## Multiple Factor Model – Fundamental Data

The Multiple Factor Model can be used to decompose returns and calculate risk. Following are some examples of the Multiple Factor Models:

- The expected returns factor model: Commonality In The Determinants Of Expected Stock Returns by R. Haugen, N. Baker (1996)
- The expected returns factor model: CSFB Quantitative Research, Alpha Factor Framework on page 11, page 49 by P. N. Patel, S. Yao, R. Carlson, A. Banerji, J. Handelman
- The risk factor model: MSCI Barra United States Equity Multi-Factor Model, page 101

The factors in the model are usually created using pricing, fundamental, analyst estimates, and proprietary data. I will only show examples of factors using pricing and fundamental data because these infromation is readily available from Yahoo Fiance and ADVFN.

This is the first post in the series about Multiple Factor Models. In this post I will show how to get company’s Fundamental Data into R, create a simple factor, and run correlation analysis. In the next posts, I will show how to:

- Build Factors and compute quantiles spreads
- Backtest Multiple Factor Model
- Calculate Risk using Multiple Factor Model

I created a fund.data() function in fundamental.data.r at github to download company’s historical Fundamental data from ADVFN. Following code loads historical quarterly fundamental data for Wal-Mart Stores and computes rolling annual Earnings per share (EPS) using the Systematic Investor Toolbox:

############################################################################### # Load Systematic Investor Toolbox (SIT) # http://systematicinvestor.wordpress.com/systematic-investor-toolbox/ ############################################################################### con = gzcon(url('http://www.systematicportfolio.com/sit.gz', 'rb')) source(con) close(con) ############################################################################### # determine date when fundamental data is available # use 'date preliminary data loaded' when available # otherwise lag 'quarter end date' 2 months for Q1/2/3 and 3 months for Q4 ############################################################################### date.fund.data <- function(data) { # construct date quarter.end.date = as.Date(paste(data['quarter end date',], '/1', sep=''), '%Y/%m/%d') quarterly.indicator = data['quarterly indicator',] date.preliminary.data.loaded = as.Date(data['date preliminary data loaded',], '%Y-%m-%d') + 1 months = seq(quarter.end.date[1], tail(quarter.end.date,1)+365, by='1 month') index = match(quarter.end.date, months) quarter.end.date = months[ iif(quarterly.indicator == '4', index+3, index+2) + 1 ] - 1 fund.date = date.preliminary.data.loaded fund.date[is.na(fund.date)] = quarter.end.date[is.na(fund.date)] return(fund.date) } #***************************************************************** # Load historical fundamental data # http://advfn.com/p.php?pid=financials&symbol=NYSE:WMT&mode=quarterly_reports #****************************************************************** Symbol = 'NYSE:WMT' fund = fund.data(Symbol, 80) # construct date fund.date = date.fund.data(fund) #***************************************************************** # Create and Plot Earnings per share #****************************************************************** EPS.Q = as.double(fund['Diluted EPS from Total Operations',]) EPS.Q = as.xts(EPS.Q, fund.date) EPS = runSum(EPS.Q, 4) # Plot layout(1:2) par(mar=c(2,2,2,1)) x = barplot(EPS.Q, main='Wal-Mart Quarterly Earnings per share', border=NA) text(x, EPS.Q, fund['quarterly indicator',], adj=c(0.5,-0.3), cex=0.8, xpd = TRUE) barplot(EPS, main='Wal-Mart Rolling Annual Earnings per share', border=NA)

You can see a pronounced seasonality in the Quarterly EPS for Wal-Mart, the Q4 always strong and stands out. The common way to deal with seasonality in the income statement is to use rolling annual sum, i.e. sum last 4 quarters.

Next let’s align Wal-Mart prices and EPS and plot them on the same graph.

#***************************************************************** # Load historical data #****************************************************************** load.packages('quantmod') tickers = 'WMT' data <- new.env() getSymbols(tickers, src = 'yahoo', from = '1980-01-01', env = data, auto.assign = T) for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T) data$WMT = merge(data$WMT, EPS) # back fill EPS data$WMT$EPS = ifna.prev(coredata(data$WMT$EPS)) # Plot y = data$WMT['1990::'] plota(Cl(y), type = 'l', LeftMargin=3) plota2Y(y$EPS, type='l', las=1, col='red', col.axis = 'red') plota.legend('WMT(rhs),WMT.EPS(lhs)', 'blue,red', list(Cl(y),y$EPS))

Next let’s repeat the above steps for all companies in the Dow Jones index.

