CVXPY country/sector/industry like constraints for min variance optimization

Question

I am trying to implement a portfolio optimization that uses constraints to define e.g. max exposure to country/ sector/ industry etc. I have implemented the following code below, where I pass in a 'africa' vector to map stocks to country africa, in my constraints I then bound those to be not more then 40% in weights overall. The only way that I managed to implement it is to use sum_weights over the indexes where africa = 1. I also tried using the Parameter function but didn't succeed. There must be a more elegant way to apply these kind of constraints, hopefully. Any suggestion is appreciated. Also if anyone knows about an example that shows the use of tracking error constraints, turnover constraints or volatility constraints, these are the ones where I am also still struggling with.

import numpy as np
from cvxpy import *

np.random.seed(1)
n = 10 # number of assets

mu = np.abs(np.random.randn(n,1)) #mean
Sigma = np.random.randn(n,n)
Sigma = Sigma.T.dot(Sigma)


# Long only PFO Opt
w = Variable(n)

#africa = Parameter(10, sign='positive') 
#africa.value = [1,1,1,0,0,0,0,0,0,0]

africa = [0,0,0,0,0,0,0,1,1,1]

gamma = Parameter(sign='positive')
ret = mu.T*w
risk = quad_form(w,Sigma)

filters = [i for i in range(len(africa)) if africa[i] == 1]

constraints = [sum_entries(w) == 1, w >=0, w[1] > 0.50, w[0] == 0,   sum_entries(w[filters]) == 0.4]

#prob = Problem(Maximize(ret - gamma*risk), [sum_entries(w) == 1, w >=0])  

prob = Problem(Minimize(risk), constraints)

SAMPLE = 1000
risk_data = np.zeros(SAMPLE)
ret_data = np.zeros(SAMPLE)
gamma_vals = np.logspace(-2,3,num=SAMPLE)

for i in range(SAMPLE):
    gamma.value = gamma_vals[i]
    prob.solve()
    risk_data[i] = sqrt(risk).value
    ret_data[i] = ret.value

print(prob.status)
print(prob.value)

print('OPT WEIGHTS : ')
for i in range(n):
    print(round(w[i].value,3))

score -2 · Answer 1 · answered Jan 21 '21 at 10:39

I think you may want to have a look at these examples. The developer has incorporated portfolio risk constraint as follows:

import cvxpy as cp

w = cp.Variable(n)
gamma = cp.Parameter(nonneg=True)
ret = mu.T*w 
risk = cp.quad_form(w, Sigma)
Lmax = cp.Parameter()

# Portfolio optimization with a leverage limit and a bound on risk.
prob = cp.Problem(cp.Maximize(ret), 
              [cp.sum(w) == 1, 
               cp.norm(w, 1) <= Lmax,
               risk <= 2])

Here's the link to jupyter nbviewer

CVXPY country/sector/industry like constraints for min variance optimization

1 Answers1