**Systematic Investor » R**, and kindly contributed to R-bloggers)

The Minimum Correlation Algorithm is a heuristic method discovered by David Varadi. Below I will benchmark the execution speed of 2 versions of the Minimum Correlation Algorithm versus the traditional minimum variance optimization that relies on solving a quadratic programming problem.

############################################################################### # 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) #***************************************************************** # Setup test input assumptions #***************************************************************** load.packages('quadprog,corpcor') n = 100 hist = matrix(rnorm(1000*n), nc=n) # 0 <= x.i <= 1 constraints = new.constraints(n, lb = 0, ub = 1) constraints = add.constraints(diag(n), type='>=', b=0, constraints) constraints = add.constraints(diag(n), type='<=', b=1, constraints) # SUM x.i = 1 constraints = add.constraints(rep(1, n), 1, type = '=', constraints) # create historical input assumptions ia = list() ia$n = n ia$risk = apply(hist, 2, sd) ia$correlation = cor(hist, use='complete.obs', method='pearson') ia$cov = ia$correlation * (ia$risk %*% t(ia$risk)) ia$cov = make.positive.definite(ia$cov, 0.000000001) ia$correlation = make.positive.definite(ia$correlation, 0.000000001) #***************************************************************** # Time each Algorithm #***************************************************************** load.packages('rbenchmark') benchmark( min.var.portfolio(ia, constraints), min.corr.portfolio(ia, constraints), min.corr2.portfolio(ia, constraints), columns=c("test", "replications", "elapsed", "relative"), order="relative", replications=100 )

I have run the code above for n=10 (10 assets), n=100 (100 assets), n=500 (500 assets), n=1000 (1000 assets)

[Please note that for n=1000 I have only run 5 replication]

n=10 (10 assets) replications elapsed relative min.var.portfolio 100 0.02 1.0 min.corr2.portfolio 100 0.02 1.0 min.corr.portfolio 100 0.03 1.5 n=100 (100 assets) replications elapsed relative min.corr2.portfolio 100 0.07 1.00 min.corr.portfolio 100 0.25 3.57 min.var.portfolio 100 0.31 4.42 n=500 (500 assets) replications elapsed relative min.corr2.portfolio 100 2.18 1.00 min.corr.portfolio 100 9.59 4.39 min.var.portfolio 100 139.13 63.82 n=1000 (1000 assets) replications elapsed relative min.corr2.portfolio 5 0.25 1.00 min.corr.portfolio 5 1.39 5.56 min.var.portfolio 5 113.27 453.08

For small universe (i.e. n ~ 100) all algorithms are fast. But once we attempt to solve 500 or 1000 assets portfolio allocation problem, the minimum variance algorithm is many times slower than the both versions of the minimum correlation algorithm.

So if we are considering a 500 assets weekly back-test for the 10 yrs the run-times in seconds (i.e. 52*10*single tun-time):

elapsed min.corr2.portfolio 11.3 min.corr.portfolio 49.8 min.var.portfolio 723.4

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

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