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Correlation Matrix BullGlobe

Correlation Matrix

Asset correlation

Asset correlation is a measure of how investments move relative to one another. When assets move in the same direction at the same time, they are considered to be positively correlated. When one asset tends to move up when the other goes down, the two assets are considered to be negatively correlated.

The correlation measurement is expressed as a number between +1 and -1. A zero correlation indicates there is no relationship between the assets. A +1 indicates an absolute positive correlation (they always move together in the same direction). A -1 indicates an absolute negative correlation (they always move together in opposite directions of each other).

Why is Correlation Important?

The financial concept of asset correlation is important because the goal of asset allocation is to combine assets with low correlation. The purpose of asset allocation is to lower portfolio volatility. By putting low correlation and/or negatively correlated investments in a portfolio, the overall volatility of the portfolio is lowered.

Combining asset categories that have a low correlation reduces the volatility of the portfolio as a whole and allows the portfolio manager to invest more aggressively. In other words, a portfolio manager willing to accept a given amount of volatility can invest in higher return/risk investments. This is because the volatility of the overall portfolio is lower due to combining non-correlated assets. This is called portfolio optimization.

Correlation Matrix

A correlation matrix is a table showing correlation coefficients between variables. Each cell in the table shows the correlation between the returns of two stocks or portfolios. In addition, the matrix displays a heatmap that helps you identify stocks with low correlation. Green cells indicate the two assets are highly correlated, yellow cells show mildly or non-correlated stock pairs, and red cells indicate that two assets have a very low or negative correlation.

The line of 1.00s going from the top right to the bottom left (in dark green) is the main diagonal, which shows that each variable always perfectly correlates with itself. The matrix is symmetrical, with the same correlation is shown above the main diagonal being a mirror image of those below the main diagonal.

Reading A Correlation Matrix

Below you can see a real example of one of our portfolios’ correlation matrices. It displays the correlation of all assets in the portfolio, the actual portfolio, its optimized version, and the S&P 500.

The matrix allows us to, for instance, determine the coefficient of correlation between the S&P 500 and BND (an ETF that tracks a broad bond portfolio) by following these steps:

  • Identify each component of the correlation pair, one on the vertical side of the matrix above and the other one on the horizontal side.
  • E.g. find BND on the vertical list of assets and find S&P 500 on the horizontal list.
  • Trace a vertical and horizontal line from each of the assets (S&P 500 and BND) until they cross to find the cell that displays their correlation coefficient.
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