A simple dimension reduction procedure for corporate finance composite indicators 211To evaluate if our result depends on the company capitalisation, we divide the
companies into two groups: the 194 companies with a capitalisation less than EUR
five billion and the remaining 146 with a capitalisation greater than EUR five billion.
We adopted the same criterion used by the anonymous financial firm that gave us the
data. For the “small cap” companies we obtained the following results
s′(R 4 , 4 R 3 )= 0. 954 , s′(R 4 , 3 R 3 )= 0. 903 , s′(R 4 , 2 R 3 )= 0. 969 , s′(R 4 , 1 R 3 )= 0. 953 ;
s′( 2 R 3 , 4 , 2 R 2 )= 0. 944 , s′( 2 R 3 , 3 , 2 R 2 )= 0. 909 , s′( 2 R 3 , 1 , 2 R 2 )= 0. 907 ;
s′( 2 , 4 R 2 , 3 , 2 , 4 R 1 )= 0. 689 , s′( 2 , 4 R 2 , 1 , 2 , 4 R 1 )= 0. 817 ;therefore the first liquidity ratio that is excluded is the quick ratioX 2 , the second
is the cash flow to interest expense ratioX 4 and finally the current ratioX 1 .The
procedure suggests focusing on the interest coverage ratioX 3 when ranking the small
cap companies.
For the “large cap” companies we obtained the following results
s′′(R 4 , 4 R 3 )= 0. 977 , s′′(R 4 , 3 R 3 )= 0. 931 , s′′(R 4 , 2 R 3 )= 0. 974 , s′′(R 4 , 1 R 3 )= 0. 967 ;
s′′( 4 R 3 , 3 , 4 R 2 )= 0. 781 , s′′( 4 R 3 , 2 , 4 R 2 )= 0. 967 , s′′( 4 R 3 , 1 , 4 R 2 )= 0. 959 ;
s′′( 2 , 4 R 2 , 3 , 2 , 4 R 1 )= 0. 698 , s′′( 2 , 4 R 2 , 1 , 2 , 4 R 1 )= 0. 808.These results are again similar to those obtained before, both for all the companies
and for the small cap ones. The conclusion is that the dimension reduction procedure
is not much affected by the fact that a company is a large cap one or a small cap
one. It should be cautioned that this result (as well as the other ones) applies only
to the data set that has been considered in the paper, but the analysis may be easily
applied to other data sets or to other financial ratios (efficiency, profitability,...).
Moreover, attention should be paid to the industry sector the companies belong to.
For example, as we have already noted, the role of the inventory might be different
between the manufacturing industry and the financial industry. Therefore we suggest
financial analysts to group the companies on the basis of the industry sector before
applying the reduction procedure. This question is not addressed here and requires
further research.
The data have been reanalysed through principal component analysis, which is the
most used dimension reduction method. Principal component analysis suggests that
there are two principal components, the first explains 62.9% and the second 30.2%
of the variance. The first component is a weighted mean of the liquidity ratios with
similar weights so that it may be seen as a sort of generic indicator for company
liquidity. The loadings on component one are 0.476 forX 1 , 0.488 forX 2 , 0.480 for
X 3 and 0.552 forX 4. The loadings on component two are respectively 0.519, 0.502,
− 0 .565 and− 0 .399. Note that the loadings are positive forX 1 andX 2 , which compare
assets with liabilities, while they are negative forX 3 andX 4 , which are measures of
company ability to meet its interest payments on outstanding debt. The correlation
between the ranking based onX 3 and that based on the first principal component
is 0.936. Therefore the rankings are very similar, but the method proposed in this
paper is simpler to understand and be employed by financial analysts, who do not