The fund does nothing. Certain big players are allowed to either add buckets of Bitcoin to the fund in exchange for shares or redeem shares in exchange for Bitcoins. Whenever the price of the fund doesn't match the price of Bitcoin in the overall market this will be an opportunity for arbitrage for these players. We let the free market do the rest and presto, the price will follow the market price with a very narrow error margin.
Ok, thats basically like another exchange and every buy in the ETF equals a buy on a regular exchange.
No it doesn't. The shares are traded and can go up in value. If the value of a share is larger than the value of 0.2 BTC and there is sufficient liquidity a market maker will arbitrage, buy a number of Bitcoins (with the number as defined basket size in the filing) send these to the fund and will in exchange get new shares. Subsequently it can sell these shares on the open market making money (remember the shares were trading above the value for Bitcoin on the open market).
1 share in the fund will always represent 0.2 BTC (unless they do a share split) and if more Bitcoin are deposited into the fund more shares will be given out (without diluting shareholders!). Reversely, a market maker can also buy shares in COIN and subsequently redeem these in exchange for the underlying Bitcoins (also per basket). It will do so when the market price of COIN is below that of Bitcoin (and subsequently they can sell the received Bitcoins on the open market to complete the arbitrage cycle).
If the price of COIN was above 1/5 the price of BTC then people would buy BTC on the exchanges in anticipation of APs buying bitcoin with the intention of redeeming it for COIN and selling the COIN on the market.