The references refer to the CFA text book.

2 Correlation Analysis

2.1 Scatter Plots

A scatter plot is a graph that shows the relationship between the observations for two data series in two dimensions.

Included 2 scatter plots related to BHP. Data is included below.

Note that I use a log scale to ensure ease of comparison.

Logarithmic scale.

On a logarithmic scale or graph, comparable percentage changes in the value of an investment, index, or average appear to be similar. However, the actual underlying change in value may be significantly different.

For example, a stock whose price increases during the year from $25 to $50 a share has the same percentage change as a stock whose price increases from $100 to $200 a share.

On a logarithmic scale, it's irrelevant that the dollar value of the second stock is four times the value of the first.

Similarly, the percentage change in the Dow Jones Industrial Average (DJIA) as it rose from 1,000 to 2,000 is comparable to the percentage change when it moved from 4,000 to 8,000.

2.2 Correlation Analysis

Scatter diagrams depicts the relationship between 2 data series.

Correlation analysis expresses the same relationship using a single number – Term is correlation coefficient.

CC measures direction AND extent of linear relationship.

CC is between 1 and -1.

A CC of >0 to 1 indicates a positive linear relationship.

NB: If CC is 1, it means that the relationship increases at the same rate. It does not necessarily means that if Variable A increase by one unit, Variable B must increase by one unit. (It could mean that!)

What it does mean that the relationship is consistent, e.g. if A increases by 1, variable B consistently increases by ½ for example.

2.3 Practical Example – BHP revenue vs Dividends per ordinary share - Correlation coefficient

Included below 2 examples using BHP data. You can check your answers for other examples using the following web site: http://easycalculation.com/statistics/correlation.php

1. Data
Year	2010	2009	2008	2007	2006
Revenue US $m	52798	50211	59473	47473	39099
Dividends per ordinary share - declared in respect of the period (US sent)	87	82	56	38.5	32

2. Calculation
	Year	Revenue $	Dividends	Cross product	Squared deviations Revenue	Squared deviations Dividends
	2010	52798	87	83,342.88	8,923,363.84	778.41
	2009	50211	82	9,164.58	160,160.04	524.41
	2008	59473	56	-29,952.82	93,358,108.84	9.61
	2007	47473	38.5	48,158.68	5,465,308.84	424.36
	2006	39099	32	290,289.78	114,742,659.24	734.41
*Average*		49810.8	59.1

*Covariance*	Sum			401,003.10	222,649,600.80	2,471.20
	(N-1)			4.00
	Answer			100,250.78

*Variance*	Sum Squared deviations				222,649,600.80	2,471.20
	(N-1)				4.00	4.00
	Answer				55,662,400.20	617.80

*Standard deviation*					7,460.72	24.86

*Coefficient Correlation*	1.Covariance			100,250.78
	2.Standard deviation X Standard deviation			185,440.64
	Answer			0.54

2.4 Practical example – BHP revenue vs Earnings per ordinary share - Correlation coefficient

1. Data
Year	2010	2009	2008	2007	2006
Revenue US $m	52798	50211	59473	47473	39099
Earnings per ordinary share (diluted) (US sent)	227.8	105.4	274.8	228.9	172.4

2. Calculation
	Year	Revenue $	Dividends	Cross product	Squared deviations Revenue	Squared deviations Dividends
	2010	52798	227.80	77,487.97	8,923,363.84	672.88
	2009	50211	105.40	-38,603.29	160,160.04	9,304.53
	2008	59473	274.80	704,760.87	93,358,108.84	5,320.24
	2007	47473	228.90	-63,214.11	5,465,308.84	731.16
	2006	39099	172.40	315,569.63	114,742,659.24	867.89
Average		49810.8	201.86

*Covariance*	Sum			996,001.06	222,649,600.80	16,896.71
	(N-1)			4.00
	Answer			249,000.27

*Variance*	Sum Squared deviations				222,649,600.80	16,896.71
	(N-1)				4.00	4.00
	Answer				55,662,400.20	4,224.18

*Standard deviation*					7,460.72	64.99


*Coefficient Correlation*	1. Covariance			249,000.27
	2. Standard deviation X Standard deviation			484,899.87
	Answer (1/2)			0.51