The correlation between any two variables (or sets of variables) summarizes a relationship, whether or not there is any realworld connection between the two variables. The correlation coefficient will always be between 1 and +1. These two extremes are considered 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).
If we compare the US Dollar Index (USDX), an index that 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 20year period, the correlation coefficient calculated for the USDX versus the DJIA, Nasdaq and S&P 500, 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. Notice also 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 main ways: when the amount of currency units available in the world market place is reduced (for example, 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 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 are positively correlated. One possible explanation for this relationship is foreign investment. As more and more investors put their money in U.S. equities, they are required to first buy U.S. dollars, which can be used to purchase American stocks, causing the indexes to increase in value.
For more insight, see Commodity Prices And Currency Movements and Using Currency Correlations To Your Advantage.

How do I calculate correlation between market indicators and specific stocks?
Discover how to calculate the correlation coefficient between market indicators and stock prices, a critical skill in technical ... Read Answer >> 
Can the correlation coefficient be used to measure dependence?
Understand the coefficient of correlation and its use in determining the relationship between two variables through the concepts ... Read Answer >> 
What does a negative correlation coefficient mean?
Discover the meaning of a negative correlation coefficient, how this compares to other correlation coefficients and examples ... Read Answer >> 
How does correlation affect the stock market?
Learn about the role correlation plays in prudent stock market investing, and how the correlation coefficient is used to ... Read Answer >> 
How do I find positive correlation in the stock market?
Learn how positive correlation is found in the stock market, how correlation is calculated and how positive correlation is ... Read Answer >> 
How can you calculate correlation using Excel?
Find out how to calculate the Pearson correlation coefficient between two data arrays in Microsoft Excel through the CORREL ... Read Answer >>

Investing
Correlation
In the world of finance, correlation is a statistical measure of how two securities move in relation to each other. 
Investing
Understanding the Oil & Gas Price Correlation
Learn how the correlation between the commodity prices for natural gas and oil changed from 2004 to 2015 due to increased natural gas production. 
Investing
How To Trade Currency And Commodity Correlations
Relationships between currencies and commodities exist throughout the financial markets. Find out how to trade these trends. 
Investing
Could Higher Correlations Wreck Your Diversification Strategy?
Rising asset correlations could make your portfolio riskier than you think. 
Insights
Prices of Stocks and Bonds Move More in Tandem
Correlation between stock and bond prices in the U.S. have reached a 10year high, reversing a broader trend of negative correlation. 
Investing
Calculating the Coefficient Of Variation (CV)
Coefficient of variation measures the dispersion of data points around the mean, a statistical average. 
Investing
Commodities: The Portfolio Hedge
These diverse asset classes can provide downside protection and upside potential. Find out how to use them. 
Investing
Tales From The Trenches: Perfectly Negative Profitability
Use correlations to profit when two specific instruments move in opposite directions. 
Investing
ETF Case Study: Do Utilities ETFs Protect in Down Markets? (XLU, VPU)
Explore the historical performance of large utilities ETFs relative to market indexes during bear markets to find out if utilities ETFs provide downside protection. 
Investing
Diversification: Protecting Portfolios From Mass Destruction
This investing strategy retains its charm as a protection against random events in the market.

Correlation Coefficient
A measure that determines the degree to which two variable's ... 
Pearson Coefficient
A type of correlation coefficient that represents the relationship ... 
Coefficient of Determination
A measure used in statistical model analysis to assess how well ... 
Benchmark For Correlation Values
A benchmark or point of reference chosen by an investment fund ... 
Correlation
In the world of finance, a statistical measure of how two securities ... 
Serial Correlation
The relationship between a given variable and itself over various ...