Of course, bad news would drive the traders to trade the stock at a lower price, but theoretically, if the traders didn't bother, can the stock price stay at the same value?
Traders = every market participant. Not some shadow figure that excludes you just because you passively drop cash into a 401k Vanguard fund every paycheck.
So yes, if everyone stopped trading then the price won't move. Trades are 100% responsible for the prices you see on charts and tickers.
A stock won't be worth "$100" if nobody ever traded $100 for it. It only has that price now or in the past because somebody placed an order for it at $100 and somebody else filled that order at $100
When people talk about "the price" of a stock, they usually mean one of the following:
Last price: The price at which a trade most recently took place. If someone sold (and someone else bought) shares of XYZ for $20 each, then until another trade occurs, the last price of the stock will be quoted at $20.
Bid price: The highest price at which someone is currently offering to buy the stock.
Ask price: The lowest price at which someone is currently offering to sell the stock.
As you can see, all of these are completely determined by the people buying and selling the stock.
Value is the key word here.
Traders should ideally trade on the perceived future value of a company. Changes in the perceived future value is what leads them to buy and sell shares.
That said, if a company were to have some catastrophe happen (say it and all of its employees and property disappeared) and somehow every shareholder agreed to not sell, the companies market capitalization would remain unmoved even though the value of the company is gone.
So theoretically yes, but it is unlikely.
Yes, the value of a stock is completely, 100% determined by what people are willing to pay for it in conjunction with what people who have it are willing to sell it for.
If something really bad happened to a company, like their only factory burned to the ground, and the traders didn't care, then I guess, in that scenario, the value of the stock would not change.
But you can spin all sorts of hypotheticals of that sort. If dogs could talk, would German Shepherds speak German? Etc. Any answer is pretty meaningless because the premise is wildly unlikely.
As CQM notes, "traders" in this context means everyone who buys or sells stock. If you buy stock, that includes you. They're not some mystical cabal somewhere. If you see a stock listed at, whatever, $50, and you are not willing to pay more than $40 for it, then you refuse to buy, and so you tend to force the price down. If you're not a billionaire, then your impact on the market is tiny, but the market is made up of millions of people each with tiny influence.
Note that all this is true not just of the stock market, but of every product on the market. A product is worth whatever the owner is willing to sell it for and people are willing to pay. This is what determines the price of everything from houses to toasters. It's a little theory I've invented that I like to call, "the law of supply and demand". :-)
Yes traders, living or algorithmic, are the only direct factors that can cause a change in the price of a marketable item.
Traders can be affected by news, broken exchanges ;), emotional cycles, lunar cycles, time the trader goes to lunch (or a power cycle if you are an algo running on that unfortunate OS), anything.