#***************************************************************** # Load historical data #****************************************************************** load.packages('quantmod') tickers = dow.jones.components() # get fundamental data data.fund <- new.env() temp = paste(iif( nchar(tickers) <= 3, 'NYSE:', 'NASDAQ:'), tickers, sep='') for(i in 1:len(tickers)) data.fund[[tickers[i]]] = fund.data(temp[i], 80) save(data.fund, file='data.fund.Rdata') # get pricing data data <- new.env() getSymbols(tickers, src = 'yahoo', from = '1970-01-01', env = data, auto.assign = T) for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T) save(data, file='data.Rdata') #load(file='data.fund.Rdata') #load(file='data.Rdata') # combine fundamental and pricing data for(i in tickers) { fund = data.fund[[i]] fund.date = date.fund.data(fund) EPS.Q = as.double(fund['Diluted EPS from Total Operations',]) EPS.Q = as.xts(EPS.Q, fund.date) EPS = runSum(EPS.Q, 4) data[[i]] = merge(data[[i]], EPS) } bt.prep(data, align='keep.all', dates='1995::2011')

It takes a while to download historical fundamental data for all companies in the Dow Jones index, so I recommend saving your results with save(data.fund, file=’data.fund.Rdata’) command. Later on if you want to run code one more time, just load(file=’data.fund.Rdata’) instead of downloading all data again.

Next let’s create monthly factors. EP factor = (Earnings per share) / Price. VOMO factor = Volume x Momentum.

#***************************************************************** # Compute monthly factors #****************************************************************** prices = data$prices prices = bt.apply.matrix(prices, function(x) ifna.prev(x)) # create factors factors = list() # E/P EPS = bt.apply(data, function(x) ifna.prev(x[, 'EPS'])) factors$EP = EPS / prices # VOMO - Volume x Momentum volume = bt.apply(data, function(x) ifna.prev(Vo(x))) factors$VOMO = (prices / mlag(prices,10) - 1) * bt.apply.matrix(volume, runMean, 22) / bt.apply.matrix(volume, runMean, 66) # find month ends month.ends = endpoints(prices, 'months') prices = prices[month.ends,] n = ncol(prices) nperiods = nrow(prices) ret = prices / mlag(prices) - 1 next.month.ret = mlag(ret, -1) factors$EP = factors$EP[month.ends,] factors$VOMO = factors$VOMO[month.ends,]

Next let’s run correlation analysis for EP factor. You can do correlation analysis for VOMO factor as a homework.

#***************************************************************** # Correlation Analysis #****************************************************************** x = as.vector(factors$EP) y = as.vector(next.month.ret) cor.test(x, y, use = 'complete.obs', method = 'pearson') # Plot par(mar=c(4,4,2,1)) plot(x, y, pch=20, main='Correlation Analysis for EP factor', xlab='EP', ylab='Next Month Return') abline(lm(y ~ x), col='blue', lwd=2)

> cor.test(x, y, use = 'complete.obs', method = 'pearson') Pearson's product-moment correlation data: x and y t = 3.6931, df = 5867, p-value = 0.0002235 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.02260247 0.07365350 sample estimates: cor 0.04815943

The correlation between EP and Next Month Returns is small, but significantly different from zero. The small correlation is not a surprise and is usual for this type of analysis. In the next posts, I will show that even this weak dependence can be profitable.

To view the complete source code for this example, please have a look at the fm.fund.data.test() function in factor.model.test.r at github.

This is tremendously helpful! I created my own function to retrieve fundamental data from ADVFN, but it is not nearly as well-written as yours.

One recommendation might be to treat financial companies differently from other companies in any type of fundamental model, primarily because reporting is so different. But, this is less of a problem with EPS since it works across industries. Additionally, industry-specific estimates would likely improve any fits.

This is exactly what I’ve been looking for (at the stage of looking at fundamentals for my own research); thank you so much for it and keep up the good work!

Just as Amol said; that factoring in industry/sector information along with overall market ‘state’ might be very useful. E.g. looking at how a companies fundamentals compares to industry averages instead of just by themselves.

Similarly, if we assume that some sectors will perform better during higher/lower GDP growth/Interest Rates/Unemployment/etc then a modifier for this at the industry level may further improve the fit.

Amol and Pete,

Thank you for reading my blog. I will build factors presented in the CSFB Alpha Factor Framework in my next post. This framework has both traditional and industry relative factors.

Hi, can i know where i can get more information on your vomo factor ? looks very interesting but diff from the usual momentum factor which is purely excess returns over the last 12 months

Excellent post, I am just wondering how to download data from international stock Exchange. In fact ADVFN requires authentication (for example, check the ticker “BIT:UCG” or “EU:ALU”, which can be seen in the website after authentication, but with the script, we receive “No Data Found”). Thanks a lot.