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 $3 \times 10$ matrix of simulations, and evaluate the 0.9-CV@R risk parity portfolio (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)