Example of allocating contribution to 3 funds based on desired target percents

allocations-example.ipynb

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   "source": [
    "import numpy as np\n",
    "import scipy.optimize"
   ]
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   "cell_type": "code",
   "execution_count": 42,
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   "source": [
    "# Current investments\n",
    "S = 9500.00   # US Stocks Indx Fund\n",
    "F = 3250.00    # Foreign Stocks Indx Fund\n",
    "B = 2250.00    # US Bond Indx Fund\n",
    "\n",
    "T = S + F + B  # Total investment\n",
    "\n",
    "# Target percent allocations\n",
    "P_S = 0.6375\n",
    "P_F = 0.2125\n",
    "P_B = 0.15\n",
    "\n",
    "T_d = 500.0   # Today's deposit"
   ]
  },
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   "cell_type": "code",
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   "source": [
    "b = np.array([P_S*T - S, P_F*T - F, P_B*T - B])\n",
    "A = np.array([[1 - P_S, -P_S, -P_S],\n",
    "              [-P_F, 1 - P_F, -P_F],\n",
    "              [-P_B, -P_B, 1 - P_B]])"
   ]
  },
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   "cell_type": "code",
   "execution_count": 44,
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   "source": [
    "def f(x):\n",
    "    y = np.dot(A, x) - b\n",
    "    p1 = np.dot(y,y)\n",
    "    p2 = x.sum()\n",
    "    return p1\n",
    "\n",
    "# Constraint to ensure that all of the money is allocated\n",
    "def scons(x):\n",
    "    return T_d - x.sum()\n",
    "\n",
    "cons = [{'type': 'eq', 'fun': scons}]\n",
    "bnds = [(0, T_d), (0, T_d), (0, T_d)]"
   ]
  },
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   "cell_type": "code",
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    {
     "name": "stdout",
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     "text": [
      "Current Allocations v Desired\n",
      "US Stocks           : 0.633  0.637\n",
      "Foreign Stocks      : 0.217  0.212\n",
      "Bonds               : 0.150  0.150\n"
     ]
    }
   ],
   "source": [
    "fmt_str = '{:20}: {:5.3f}  {:5.3f}'\n",
    "print 'Current Allocations v Desired'\n",
    "print fmt_str.format('US Stocks', S / T, P_S)\n",
    "print fmt_str.format('Foreign Stocks', F / T, P_F)\n",
    "print fmt_str.format('Bonds', B / T, P_B)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 46,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 4.31773141557e-17\n",
      "            Iterations: 6\n",
      "            Function evaluations: 31\n",
      "            Gradient evaluations: 6\n"
     ]
    }
   ],
   "source": [
    "init_x = T_d * np.array([P_S, P_F, P_B])\n",
    "\n",
    "res = scipy.optimize.minimize(f, init_x, method='SLSQP', constraints=cons, \n",
    "                        bounds=bnds, options={'disp': True, 'ftol': 1.0E-10,})\n",
    "\n",
    "# Amount to allocate for each indx fund\n",
    "S_d = res.x[0]\n",
    "F_d = res.x[1]\n",
    "B_d = res.x[2]\n",
    "\n",
    "# Today's total investment\n",
    "T_da = S_d + F_d + B_d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Investments - init: optimized \n",
      "US Stocks           : 318.750  381.250\n",
      "Foreign Stocks      : 106.250   43.750\n",
      "Bonds               :  75.000   75.000\n",
      "\n",
      "Total new investment: 500.00 / 500.0\n",
      "New total: 15500.0\n"
     ]
    }
   ],
   "source": [
    "fmt_str = '{:20}: {:>7.3f}  {:>7.3f}'\n",
    "\n",
    "print 'Investments - init: optimized '\n",
    "print fmt_str.format('US Stocks', init_x[0], S_d)\n",
    "print fmt_str.format('Foreign Stocks', init_x[1], F_d)\n",
    "print fmt_str.format('Bonds', init_x[2], B_d)\n",
    "\n",
    "print\n",
    "print 'Total new investment: {:.2f} / {}'.format(T_da, T_d)\n",
    "print 'New total: {}'.format(T + T_da)"
   ]
  },
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   "cell_type": "code",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New Allocations v Desired\n",
      "US Stocks           : 0.6375  0.6375\n",
      "Foreign Stocks      : 0.2125  0.2125\n",
      "Bonds               : 0.1500  0.1500\n"
     ]
    }
   ],
   "source": [
    "fmt_str = '{:20}: {:5.4f}  {:5.4f}'\n",
    "print 'New Allocations v Desired'\n",
    "print fmt_str.format('US Stocks', (S + S_d) / (T + T_da), P_S)\n",
    "print fmt_str.format('Foreign Stocks', (F + F_d) / (T + T_da), P_F)\n",
    "print fmt_str.format('Bonds', (B + B_d) / (T + T_da), P_B)"
   ]
  },
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