Solves the mean-variance optimization problem using the Critical Line Algorithm developed by Harry Markowitz. A description of the algorithm is available in his 1959 monograph Portfolio Selection. This implementation is based on the 2000 edition of the book Mean-Variance Analysis in Portfolio Choice and Capital Markets by Markowitz and Todd.
(v1.0) pkg> add https://github.com/ungil/Markowitz.jl.gitSee examples/frontier.jl
m = markowitz(E, V, names=assets)
unit_sum(m) # total weight = 100%
f=frontier(m)
plot_frontier()
optimal(f) # volatility, return and weights for the minimum variance portofolio
optimal(f,4) # volatility, return and weights for the optimal portofolio with return = 4
m=markowitz(E, V, names=assets, lower=0.05, upper=0.15) # min 5%, max 15% per position
unit_sum(m)
f=frontier(m)
plot_frontier()
m=markowitz(E, V, names=assets, # asset bounds by class: stocks -10/30, bonds 0/20, alt. 0/10
lower = -0.1 * (class .== :EQ),
upper = 0.3 * (class .== :EQ) + 0.2 * (class .== :FI) + 0.1 * (class .== :ALT))
unit_sum(m)
add_constraint(m, 1 * (class .== :EQ), '>', 0.3) # net equity exposure between 30% and 60%
add_constraint(m, 1 * (class .== :EQ), '<', 0.6)
add_constraint(m, [1 1 0 0 0 0 0 0 0 0 0 0 0 0], '=', 0.25) # US govt + Investment Grade = 25%
f=frontier(m)
plot_frontier()