SamplingRB is a package designed to calculate long-only weights for coherent Risk Parity and Risk Budgeting portfolios, given arbitrary simulations of relative losses of each asset.
It provides a general cutting plane algorithm for a coherent risk measures. Special risk measures, such as CVaR and distortion risk measures are already provided for ease of use.
In the special case of CVaR, it implements a cutting plane algorithm with dedicated initialization for numerical stability and performance, allowing for several thousand simulations. It also implements two stochastic gradient algorithms, taking samples from a user-defined function that allows for arbitrary distributions. One is based on the Lagrangian reformulation of the problem, while the other is a projected version into the feasible domain.
We generate a simple B = ones).
using Random: MersenneTwister
using SamplingRB
rng = MersenneTwister(1)
# Parameters
d = 3 # dimension
nsim = 10 # Nb of simulations
B = ones(d)
alpha = 0.90
relative_losses = randn(rng, d, nsim)
status, w = cvar_rbp(B, alpha, relative_losses)
@assert status == 0
@assert isapprox(w, [0.2280, 0.2706, 0.5014]; atol=1e-4)