What does it mean when stocks gain (or fall) in value? Obviously it means that price goes up (or down), but what's really happening is that stocks are gaining (or falling) against the currency used to purchase them-the dollar.
Another way of saying this is that the dollar depreciates or appreciates against stocks, almost as if a currency pair called S&P/USD exists.
Traders get confused with this because there are days when you'll see the S&P rise along with the dollar. They'll look at the overall daily movement and conclude that the connection is broken, but what's happened more often than not is that they haven't accounted for movement in another market-the S&P futures market that trades when the S&P (cash market) is closed.
The dollar moves right along with this market and it will move with the cash market when it's trading between the hours of 09:30 EST and 16:00 EST. Friday was a perfect example.
At around 07:30, the news regarding Citigroup's stock swap with the government was announced. The S&P futures began to fall on the news, dropping below the previously established daily low. The pound did exactly the same, falling by nearly 80 pips in the process. The euro and aussie declined as well.
Later on, stocks began to rise off the lows. S&P futures hit a bottom around 08:20 and rose thereafter. The pound did the same, gaining about 200 pips. The aussie and euro followed suit. And of course, the dollar gained on the yen.
All the yen cross pairs rose beginning at 08:30. Why? Because their price is derived synthetically from the dollar. For example, the price of GBP/JPY is equal to the price of GBP/USD multiplied by the price of USD/JPY. EUR/JPY and AUD/JPY are derived the same way (using EUR/USD and AUD/USD respectively).
So here's why it can look on the overall daily chart as if the dollar and the S&P are disconnected. Let's say the S&P futures trade 4% lower overnight and the dollar gets stronger. Later, the cash market manages a 1% gain for the day. Overall, it will look like the dollar gained as the S&P went up. But what's really happened is that the cash market partially reversed the futures, and the dollar still traded higher overall on the day even as stocks rose.