I'm looking into CVXPY at the moment.
Main goal would be to be able to calculate the optimal portfolio, which in my opinion would mean that we need to maximise
(expected return - risk free) / volatility
To make it simpler I would like to drop risk free out of the equation (it's anyway near zero at the moment).
My problem is: I would like to constrain the weights in the portfolio based on maximum allocation that can be allocated to a certain sector.
Sector Stocks A 1 2 3 B 4 5 6
how can i achieve, that the minimum and maximum of an allocation to every sector lies in between some bands?
I've already seen this post: industry level constraints
But i really would like to implement it with cvxpy as the answer suggested. Unfortunately I have no idea how to implement this?
I already got the covarmatrix, return estimates and bands on hand but simply can't find a way how to implement those constraints. Any help would be highly appreciated!
EDIT: I tried my very best and came up with this script: thanks to the comment from @Attack68 in combination with this paper: Sharpe Quadratic Optimization
import cvxpy as cp import numpy as np np.random.seed(101) ## NUMBER OF ASSETS n_assets = 4 ## NUMBER OF OBSERVATIONS n_obs = 1000 ## GENERATE RANDOM RETURNS return_vec = np.random.randn(n_assets, n_obs) ## SET UP PROBLEM C = np.asmatrix(np.cov(return_vec)) # Covar Matrix mu = np.asmatrix(np.mean(return_vec,axis=1)) # return estimat mu0 = -0.0075 # risk free rate y = cp.Variable(n_assets) # "weights" A = np.asmatrix([[0.6,0.6,0,0],[-1.2,-1.2,0,0],[0,0,0.2,0.2],[0,0,-1.2,-1.2]]) bounds = np.asmatrix([0.4,0.2,0.8,0.2]) # HOW CAN I SUBSTRACT THE BOUNDS FROM ONLY THE NON-NULL VALUES? (AS FAR AS THIS WILL BE NEEDED?) A_mod = A #- bounds.T ## CREATE CONSTRAINTS constraints = [(mu-mu0)@y==1, y >= 0, y@A_mod >= 0] ## FORM OBJECTIVE obj = cp.Minimize(cp.quad_form(y,C)) ## FORM AND SOLVE PROBLEM prob = cp.Problem(obj, constraints) prob.solve() w = y.value/sum(y.value) w array([0.35386785, 0.17693393, 0.4034641 , 0.06573412])
Unfortunately this solution doesn't meet the constraints. What am I doing wrong?