds up" are meaningless questions. They are just two different ways of saying the same thing.
Prior to the fork, there is one coin. That coin has an exchange rate that is determined by people willing to exchange other things of value for that coin.
After the fork, there are two coins. Each coin has an exchange rate that is determined by people willing to exchange other things of value for either of those coins.
Imagine you are manufacturing hammers with wooden handles, and are selling them. You have found that people are willing to spend $1 for one of your hammers. Now imagine that one day after you have been in business for a while, I use some wood from the same forest to manufacture and sell screwdrivers. Some people that might have bought your hammers, but don't have enough money for BOTH a hammer AND screwdriver may choose to buy my screwdrivers instead of your hammers. As such, there is a bit less demand for your hammers, and there is sudden demand for my screwdrivers that didn't exist when I wasn't making them. You quickly discover that (given your large supply and the decrease in demand) people are only willing to spend $0.90 for your hammers. Meanwhile, I find that my screw drivers are useful enough that demand has driven the price up to $0.80 each.
What happened here when I started selling screwdrivers? Did the "tool" market SPLIT and each of our tools was instantly worth $0.50 (even though neither of us EVER sold a tool for less than $0.80) which then corrected itself? Or were my screwdrivers valued at zero and then instantly built up to $0.80?
It would seem more accurate to say that a new tool was created. It had it's own value to the population, and that the changes in the market had an overall effect on the exchange rate for your tool.
Note that the creation of new tools, or coins, aren't the only changes in the market that can effect exchange rate. The creation of a new coin (or tool) is only one of billions of variables that drive individuals to be willing to make a purchase decision. Some of the variables that have a large effect are things like good or bad news, usefulness, marketing, competing products, etc. But the decision of any single individual to buy or sell at a given price can also be effected by things as simple as how long ago they ate their last meal, what time of day it is, what the weather is like, who they talked to last, etc.