SamplingRB

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 is essentially based on the paper Risk budgeting portfolios from simulations by Bernardo Freitas Paulo da Costa, Silvana M. Pesenti and Rodrigo Targino.

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.

Simple usage

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)

Interfaces

• From R: https://github.com/dccsillag/samplingrb.r
• From python: https://github.com/dccsillag/sampling_rb.py