# Cross Sectional Correlation

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Diversification is hard to find nowadays because financial markets are becoming increasingly correlated. I found a good visually presentation of Cross Sectional Correlation of stocks in the S&P 500 index in the Trading correlation by D. Varadi and C. Rittenhouse article.

Let’s compute and plot the average correlation among stocks in the S&P 500 index and the the average correlation between SPY and stocks in the S&P 500 index 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) #***************************************************************** # Load historical data #****************************************************************** load.packages('quantmod') tickers = sp500.components()$tickers data <- new.env() getSymbols(tickers, src = 'yahoo', from = '1970-01-01', env = data, auto.assign = T) for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T) bt.prep(data, align='keep.all', dates='1970::') spy = getSymbols('SPY', src = 'yahoo', from = '1970-01-01', auto.assign = F) ret.spy = coredata( Cl(spy) / mlag(Cl(spy))-1 ) #***************************************************************** # Code Logic #****************************************************************** prices = data$prices['1993:01:29::'] nperiods = nrow(prices) ret = prices / mlag(prices) - 1 ret = coredata(ret) # require at least 100 stocks with prices index = which((count(t(prices)) > 100 )) index = index[-c(1:252)] # average correlation among S&P 500 components avg.cor = NA * prices[,1] # average correlation between the S&P 500 index (SPX) and its component stocks avg.cor.spy = NA * prices[,1] for(i in index) { hist = ret[ (i- 252 +1):i, ] hist = hist[ , count(hist)==252, drop=F] nleft = ncol(hist) correlation = cor(hist, use='complete.obs',method='pearson') avg.cor[i,] = (sum(correlation) - nleft) / (nleft*(nleft-1)) avg.cor.spy[i,] = sum(cor(ret.spy[ (i- 252 +1):i, ], hist, use='complete.obs',method='pearson')) / nleft if( i %% 100 == 0) cat(i, 'out of', nperiods, '\n') } #***************************************************************** # Create Report #****************************************************************** sma50 = SMA(Cl(spy), 50) sma200 = SMA(Cl(spy), 200) cols = col.add.alpha(spl('green,red'),50) plota.control$col.x.highlight = iif(sma50 > sma200, cols[1], cols[2]) highlight = sma50 > sma200 | sma50 < sma200 plota(avg.cor, type='l', ylim=range(avg.cor, avg.cor.spy, na.rm=T), x.highlight = highlight, main='Average 252 day Pairwise Correlation for stocks in SP500') plota.lines(avg.cor.spy, type='l', col='blue') plota.legend('Pairwise Correlation,Correlation with SPY,SPY 50-day SMA > 200-day SMA,SPY 50-day SMA < 200-day SMA', c('black,blue',cols))

The overall trend for correlations is up. Moreover, correlations are usually rising in the bear markets, when SPY 50-day SMA < 200-day SMA.

To view the complete source code for this example, please have a look at the bt.rolling.cor.test() function in bt.test.r at github.

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