{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "import cvxpy as cvx\n", "\n", "# logs - export only the logger\n", "import logging\n", "reload(logging) #for iPython interactive usage\n", "logger = logging.getLogger()\n", "logger.setLevel(logging.INFO)\n", "formatter = logging.Formatter('%(asctime)s - %(levelname)s - %(message)s')\n", "\n", "ch = logging.StreamHandler()\n", "ch.setLevel(logging.INFO)\n", "ch.setFormatter(formatter)\n", "logger.addHandler(ch)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Helper functions " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def simulate_trajectories(sampled_returns, b):\n", " \"\"\"Simulate log-wealth trajectories.\"\"\"\n", " N_SAMPLES, T, n = sampled_returns.shape\n", " return np.hstack([np.zeros((N_SAMPLES, 1)),\n", " np.cumsum(log(np.dot(sampled_returns, b)), axis=1)])\n", "\n", "def growth_rate_Wmins(logw_samples):\n", " \"\"\"Simulate expected log growth rate and samples W_min.\"\"\"\n", " T = logw_samples.shape[1] - 1\n", " return mean(logw_samples[:,-1])/T, exp(np.min(logw_samples, axis=1))\n", "\n", "def drawdown_prob(W_mins, alpha):\n", " return sum(W_mins < alpha)/float(len(W_mins))\n", "\n", "def empirical_cdf(samples, grid):\n", " return array([sum(samples <= el) for el in grid], dtype=float) / len(samples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Definitions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Constants " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n = 20 # number of assets, including risk-free \n", "\n", "# generate returns\n", "np.random.seed(0)\n", "mean_return1 = .05 #1.25\n", "mean_return2 = -.1 # 0.85\n", "sigma_idyo = .05\n", "sigma_fact = .30 #.2 \n", "NFACT = 5 #5\n", "\n", "factors_1 = matrix(np.random.uniform(size=(n,NFACT)))\n", "Sigma1 = diag([sigma_idyo**2]*n) + factors_1*diag([sigma_fact**2]*NFACT)*factors_1.T\n", "Sigma1[:,-1] = 0\n", "Sigma1[-1,:] = 0\n", "\n", "factors_2 = matrix(np.random.uniform(size=(n,NFACT)))\n", "Sigma2 = diag([sigma_idyo**2]*n) + factors_2*diag([sigma_fact**2]*NFACT)*factors_2.T\n", "Sigma2 *= 5\n", "Sigma2[:,-1] = 0\n", "Sigma2[-1,:] = 0\n", "\n", "mu1 = np.concatenate([mean_return1 + np.random.randn(n-1)*mean_return1/3., [0.]])\n", "mu2 = np.concatenate([mean_return2 + np.random.randn(n-1)*mean_return2/3., [0.]])\n", "\n", "prob1 = .5\n", "prob2 = .5\n", "\n", "# draw batch returns\n", "def draw_batch_returns(N_DRAWS):\n", " result = np.vstack([\n", " exp(np.random.multivariate_normal(mu1, Sigma1, size = int(N_DRAWS * prob1))),\n", " exp(np.random.multivariate_normal(mu2, Sigma2, size = int(N_DRAWS * prob2)))\n", " ])\n", " np.random.shuffle(result)\n", " return result\n", "\n", "MC_N_SAMPLES = 10000\n", "MC_T = 100\n", "N_ITER = 1000000\n", "batch_size = 100\n", "\n", "np.random.seed(10)\n", "learning_sample = draw_batch_returns(N_ITER)\n", "\n", "monte_carlo_sample = draw_batch_returns(MC_N_SAMPLES*MC_T)\n", "monte_carlo_sample_plain = np.array(monte_carlo_sample)\n", "monte_carlo_sample = monte_carlo_sample.reshape((MC_N_SAMPLES, MC_T, n))\n", "\n", "# risk constraint\n", "alpha = .7\n", "beta = .1\n", "\n", "SAVE_FIGURES = True" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def simplex_project(vector):#, precision = 1E-9):\n", " vector = np.array(vector)\n", " low = np.max(vector) - 1\n", " high = np.max(vector)\n", " while np.sum(vector < low) < np.sum(vector < high):\n", " probe = (low + high)/2.