Principal Components Analysis of the Romanian Equity Market

Principal Components Analysis (PCA) is a dimension reduction technique that aims at identifying communalities between the initial number of variables and scale down to the number to few meaningful components that are able to explain certain amount of variance. In other words, the underlying idea behind the PCA is to extract common features of the shares’ returns, i.e. instead of looking at all shares the PCA concentrates on communalities and extracts several components that are able to explain certain amount of the variability of all data. What remains unexplained by the factors is the specific risk.  

PCA extracts the factors but does not name these factors, i.e. it is only doing a partial job. But nevertheless, it is useful to identify the specific and systematic risks of the listed shares.

There are several key features that make PCA quite a sensitive technique (but as a bottom-line this is valid to all kind of techniques that deal with identifying key meaningful factors):

(1)    Identifying the number of components – a number of stopping rules apply – as the graphical analysis - scree plot (the point at which the line levels out), Kaiser’s stopping rule (only components with eigenvalue over 1.0 should be taken into consideration), etc.

(2)    Defining the options for the PCA – namely analysis of correlation or covariance and rotation method.  Generally, the covariance matrix is preferred when the variables have similar scales (for instance logarithmic stock returns) or when the variables have been transformed, while the correlation matrix is used when variables are on different scales (and correlation standardized the data). On rotation method, seems more widely accepted to use direct oblimin that allows components to be correlated (non-orthogonal solution), the alternative solution is varimax rotation (orthogonal solution – components are not correlated).

The PCA analysis of 14 Romanian listed shares for the period Sept 3, 2012 – Dec 31, 2014 (excluding several blue chips that arrived on the market after Sept 2012 – Romgaz, Electrica, Nuclearelectrica) is based on 581 daily log-return series for each company. Before conducting the PCA analysis two preliminary tests were taken into consideration – Kaiser-Meyer-Olkin Measure of Sampling Adequacy (KMO) that has a value of 0.892 (threshold value of 0.6 is considered as a minimum; closer to 1.0 the better) and Bartlett's Test of Sphericity.

The results:

(1)      Percent of variance of returns series of the 14 Romanian shares explained by the first component – 30.3% and by the second component – 7.8%; so cumulatively the first two components are able to explain as much as 38.1% of the variance of the returns. And together with the third component the % of the variance explained is 44.2%.  The first component can be interpreted as “market wide” component.

(2)    Proportion of variance of the 14 Romanian shares that can be explained by the 2 components (can be defined as the sum of the squared factor loadings) - high for SIF3, SIF1 and Transelectrica but rather low for the pharma shares – Biofarm (BIO), Antibiotice (ATB) and Fondul Proprietatea (FP).

(3)    How the companies can be combined into groups with respect to how they respond to the 2 components? Answer to this question provides the “pattern matrix”. So, in the first group we have: Transelectrica, Bucharest Stock Exchange, BRD, Banca Transilvania, Transgaz and Petrom. Almost all the large caps fall in one group (intuitive, isn’t; but this also means in case the first component is the general market we cannot rely on having sort of safe havens and really defensive stocks). Also interesting is the second group – all the SIFs (negative loadings to the second component). The SIFs have low loadings with respect to the first component (market component) – so there is opportunity for diversification between the 2 group of stocks identified. The correlation between the 2 components is -0.519.

This publication is for information purposes only and should not be construed as a solicitation or an offer to buy or sell any securities.