diff options
| -rw-r--r-- | python/optim_alloc.py | 109 |
1 files changed, 65 insertions, 44 deletions
diff --git a/python/optim_alloc.py b/python/optim_alloc.py index 5db00df8..313d37c1 100644 --- a/python/optim_alloc.py +++ b/python/optim_alloc.py @@ -1,6 +1,8 @@ import cvxpy import numpy as np import math +from matplotlib import pyplot as plt +plt.style.use('ggplot') def cor2cov(Rho, vol): return np.diag(vol) @ Rho @ np.diag(vol) @@ -17,53 +19,72 @@ def var(rho, delta, volF): """ computes the variance of the asset """ return delta**2*volF**2+resid_vol(rho, delta, volF)**2 -volHY = 0.4 -rho = {'CLO': 0.9, - 'CSO': 0.6, - 'Subprime': 0.4} -delta = {'CLO': 0.3, - 'CSO': 0.4, - 'Subprime': 1} +def compute_allocation(rho_clo = 0.9, rho_cso=0.6, rho_subprime=0.2, + delta_clo=1.2, delta_cso=0.4, delta_subprime=0.8, + mu_HY=0.02, mu_clo=0.08, mu_cso=0.07, mu_subprime=0.25): + rho = {'CLO': rho_clo, + 'CSO': rho_cso, + 'Subprime': rho_subprime} + delta = {'CLO': delta_clo, + 'CSO': delta_cso, + 'Subprime': delta_subprime} + assets = ['CLO', 'CSO', 'Subprime'] + mu = np.array([mu_HY, mu_clo, mu_cso, mu_subprime]) + u = volHY * np.array([delta[a] for a in assets]) + Sigma = np.outer(u, u) + np.diag([resid_vol(rho[a], delta[a], volHY)**2 + for a in ['CLO', 'CSO', 'Subprime']]) + v = volHY**2 * np.array([1] + [delta[a] for a in assets]) + Sigma = np.vstack((v, np.c_[v[1:], Sigma])) + sharpe = mu/np.sqrt(np.diag(Sigma)) -u = volHY * np.array([delta['CLO'], delta['CSO'], delta['Subprime']]) -Sigma = np.outer(u, u) + np.diag([resid_vol(rho[a], delta[a], volHY)**2 - for a in ['CLO', 'CSO', 'Subprime']]) -v = volHY**2 * np.array([1, delta['CLO'], delta['CSO'], delta['Subprime']]) -Sigma = np.vstack((v, np.c_[v[1:], Sigma])) + gamma = cvxpy.Parameter(sign='positive') + w = cvxpy.Variable(4) + ret = mu.T*w + risk = cvxpy.quad_form(w, Sigma) + prob = cvxpy.Problem(cvxpy.Maximize(ret-gamma*risk), + [cvxpy.sum_entries(w[1:]) - 0.1*w[0] == 1, + w[1:] >= 0, + w[0] <= 0]) -mu = np.array([0.02, 0.07, 0.08, 0.25]) -sharpe = mu/np.sqrt(np.diag(Sigma)) + gamma_x = np.linspace(0, 20, 500) + W = np.empty((4, gamma_x.size)) + for i, val in enumerate(gamma_x): + gamma.value = val + prob.solve() + W[:,i] = np.asarray(w.value).squeeze() -gamma = cvxpy.Parameter(sign='positive') -w = cvxpy.Variable(4) -ret = mu.T*w -risk = cvxpy.quad_form(w, Sigma) -prob = cvxpy.Problem(cvxpy.Maximize(ret-gamma*risk), - [cvxpy.sum_entries(w[1:]) - 0.1*w[0] == 1, - w[1:] >= 0, - w[0] <= 0]) + fund_return = mu@W + fund_vol= np.array([math.sqrt(W[:,i]@Sigma@W[:,i]) for i in range(gamma_x.size)]) + return (W, fund_return, fund_vol) -W = np.empty((4, 100)) -gamma_x = np.linspace(0, 1, 100) -for i, val in enumerate(gamma_x): - gamma.value = val - prob.solve() - W[:,i] = np.asarray(w.value).squeeze() +def plot_allocation(W, fund_return, fund_vol): + gamma_x = np.linspace(0, 20, fund_return.size) + fig, ax1 = plt.subplots() + ax1.stackplot(fund_vol, W[1:,], labels=['CLO', 'CSO', 'Subprime']) + ax1.set_xlabel('risk factor') + ax1.set_ylabel('portfolio weights') + ax1.legend() + # ax1.text(0.3, 0.82, 'RMBS') + # ax1.text(0.5, 0.45, 'CSO') + # ax1.text(0.5, 0.15, 'CLO') + ax1.set_ylim([0, 1]) + ax2 = ax1.twinx() + ax2.plot(fund_vol, fund_return, lw=1, color="grey") + ax2.set_ylabel('fund volatility') + plt.show() -fund_return = mu@X -fund_vol= np.array([math.sqrt(X[:,i]@Sigma@X[:,i]) for i in range(100)]) +if __name__=="__main__": + volHY = 0.07 -from matplotlib import pyplot as plt -plt.style.use('ggplot') -fig, ax1 = plt.subplots() -ax1.stackplot(gamma_x, W[1:,]) -ax1.set_xlabel('risk factor') -ax1.set_ylabel('portfolio weights') -ax1.text(0.3, 0.82, 'RMBS') -ax1.text(0.5, 0.45, 'CSO') -ax1.text(0.5, 0.15, 'CLO') -ax1.set_ylim([0, 1]) -ax2 = ax1.twinx() -ax2.plot(gamma_x, fund_vol, lw=1) -ax2.set_ylabel('fund volatility') -plt.show() + rho = {'CLO': 0.6, + 'CSO': 0.5, + 'Subprime': 0.3} + delta = {'CLO': 0.4, + 'CSO': 0.2, + 'Subprime': 0.6} + mu = np.array([0.01, 0.075, 0.065, 0.25]) + + W, fund_return, fund_vol = compute_allocation(rho['CLO'], rho['CSO'], rho['Subprime'], + delta['CLO'], delta['CSO'], delta['Subprime'], + mu[0], mu[1], mu[2], mu[3]) + plot_allocation(W, fund_return, fund_vol) |