## Correlation

Correlation describes the strength and direction of linear relationship between quantitative variables. In other words it is a measurement of the degree of association between two sets of numbers that describes how closely they track or are related to one another.

We begin this course by elaborating on the definition of correlation and by presenting an overview of the various ways in which the relationship between two variables may be assessed:

Next we present a more detailed review of each of the methods of viewing correlation starting with raw data time series line graphs such as price trends and derived data graphs such as volatility trend lines including the methodology for constructing line graphs in EXCEL:

We then look at scatter plots, a visual representation of the correlation coefficient tackled a little bit later on the course. We cover the construction of the scatter plot and the line of best fit and then address the four uses and interpretation of the plot:

The calculation of the correlation coefficient method is discussed next. We look at the statistical formula of the measure and then review EXCEL’s CORREL() function for calculating the same value. We also look at how an entire correlation matrix may be constructed in EXCEL for a larger set of variables using the DATA ANALYSIS Tool. An example of the calculation of the correlation coefficient method is given in our available-for-sale Computational Finance – EXCEL examples course “Portfolio Risk Metrics Example”.

Interpretations of the magnitude of the numeric measure are addressed using the Rules of Thumb whereas the statistically significance of the calculated values are covered using hypothesis testing.

We also look at the reason for calculating correlation coefficients for different study window lengths and periods. This reason (the reason why correlation is an enemy for the risk manager) was also addressed in one of our available-for-sale Finance Video Courses, namely the Quant Crash Course.

To illustrate the importance of looking beyond a point estimate of correlation we then review the construction of the trailing correlations graph, a graphical representation of how correlations have changed over a period of time. We see how correlations between some factors remain fairly stable over time while others show greater variance:

Finally, we look at an additional way of viewing the time series data of two factors- the relative price graph and its various uses:

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