Portfolio Analytics by Wolfgang Marty

Author:Wolfgang Marty
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.2.3)

Definition 3.8

The correlation of the portfolios P and is defined by

(3.2.4)

In the following example we illustrate the difference between the covariance and the correlation by means of two different pairs of time series.

Example 3.4

We consider for N = 1, 2, 3, ….

Then we have

We consider a second portfolio for .

Then we have

and

We consider a third portfolio for .

Then we have

and

We see that the correlation detects the similar behavior of portfolios 2 and 3 and yields the same value. Mathematically, the difference between series 2 and 3 is their difference in the standard deviation and also affects their covariance to series 1. However, the division by the standard deviation eliminates this difference in the covariances and leads to the same value for the correlation of series 1 versus series 2 and series 1 versus series 3.

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