Multi-period portfolio optimization in python

Question

Scenario: I am trying to do multiple portfolio optimizations, with different constraints (weights, risk, risk aversion...) in a multi-period scenario.

What I already did: From the examples of cvxpy I found how to optimize a portfolio under a non-linear quadratic formula that results in a list of weights for the assets in the portfolio composition. My problem is that, although I have 15 years of monthly data, I don't know how to optimize for different periods (the code, as of its current form, yields the best composition for the entire time span of my data).

Question 1: Is it possible to make the code optimize for different periods. such as 1, 3, 4, 6, 9, 12 months (in that case, yielding different weights for each of those periods) If so, how could one do that?.

Question 2: Is it possible to restrain the number of assets in each portfolio composition? What is the best way to achieve that? (the current code uses all of them, but I would like to test when the number of assets is limited, to control the turnover level).

Code:

from cvxpy import *
from cvxopt import *
import pandas as pd
import numpy as np 

prices = pd.DataFrame()
logret = pd.DataFrame()
normret = pd.DataFrame()
returns = pd.DataFrame()

prices = pd.read_excel(open('//folder//Dgms89//calculation v3.xlsx', 'rb'), sheetname='Prices Final')
logret = pd.read_excel(open('//folder//Dgms89//calculation v3.xlsx', 'rb'), sheetname='Returns log')
normret = pd.read_excel(open('//folder//Dgms89//calculation v3.xlsx', 'rb'), sheetname='Returns normal')

returns = normret

def calculate_portfolio(returns, selected_solver):

    cov_mat = returns.cov()
    Sigma = np.asarray(cov_mat.values)
    w = Variable(len(cov_mat))
    gamma = quad_form(w, Sigma)
    prob = Problem(Minimize(gamma), [sum_entries(w) == 1])    
    prob.solve(solver=selected_solver)

    weights = []
    for weight in w.value:
        weights.append(float(weight[0]))

    return weights

Answer 1

1. The standard mean-variance portfolio model is a static model. No dynamics in the model. (Time series are only used to estimate the variance-covariance matrix and the expected return). Some related models can answer questions like when and how to rebalance.
2. Restricting the number of assets in a portfolio leads to what is called the cardinality-constrained portfolio problem. This becomes basically an MIQP (Mixed-Integer Quadratic Programming problem).

Answer 2

The problem of multiperiod is that your model will be overfitted. On the other hand, you can backtest traditional portfolio optimization models asumming a rebalancing period. Riskfolio-Lib has an example using backtrader where it compares S&P500 with diferent portfolios using quarterly rebalancing. You can check the example in this link: https://riskfolio-lib.readthedocs.io/en/latest/examples.html