\n", " result = np.maximum(vector - probe, 0)\n", " if np.sum(result) > 1:\n", " low = probe\n", " else:\n", " high = probe\n", " lambda_var = (np.sum(vector[vector >= high]) - 1.) / np.sum(vector >= high)\n", " return np.maximum(vector - lambda_var, 0)\n", "\n", "def stoch_mir_approx_kelly(learn_rets, lambda_risk, b_1, kappa_1, M = 1., \n", " C = 0.01, averaging = True, batch = 1):\n", "\n", " N_SAMPLES, n = learn_rets.shape\n", " N_ITER = int(N_SAMPLES/batch)\n", " \n", " bs = np.zeros((n,N_ITER+1))\n", " kappas = np.zeros(N_ITER+1)\n", " ts = C*np.arange(1, N_ITER+2)**(-.5)\n", " \n", " b_k = b_1\n", " kappa_k = kappa_1\n", " \n", " bs[:,0] = b_1\n", " kappas[0] = kappa_1\n", " \n", " for k in range(N_ITER):\n", " r_k = learn_rets[k*batch:(k+1)*batch,:]\n", " \n", " kappa_k_old = float(kappa_k)\n", " b_k_old = np.array(b_k)\n", "\n", " g_k = mean(- np.divide(r_k.T, np.dot(r_k,b_k)) - \\\n", " kappa_k_old * lambda_risk * np.multiply(r_k.T, np.dot(r_k,b_k)**(-lambda_risk-1)), 1)\n", " b_k = b_k - ts[k-1] * g_k \n", " \n", " h_k = mean(np.dot(r_k, b_k_old)**(-lambda_risk) - 1, 0)\n", " kappa_k = kappa_k + ts[k-1] * h_k\n", "\n", " b_k = simplex_project(b_k)\n", " kappa_k = max(min(kappa_k, M), 0) \n", "\n", " bs[:,k+1] = b_k\n", " kappas[k+1] = kappa_k\n", " \n", " if averaging:\n", " return np.cumsum(bs[:,:] * ts, axis=1)/np.cumsum(ts), np.cumsum(kappas[:] * ts)/np.cumsum(ts) \n", " else:\n", " return bs, kappas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define QRCK " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rhos = matrix(learning_sample.T-1)\n", "mu = mean(rhos, 1)\n", "second_moment = np.cov(rhos) + mu * mu.T\n", " \n", "b_qrck = cvx.Variable(n)\n", "lambda_qrck = cvx.Parameter(sign='positive')\n", "growth = b_qrck.T*mu\n", "variance = cvx.quad_form(b_qrck, second_moment)\n", "risk_constraint_qrck = lambda_qrck*(lambda_qrck + 1) * variance/2. <= lambda_qrck*growth\n", "constraints = [cvx.sum_entries(b_qrck) == 1, b_qrck >= 0, risk_constraint_qrck] \n", "probl_qrck = cvx.Problem(cvx.Maximize(growth - variance/2.), constraints)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Comparison of RCK and Kelly bets " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Table " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lambd\tgr_MC\tprob_th\tprob_MC\n", "0.000 & 0.077 & 1.000 & 0.569 \\\\\n", "6.456 & 0.039 & 0.100 & 0.080 \\\\\n", "5.700 & 0.043 & 0.131 & 0.101 \\\\\n" ] } ], "source": [ "print \"lambd\\tgr_MC\\tprob_th\\tprob_MC\"\n", "cached_bets_rck = {}\n", "for lambda_risk in [0, log(beta)/log(alpha), 5.7]:\n", " print '%.3f '% lambda_risk,\n", " C = 1. / (1 + lambda_risk)\n", " lambda_qrck.value = lambda_risk\n", " probl_qrck.solve()\n", " b_1 = b_qrck.value.A1\n", " kappa_1 = risk_constraint_qrck.dual_value\n", " bs, kappas = stoch_mir_approx_kelly(learning_sample, lambda_risk, b_1, kappa_1, M = kappa_1 * 20., \n", " C = C, averaging = True, batch = batch_size)\n", " cached_bets_rck[lambda_risk] = bs[:, -1]\n", " exp_growth_rate, W_mins = growth_rate_Wmins(simulate_trajectories(monte_carlo_sample, \n", " cached_bets_rck[lambda_risk]))\n", " print '& %.3f '% (exp_growth_rate),\n", " print '& %.3f '% (exp(lambda_risk * log(alpha))),\n", " print '& %.3f \\\\\\\\'% drawdown_prob(W_mins, alpha)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Wealth trajectories " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "trajectories with W_min < alpha: 6 of 10\n", "trajectories with W_min < alpha: 1 of 10\n" ] }, { "data": { "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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eOhSYNAkIC3Nu/7RsrXjwADCZLMtJvRZBQUHw8/NLcr+8FR2zFUXxJlw5ZmvJ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\ndrVevfg7sG9fzHlUJpPF2qnEz7ffcowuXtzxdq6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P++3Fq4+nT5XKnl2pBQuU0umU6tED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\n9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X708cciU6eKnDolEh9Pg5qPPxb5/XeRkydpJmOOx49FduwQuXBBZN48kY4daZazbRv/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\nRGBU8+dnMlCwILI5o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7Vr817bXtWr8/dtDL+X8eP5KlvWXl8EYH2KkydptBDheZOS+IyV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\ndDRdMHbvTm3Zfv99poq7/34GMtapQ0V60SLXreDTprHa5caNGR+zbRut1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N_TRAJ = 10\n", "lambda_star = 5.7\n", "OFFSET = 2\n", "\n", "figure(figsize(12,6))\n", "f, (ax1, ax2) = subplots(1, 2, sharey=True)\n", "ax1.semilogy(arange(MC_T), [alpha]*MC_T, 'r--', label = 'alpha')\n", "ax2.semilogy(arange(MC_T), [alpha]*MC_T, 'r--', label = 'alpha')\n", "ax1.set_xlabel(\"Kelly trajectories\")\n", "ax2.set_xlabel(\"RCK trajectories\")\n", "ax1.set_ylabel(\"wealth\")\n", "ax1.legend(loc='upper left')\n", "\n", "for ax, lambda_risk in zip([ax1, ax2], [0., lambda_star]):\n", " logw_samples = simulate_trajectories(monte_carlo_sample, cached_bets_rck[lambda_risk])\n", " logw_samples = logw_samples[OFFSET:OFFSET+N_TRAJ, :]\n", " \n", " print \"trajectories with W_min < alpha: %d of %d\" %\\\n", " (sum(exp(np.min(logw_samples,axis=1)) < alpha), N_TRAJ)\n", " \n", " for i in range(N_TRAJ): \n", " wealth = exp(logw_samples[i,:])\n", " ax.semilogy(wealth, 'b') \n", "\n", "if SAVE_FIGURES:\n", " savefig('wealth_trajectories_infinite.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sample CDF of Wmin " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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i4UpsM8bmbPHx8bzwwgt4eXkxadIkSWpCOENCgqlMfP16mpdERsLDD8P69bB1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\nUKmS1ZEIIdJiq8QmLTZhG5G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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "W_min_samples = []\n", "\n", "for lambda_risk in [0, log(beta)/log(alpha)]:\n", " exp_growth_rate, W_mins = growth_rate_Wmins(simulate_trajectories(monte_carlo_sample, \n", " cached_bets_rck[lambda_risk]))\n", " W_min_samples.append(W_mins)\n", "\n", "step = 0.001\n", "x = np.arange(0,1+step,step)\n", "\n", "figure(figsize=(7,5))\n", "semilogy(x, empirical_cdf(W_min_samples[0], x), 'k', label='Kelly')\n", "semilogy(x, empirical_cdf(W_min_samples[1], x), 'b', \n", " label='RCK, $\\lambda = %.3f$'%(log(beta)/log(alpha)))\n", "\n", "_ = ylim()\n", "semilogy(x, x**(log(beta)/log(alpha)), 'r--',label = '$\\\\alpha^\\lambda$')\n", "ylim(_)\n", "title('$\\mathbf{Prob}(W^{\\mathrm{min}} < \\\\alpha )$')\n", "xlabel('$\\\\alpha$')\n", "legend(loc='lower right')\n", "\n", "if SAVE_FIGURES:\n", " savefig('sample_cdf_wmin_infinite.