Principal component analysis biplots - Understanding Biplots - page 68

Ta b l e 3 . 1 95% VAR of financial instruments constituting a portfolio.

Day CM IRD MM ALCO SE EDSA EDM

1 − 1.765 − 0.248 − 0.281 − 0.296 − 0.141 − 0.226 − 0.941

2 − 0.818 − 1.326 − 0.281 − 0.296 − 0.142 − 0.012 − 3.384

3 − 1.715 − 1.140 − 0.596 − 0.296 − 0.141 − 0.182 − 2.872

4 − 1.771 − 1.641 − 0.596 − 0.296 − 0.145 − 0.890 − 1.946

5 − 1.661 − 1.302 − 0.412 − 0.476 − 0.132 − 0.215 − 1.290

6 − 0.022 − 1.364 − 0.608 − 0.279 − 0.216 − 0.299 − 1.377

7 − 0.889 − 1.137 − 0.457 − 0.453 − 0.152 − 0.255 − 1.129

8 − 0.914 − 1.199 − 0.457 − 0.404 − 0.147 − 0.083 − 1.137

9 − 1.149 − 1.182 − 0.457 − 0.404 − 0.149 − 0.357 − 1.175

10 − 1.273 − 0.733 − 0.457 − 0.404 − 0.156 − 0.556 − 0.894

11 − 0.817 − 0.851 − 0.457 − 0.404 − 0.167 − 0.379 − 0.888

12 − 1.207 − 1.513 − 0.457 − 0.457 − 0.161 − 0.038 − 0.804

13 − 0.862 − 1.819 − 0.459 − 0.457 − 0.158 − 0.139 − 0.939

14 − 2.552 − 1.400 − 0.459 − 0.457 − 0.165 − 0.140 − 0.914

15 − 1.431 − 1.320 − 0.459 − 0.457 − 0.168 − 0.137 − 1.097

16 − 2.838 − 1.318 − 0.459 − 0.457 − 0.158 − 0.369 − 0.162

17 − 1.077 − 1.273 − 0.730 − 0.457 − 0.256 − 0.089 − 1.125

18 − 1.026 − 1.338 − 0.730 − 0.436 − 0.277 − 0.296 − 1.024

− 1.046 − 1.307 − 0.025 − 0.031 − 0.135 − 0.365 − 0.646

19

− − − − − − −

20 0.627 2.030 0.025 0.031 0.132 0.138 0.613

π π

choice of % is interpreted as

the chance of observing a larger loss than this negative return. Plotting an instrument's
VAR over time assists management in identifying trends. The portfolio considered here
consists of seven financial instruments which are not performing independently of one
another, calling for a multivariate approach for analysing the VAR figures calculated for
each of these seven instruments on a daily basis.
Table 3.1 contains the daily 95% VAR for 20 consecutive working days for each
instrument constituting the example portfolio. This data set is available as the dataframe
VAR95.data in the package UBbipl , and Figure 3.1 is constructed with the following
R command:

invariably leads to a negative return and therefore

PCAbipl(X = VAR95.data[,-1], colours = "green", offset = c(0, 0,
0.3, 0.3), offset.m = c(-0.25, -0.25, -0.25, -0.25, -0.25,
-0.25, -0.25), pch.samples = 15, pch.sample.size = 1.1,
pos = "Hor", pos.m = c(4,4,2,2,4,1,1), side.label = c("right",
"right","left","left","right","right","left")

The call to PCAbipl resulting in Figure 3.1 accepts all the default settings except those
specifying the input data matrix ( X ), the colour and size of the symbol for plotting the
sample points ( colours and pch.samples.size ), the plotting symbol for the sample
points ( pch.samples ), the placement of the labels for the axes ( pos ), the argument
offset (the third and fourth values of offset are increased to add space between the
side of the graph and the axis name SE and IRD on side 3; and EDM on side 4) and
arguments for placement of the scales on the axes ( pos.m , offset.m and side.label ).
In general, the construction of a PCA biplot is a two-stage procedure: first PCAbipl is