For now the truth is most altcoins are pegged to Bitcoin. If the Bitcoin price is going up rapidly, then people holding altcoins will probably sell them in order to move their money to Bitcoin and ride that wave. This means – in turn – that the price of altcoins probably will go down when the price of Bitcoin goes up rapidly. However, the price of altcoins will most likely also go down when the price of Bitcoin goes down, as the holders of altcoins then exit such altcoins to go back into fiat. Accordingly, if Bitcoins value would depreciate and go down to zero, that would presumably also be the case for other coins.