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Risk-growth trade-off of RCK, QRCK, and fractional Kelly bets " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2016-03-18 00:24:39,653 - INFO - solving (Q)RCK lambda = 0.00\n", "2016-03-18 00:24:55,099 - INFO - solving (Q)RCK lambda = 1.26\n", "2016-03-18 00:25:08,188 - INFO - solving (Q)RCK lambda = 2.15\n", "2016-03-18 00:25:21,318 - INFO - solving (Q)RCK lambda = 3.69\n", "2016-03-18 00:25:35,204 - INFO - solving (Q)RCK lambda = 6.31\n", "2016-03-18 00:26:01,036 - INFO - solving (Q)RCK lambda = 10.80\n", "2016-03-18 00:26:16,306 - INFO - solving (Q)RCK lambda = 18.48\n", "2016-03-18 00:26:30,023 - INFO - solving (Q)RCK lambda = 31.62\n" ] }, { "data": { "image/png": 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7MJVS9sDDwN2AApyAXCAdOASs1VpnlEWRonxlnsvk1JxTJAclc8fbHgTmNGLY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\nHx8ffv75Z8aMGcOFCxdYvXp1qQVmWcj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# obtain fractional bets\n", "num_frac_bets = 11\n", "risk_free_bet = array([0.]*(n-1) + [1.])\n", "fractional_bets = [f * cached_bets_rck[0.] + (1-f) * risk_free_bet\n", " for f in np.linspace(0, 1, num = num_frac_bets, endpoint=True)]\n", "\n", "result_MC_frac = [growth_rate_Wmins(simulate_trajectories(monte_carlo_sample, b_frac)) \n", " for b_frac in fractional_bets]\n", "\n", "# RCK and QRCK\n", "result_MC_RCK = []\n", "result_MC_QRCK = []\n", "lambdas_risk = np.concatenate([[0.], np.logspace(.1,1.5,7)])\n", "\n", "for lambda_risk in lambdas_risk:\n", " logger.info('solving (Q)RCK lambda = %.2f'%lambda_risk)\n", " C = 1. / (1 + lambda_risk)\n", " \n", " # qrck\n", " lambda_qrck.value = lambda_risk\n", " probl_qrck.solve()\n", " result_MC_QRCK.append(growth_rate_Wmins(simulate_trajectories(monte_carlo_sample, \n", " b_qrck.value.A1)))\n", " \n", " b_1 = b_qrck.value.A1\n", " kappa_1 = risk_constraint_qrck.dual_value\n", " bs, kappas = stoch_mir_approx_kelly(learning_sample, lambda_risk, b_1, kappa_1, \n", " M = kappa_1 * 20., C = C, \n", " averaging = True, batch = batch_size)\n", " result_MC_RCK.append(growth_rate_Wmins(simulate_trajectories(monte_carlo_sample, \n", " bs[:,-1])))\n", "\n", "# plot\n", "figure(figsize=(7,5))\n", "l1 = plot(array([drawdown_prob(el[1], alpha) for el in result_MC_RCK]), \n", " [el[0] for el in result_MC_RCK], 'b-o', label='RCK', zorder=1)\n", "l2 = plot(array([drawdown_prob(el[1], alpha) for el in result_MC_frac]), \n", " [el[0] for el in result_MC_frac], 'm-o', label='fractional Kelly', zorder=1)\n", "l3 = plot(array([drawdown_prob(el[1], alpha) for el in result_MC_QRCK]), \n", " [el[0] for el in result_MC_QRCK], 'g-o', label='QRCK', zorder=1)\n", "xl = xlim()\n", "yl = ylim()\n", "s1 = scatter(drawdown_prob(result_MC_RCK[0][1], alpha),\n", " result_MC_RCK[0][0], color='k', marker='*', s=200, label='Kelly', zorder=2)\n", "lines = [s1, l2[0], l1[0], l3[0]]\n", "legend(lines, [el.get_label() for el in lines], loc='lower right', scatterpoints=1)\n", "xlabel('$\\mathbf{Prob}(W^{\\mathrm{min}} < \\\\alpha )$')\n", "ylabel('$\\mathbf{E} \\log (r^Tb)$')\n", "xl = xlim(xl)\n", "yl = ylim(yl)\n", "\n", "if SAVE_FIGURES:\n", " savefig('risk_growth_trade_off_infinite.png')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }