## Minimum Correlation Algorithm Example

Today I want to follow up with the Minimum Correlation Algorithm Paper post and show how to incorporate the Minimum Correlation Algorithm into your portfolio construction work flow and also explain why I like the Minimum Correlation Algorithm.

First, let’s load the ETF’s data set used in the Minimum Correlation Algorithm Paper using the Systematic Investor Toolbox.

############################################################################### # Load Systematic Investor Toolbox (SIT) # http://systematicinvestor.wordpress.com/systematic-investor-toolbox/ ############################################################################### setInternet2(TRUE) con = gzcon(url('http://www.systematicportfolio.com/sit.gz', 'rb')) source(con) close(con) #***************************************************************** # Load historical data for ETFs #****************************************************************** load.packages('quantmod,quadprog') tickers = spl('SPY,QQQ,EEM,IWM,EFA,TLT,IYR,GLD') 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) bt.prep(data, align='keep.all', dates='2002:08::')

Next, I created the portfolio.allocation.helper() function to ease the back-testing of portfolio construction algorithms:

#***************************************************************** # Code Strategies #****************************************************************** obj = portfolio.allocation.helper(data$prices, periodicity = 'weeks', min.risk.fns = list(EW=equal.weight.portfolio, RP=risk.parity.portfolio, MV=min.var.portfolio, MD=max.div.portfolio, MC=min.corr.portfolio, MC2=min.corr2.portfolio), custom.stats.fn = 'portfolio.allocation.custom.stats' ) models = create.strategies(obj, data)$models

Please note that I assigned acronyms to various portfolio allocation algorithms in the code above.

For example, the Minimum Correlation Algorithm’s acronym is MC and the actual function that does all computations is min.corr.portfolio() function.

Next let’s create various summary reports to see the performance and allocations of different algorithms:

#***************************************************************** # Create Report #****************************************************************** # Plot perfromance layout(1:2) plotbt(models, plotX = T, log = 'y', LeftMargin = 3) mtext('Cumulative Performance', side = 2, line = 1) out = plotbt.strategy.sidebyside(models, return.table=T) # Plot time series of components of Composite Diversification Indicator cdi = custom.composite.diversification.indicator(obj,plot.table = F) out = rbind(colMeans(cdi, na.rm=T), out) rownames(out)[1] = 'Composite Diversification Indicator(CDI)' # Portfolio Turnover for each strategy y = 100 * sapply(models, compute.turnover, data) out = rbind(y, out) rownames(out)[1] = 'Portfolio Turnover' # Plot and compare strategies across different metrics performance.barchart.helper(out, 'Sharpe,Cagr,DVR,MaxDD', c(T,T,T,T)) performance.barchart.helper(out, 'Volatility,Portfolio Turnover,Composite Diversification Indicator(CDI)', c(F,F,T)) # Plot transition maps layout(1:len(models)) for(m in names(models)) { plotbt.transition.map(models[[m]]$weight, name=m) legend('topright', legend = m, bty = 'n') } # Plot transition maps for Risk Contributions dates = index(data$prices)[obj$period.ends] for(m in names(models)) { plotbt.transition.map(make.xts(obj$risk.contributions[[m]], dates), name=paste('Risk Contributions',m)) legend('topright', legend = m, bty = 'n') }

Looking at the summary statistics, you mind wonder what makes the the Minimum Correlation Algorithm different and why do I like it?

The overall characteristics of the Minimum Correlation Algorithm makes it attractive for me. Specifically it has reasonable perfromance, limited draw-down, low turnover and high composite diversification score. The combination of these attractive properties does differentiate the Minimum Correlation Algorithm from others.

In the next post, I will show the speed benchmarks for the Minimum Correlation Algorithm.

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

fun work ,I like it

Nice work. Have you looked at different ways to adjust the relative spread between the topped ranked MCA asset weights and the lowest ranked. That is, winner take all vs. a more even weight distribution.

Is there any possibility that code available for the minimum correlation in Visual Basic?

Michael,

Thank you for providing the SIT and Minimum Correlation code in R.

FYI, two NASDAQ symbols are no longer listed: CEPH and RIMM. I replaced RIMM with SBAC, and changed ERTS to EA (new symbol).

For others who run this code and receive an error, make the changes in the symbol list in the “Load historical data for nasdaq 100 stocks” section and the code will run.

Some of the companies are no longer part of the DOW or NASDAQ but the symbols are valid.