Quantitative Finance For Dummies by Steve Bell

Author:Steve Bell
Language: eng
Format: epub
ISBN: 9781118769430
Publisher: Wiley
Published: 2016-06-14T00:00:00+00:00

Identifying clusters of data

To discover how your data is grouped, you can graph your numbers in a chart of the principal components weights, as shown in Figure 9-11. The x-axis value for the jth stock in the Dow Jones index is the value p1,j, whilst the y-axis value is p2,j. So you can construct your own charts from your data after you do your principal components analysis.

© John Wiley & Sons, Ltd.

FIGURE 9-11: PCA weight plot for the DJIA Index.

The x-axis is the PC1 weight. All the values are positive and close to 0.18 so this principal component is putting approximately equal weight on all the constituents of the Dow Jones Index. This principal component is effectively the index itself. It’s not surprising that PC1 explains a lot of the variability in the data matrix.

The second principal component separates the Dow Jones constituents into clusters above and below the x-axis. The cluster below contains defensive stocks that are expected to do fine even if the economy does badly because they sell essential goods and services. Examples are Walmart (discount stores), Proctor and Gamble (nappies and other household goods) and Verizon (telecom).

The cluster above the line contains companies that depend more on the economy doing well. These companies include investment banks and major industrials such as General Electric. This classification has happened because the principal components are calculated to be orthogonal. The second principal component of the DJIA data matrix is therefore characterising stocks by dissimilarity to the index and so naturally picks out defensive stocks. You can use this application of PCA to gain insight into the construction of investment portfolios with particular risk characteristics.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.