The correlation between any two variables (or sets of variables) summarizes a relationship, whether or not there is any real-world connection between the two variables. The correlation coefficient will always be between -1 and +1, which signify two opposite extremes of perfect correlations. A negative coefficient means that the two variables, or sets of variables, will move in opposite directions (if one variable increases, the other will decrease); a positive coefficient will mean that the two will move in the same direction (as one increases, the other will increase).

Explaining Correlations Between the U.S. Dollar and Stocks

For example, if we compared the US Dollar Index (USDX), which tracks the value of the U.S. dollar against six other major currencies, and the value of the Dow Jones Industrial Average (DJIA), Nasdaq and S&P 500 over a 20-year period (as of 2011), the correlation coefficient is 0.35, 0.39 and 0.38, respectively. Note that all of the coefficients are positive, which means that as the value of the U.S. dollar increases, so do the stock indexes, but only by a certain amount. It's also notable that each coefficient is below 0.4, which means that only about 35% to 40% of the stock indexes' movements are associated with the movement of the U.S. dollar.

A country's currency can become more valuable in relation to the rest of the world in two ways: when the amount of currency units available in the world market place is reduced (i.e., when the Fed increases interest rates and causes a reduction in spending), or by an increase in the demand for that particular currency. The fact that an increase in the U.S. dollar affects the value of American stocks seems natural, as U.S. dollars are needed to purchase stocks.

The effect of a significant depreciation in the value of the U.S. dollar on the value of an investor's U.S-based portfolio is very much a function of the portfolio's contents. In other words, if the dollar declines substantially in value against a number of other currencies, your portfolio might be worth less than before, more than before, or about the same as before – it depends on what kinds of stocks are in your portfolio.

U.S. Dollar-Stock Correlation Scenarios

The following three examples illustrate the different potential effects of a declining greenback on an investor's portfolio:

1. Worst-Case Scenario. Your portfolio is made up of shares that rely heavily on imported raw materials, energy or commodities to make money. A substantial portion of the manufacturing sector of the U.S. economy depends on imported raw materials to create finished goods. If the purchasing power of the U.S. dollar declines, it will cost manufacturers more than it did before to buy goods, which puts pressure on their profit margins and, ultimately, their bottom lines.

Companies in your portfolio that don't properly hedge against their reliance on the price of imported goods or the effects of a declining dollar can expose you to a lot of foreign exchange risk. For example, a company that makes baseball bats with imported wood will need to pay more for the wood if the U.S. dollar declines. In this case, a lower U.S. dollar will present a problem to the company because it will have to decide whether it will make less money per unit sold or raise prices (and risk losing customers) to compensate for the higher cost of wood.

2. Likely Scenario. Your portfolio is made up of a diverse collection of companies and is not overweight in any one economic sector. You have also diversified internationally and hold stock in companies that operate around the world, selling to many different markets. In this situation, a declining dollar will have both positive and negative effects on your portfolio.

The extent to which the companies you own depend on a high or low U.S. dollar to make money will be a factor, which is why diversification is crucial. Many of the companies in a typical portfolio hedge the risk of a U.S. dollar depreciation on their business, which should balance out the positive and negative effects of the change in the greenback (To learn more, see "Getting Into International Investing" and "Investing Beyond Your Borders.")

3. Best-Case Scenario. Your portfolio is made up of companies that export U.S. manufactured goods around the world. Companies that rely substantially on foreign revenue and international exports stand to do very well if the U.S. dollar depreciates in value because they get more U.S. dollars when they convert from other world currencies. These companies sell products around the globe, and a low dollar just makes high-quality American goods more price competitive in international markets.

The Bottom Line

The value of American stocks, especially those that are included in market indexes, tend to increase along with the demand for U.S. dollars – in other words, they have a positive correlation. One possible explanation for this relationship is foreign investment. As more investors place their money in U.S. equities, they are required to first buy U.S. dollars to purchase American stocks, causing the indexes to increase in value.