Factor analysis based stock classification

Factor analysis is a multivariate statistical method aimed at data reduction and summarization. It can be used to describe the covariance relationships among many variables in terms of a few hidden underlying factors.

Suppose we have a number of correlated variables. Using the correlation matrix, we can group these variables such that the variables within a particular group are highly correlated among themselves, but have relatively small correlations with variables in other groups. This means that each group of variables represents a single underlying construct or factor. These factors can have a fundamental meaning attached to them.

Use of Factor Analysis in trading

Factor analysis are used in trading and portfolio management for various reasons:

• It is used to identify hidden factors/trends which drive the asset returns. These factors will typically have a fundamental meaning(like sector/style) attached to them. 
• It is used to classify assets into groups based on their returns. There is a gamut of trading strategies(like basket long short) that can be implemented within each of these groups.
• It gives a clear picture of the major source of the portfolio risk. These risks can be either systematic (common variance) or unsystematic (specific variance) and hence handled accordingly.

Classification of LIX15 stocks

LIX15 is an Indian equity market index that consists of 15 highly liquid stocks traded on National stock exchange. Factor analysis is performed on the returns of these 15 stocks to identify any hidden trends. The observations matrix consists of normalized daily returns of these 15 stocks sampled from February to November 2013. A two factor model is chosen to decompose the data. The factor loadings are determined using maximum likelihood estimation method. It is seen that these factors accounts for about 60 % of the total variance. Now VARIMAX rotation is performed to group stocks based on their loadings. The aim of this rotation is to achieve simple structures which will possibly have a fundamental reasoning behind them. The following is the table of top 6 stocks with highest loading on each factor:

Factor I	Factor II
AXISBANK	TATASTEEL
YESBANK	HINDALCO
SBIN	JSWSTEEL
IDFC	JPASSOCIAT
BANKBARODA	RCOM
MARUTI	JINDALSTEL

Looking at the above stock list we can say that these factors approximately represent different sectorial themes. The first factor is populated with financial services stocks. The second factor has a large number of metal stocks.

	Fundamental theme
Factor 1	Financial services stocks
Factor 2	Metal stocks

There are some stocks in each factor that do not concur with the corresponding fundamental interpretation. This would primarily be sample bias. Another reason could be that these fundamental factors indirectly affect the returns of the corresponding stocks. Also there are some stocks which do not have significant loading on any of the factors. MCDOWELL-N, TATAMOTORS and CAIRN are some of these stocks. These stocks do not fall in either of the sector and hence have remained unclassified.

Classification of BANKNIFTY stocks

BANKNIFTY is the primary banking sector index of India. Similar to the LIX15 analysis, a two factor decomposition of the twelve BANKNIFTY constituents is performed. About 75% of the total variance is explained by these two factors. Following is the table of top 6 stocks with the highest loading each factor.

Factor I	Factor II
AXISBANK	CANBK
ICICIBANK	BANKINDIA
HDFCBANK	UNIONBANK
INDUSINDBK	BANKBARODA
YESBANK	PNB
KOTAKBANK	SBIN

It is clear that the Factor 1 corresponds to private sector banks and Factor 2 corresponds to public sector banks. Hence within the banking sector the most dominant segregation is along the public verses private lines.

	Fundamental theme
Factor 1	Private sector banks
Factor 2	Public sector banks

Conclusion:

The prices of stocks are typically correlated. Using factor analysis, we can group the variability in the stock market into categories. We can now view fluctuations in the stock market based on groups rather than the individual stocks. Using factor analysis we have been able to conclude that among the LIX15 constituents the major classification is on the sectorial lines. Also among the BANKNIFTY constituents the classification lies along the public vs private ownership lines.

PCA on NIFTY stocks

Principal component analysis can help to reduce a complex data set to a lower dimension to highlight a hidden structure. It is used to convert a set of observations of correlated variables to a set of values of uncorrelated variables called principal components. These principal components are linear combinations of the actual variables. The linear combinations are chosen in such a manner that the first principal component has the largest possible variance. The successive principal components have the largest amount of variance given that they are orthogonal to the preceding principal components. Hence the variance explained by the first few components tells us about the strength of the underlying trend. An implicit assumption here is that large variance represents important dynamics of the variables.

PCA on NIFTY stocks

NIFTY is one of the most widely tracked index for Indian equity market. It consists of 50 major Indian companies. PCA is used to analyze the correlated returns of these 50 stocks. The observations matrix consists of normalized daily returns of Nifty 50 stocks sampled from February to November 2013. Below is the Scree plot of the resulting principal components:

The first principal component is typically assumed to represent the broad market. The next few are assumed to be the sector/style related factors. The remaining components represent the idiosyncratic properties of stocks. For the given set of NIFTY stocks we can conclude that about 35% of all the variance is because of the broad market factor (systematic risk). Also about 15% of the variance can be explained by the sector/style related factors. The remaining 50% corresponds to the stock specific factors (unsystematic risk).  Below is the factor correlation plot:

While performing PCA, an important thing to look for is the variation of variance explained by the principal components over time.

Looking at the above plots, we can say that barring extreme rises in the broad market, stocks tend to fall together and rise independently of each other. This means that the component of market risks is higher on the downside. Also over the last couple of years, the sector/style factors have gotten stronger. It seems that the investing paradigm has shifted from timing markets to taking stock/sector level calls.