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lets say I am an equity analyst and I want to figure out what fundamental metrics I should use when I am analyzing an industry , I can use pca on a bunch of stocks in an industry using their fundamental data , I will use metrics like return on equity book value return on assets and so on .

My question is if I ran a pca on fundamental data from stocks in an industry what should the first and second principle component represent

this is the pca analysis I did

Importance of components:
                          PC1    PC2    PC3    PC4     PC5     PC6     PC7     PC8     PC9    PC10   PC11    PC12
Standard deviation     1.6224 1.4924 1.3076 1.1561 1.06703 0.97266 0.85922 0.79106 0.73160 0.71013 0.6182 0.40416
Proportion of Variance 0.2025 0.1713 0.1315 0.1028 0.08758 0.07278 0.05679 0.04814 0.04117 0.03879 0.0294 0.01256
Cumulative Proportion  0.2025 0.3738 0.5053 0.6081 0.69571 0.76849 0.82528 0.87342 0.91459 0.95338 0.9828 0.99535
                          PC13
Standard deviation     0.24599
Proportion of Variance 0.00465
Cumulative Proportion  1.00000
Rotation (n x k) = (13 x 13):
                         PC1         PC2         PC3         PC4         PC5          PC6           PC7         PC8
price_book1       -0.2326294  0.23808656 -0.34383928  0.39506594 -0.17589636  0.005631939  1.481288e-01 -0.12544212
price_sales1      -0.2953341  0.03231056 -0.39791599  0.08079662 -0.44956572  0.178211731  1.283100e-01  0.25338915
profit_margin1     0.2452919  0.15146781 -0.23584723 -0.08324291 -0.40242616 -0.415042109 -5.372024e-01 -0.36709976
operating_margin1  0.4604949  0.05695158 -0.44611853  0.02911251  0.13084999  0.141162009  9.830128e-02  0.06904643
rnd1              -0.1481195 -0.51008130  0.08082843  0.31825795 -0.14767174 -0.133578701 -2.235869e-01  0.31669428
wacc1              0.1170286  0.32598489  0.12421475  0.55174254 -0.00349785  0.050214012 -3.885664e-02  0.35618351
si1               -0.1299393  0.09449171 -0.26881615 -0.21901039  0.38126586 -0.671389356  1.775648e-01  0.41125604
revenue1           0.1000749 -0.57110300 -0.18342643  0.14168133  0.01143720 -0.095472155 -2.735005e-01  0.13974257
ev_ebitda1        -0.4190633  0.10875543 -0.30716490  0.01541679  0.04935613 -0.122987639 -9.171709e-02 -0.13389575
ebitda_revnue1     0.4892202 -0.10134004 -0.38000743  0.01587338  0.07191896  0.170465503  1.075778e-01  0.10582745
cashflow1         -0.1778912 -0.22024820 -0.20037303  0.36000644  0.53208906  0.073914046  2.114301e-05 -0.50658912
eps_growth1        0.2009673 -0.22566598  0.14730493  0.22313596 -0.31215893 -0.426656558  6.599544e-01 -0.27885383
analysts1         -0.1921450 -0.30498605 -0.20079300 -0.41950787 -0.17999617  0.253170549  2.235785e-01 -0.03446128

thank you your help will be greatly appreciated

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  • $\begingroup$ if you have "Multivariate Statistics" by Johnson and Wichern, check out the PCA chapter. They have an example that I think answers your question. I just can't remember what it is and the book is not easily accessed by me cause it's in a different state. Zivot's, SplusFinmetrics may also have an example but I'm certain that the multivariate book has one. $\endgroup$ – mark leeds Oct 29 '19 at 5:36
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    $\begingroup$ If PCA tells you that the 1st PC is a linear combination of some factors, the hard thing is giving it a name, not understanding what it is. $\endgroup$ – Lisa Ann Oct 29 '19 at 7:22
  • $\begingroup$ You will have the problem that your data is not scaled (therefore you will have to standardise which is essentially doing PCA on correlation), and is potentially not time specific or consistent (i.e. accounts are infrequently updated with some of the fundamental values) and so based on the preprocessing of data based on those problems it is entirely unclear to me what the first PC will contain. Is this within industry or accross industry? That will also hugely impact the result. $\endgroup$ – Attack68 Oct 29 '19 at 15:54
  • $\begingroup$ @Attack68 the data is scaled and it is within an industry $\endgroup$ – Pelumi Oct 29 '19 at 17:39
  • $\begingroup$ The example in Johnson and Wichern may have been contrived because I remember that the interpretation made sense ( which as Lisa Ann said, can be rare ). But it's still worth checking out. $\endgroup$ – mark leeds Oct 29 '19 at 20:25
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The first observation I make is that the proportion of variance is not very high for the first PCs, with the implication that I would hypothesise that the PCs are not very stable, nor reliable. (You can test this by varying the sample period and analysing the consistency of the PCs)

If the PCs are not stable from period to period then information you can glean from them regarding any predictions about the next period comes with gross uncertainty. Since you are making the assumption that future relationships (correlations) are repeated, and yet if they are not to be repeated then the entire analysis breaks down.

Additionally since you have scaled the data there may be structural idiosyncrasies that are destroyed. For example larger companies within the same industry may have much higher revenues but relatively lower operating margin, as compared with smaller, leaner, start ups with much lower revenues. Your PCA cannot detect this because all companies have been standardised. On the other hand if you don't standardise your PCA is dominated usually by the variables with greatest variance.

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