po7.py

po7.py

# number of stocks
n = 1000 
# random historical mean returns for each stock
mu = np.random.normal(0.1, 0.2, n)

# number of factors
m = 10

# factor covariance matrix - random symmetrical matrix
SigmaFactor = np.random.randn(m, m)/4
SigmaFactor = SigmaFactor.T @ SigmaFactor

# factor loadings, determine volatility and covariances between stocks
F = np.random.randn(n, m)
# idiosyncratic risk of each stock
D = np.diag(np.random.uniform(0, 0.9, size=n))

ret = mu.T @ w             # solve for weights that maximize portfolio return
f = F.T @ w                # portfolio factor loading
Lmax = cp.Parameter()      # leverage constraint
Lmax.value = 2
# portfolio volatility: factor risk + idiosyncratic risk
risk = cp.quad_form(f, SigmaFactor) + cp.quad_form(w, D)

prob = cp.Problem(cp.Minimize(risk),
                  [cp.sum(w) == 1, 
                   cp.norm(w, 1) <= Lmax])
prob.solve(solver=cp.OSQP)

minvol = risk.value
minvolret = ret.value
print("Min vol portfolio (return=%.4f, risk=%.4f)" % (minvolret, minvol))