"
},
"metadata": {}
}
],
"source": "figsize(12, 8)\n\nax = plt.subplot(221)\nplt.hist(log_return[u'pingan'], bins=16, alpha=0.85,\n label=u\"pingan\", color=\"#A60628\")\n#plt.hist(log_return, bins = 10, figsize = (9,6))\nleg = plt.legend(loc=\"upper left\")\n#pd.Series(list(leg.get_texts())).apply(lambda t: t.set_fontproperties(myfont))\n\nax = plt.subplot(222)\nplt.hist(log_return[u'icbc'], bins=16, alpha=0.85,\n label=u\"icbc\", color=\"#A60628\")\n#plt.hist(log_return, bins = 10, figsize = (9,6))\nleg = plt.legend(loc=\"upper left\")\n#pd.Series(list(leg.get_texts())).apply(lambda t: t.set_fontproperties(myfont))\n\nax = plt.subplot(223)\nplt.hist(log_return[u'5liang'], bins=16, alpha=0.85,\n label=u\"5liang\", color=\"#A60628\")\n#plt.hist(log_return, bins = 10, figsize = (9,6))\nleg = plt.legend(loc=\"upper left\")\n#pd.Series(list(leg.get_texts())).apply(lambda t: t.set_fontproperties(myfont))\n\nax = plt.subplot(224)\nplt.hist(log_return[u'hs300'], bins=16, alpha=0.85,\n label=u\"hs300\", color=\"#A60628\")\n#plt.hist(log_return, bins = 10, figsize = (9,6))\nleg = plt.legend(loc=\"upper left\")\n#pd.Series(list(leg.get_texts())).apply(lambda t: t.set_fontproperties(myfont))\n"
},
{
"source": "## 3. \u8fdb\u884c\u7ec4\u5408\u4f18\u5316",
"cell_type": "markdown",
"metadata": {}
},
{
"source": "### 3.1 \u6295\u8d44\u6a21\u578b\u80cc\u666f\n\u98ce\u9669\u8d44\u4ea7\u7684\u6295\u8d44\u6709\u4e24\u4e2a\u4e3b\u8981\u56e0\u7d20\uff1a\u9884\u671f\u6536\u76ca\u548c\u98ce\u9669\uff0c\u800c\u5e73\u8861\u6536\u76ca\u4e0e\u98ce\u9669\u7684\u5173\u7cfb\u662f\u6295\u8d44\u7ec4\u5408\u8003\u8651\u7684\u6838\u5fc3\u4e4b\u4e00\uff0c\u5982\u4f55\u914d\u7f6e\u4e2a\u80a1\u6210\u4e3a\u7ec4\u5408\u4f18\u5316\u7684\u91cd\u70b9\u3002
\n\u8fd9\u91cc\u7684\u6295\u8d44\u7ec4\u5408\u4f18\u5316\u6a21\u578b\u57fa\u4e8e\u9a6c\u79d1\u7ef4\u5179\u7684\u5747\u503c-\u65b9\u5dee\u6a21\u578b\u3002\u6b64\u6a21\u578b\u662f\u5728\u6709\u6548\u5e02\u573a\u5047\u8bbe\u4e0b\uff0c\u7406\u6027\u6295\u8d44\u7684\u65b9\u6cd5\uff0c\u5b83\u901a\u8fc7\u6784\u5efa\u6709\u6548\u6295\u8d44\u7ec4\u5408\u6765\u5206\u6563\u975e\u7cfb\u7edf\u98ce\u9669\uff0c\u5e76\u901a\u8fc7\u6536\u76ca\u3001\u6536\u76ca\u65b9\u5dee\u3001\u6536\u76ca\u95f4\u7684\u534f\u65b9\u5dee\u63ed\u793a\u4e86\u80a1\u7968\u6295\u8d44\u6536\u76ca\u548c\u98ce\u9669\u6210\u6b63\u6bd4\u5173\u7cfb\u3002
\n\u5747\u503c-\u65b9\u5dee\u6a21\u578b\u7684\u6570\u5b66\u8868\u8fbe\uff1a
\n\u5047\u8bbe\u4e00\u4e2a$n$\u652f\u80a1\u7968\u7684\u6295\u8d44\u7ec4\u5408\uff0c\u6bcf\u652f\u80a1\u7968\u7684\u6536\u76ca\u7387\u4e3a$R_i$\uff0c$w_j$\u4e3a\u8be5\u4e2a\u80a1\u5728\u7ec4\u5408\u4e2d\u8d44\u91d1\u5360\u6bd4\uff0c\u5219\u7ec4\u5408\u7684\u6536\u76ca\u7387$\\overline{R_p}$ \u4e3a\uff1a
\n$$ \\overline{R_p} = \\sum_{j=1}^n{w_j*R_j} $$\n\u7ec4\u5408\u7684\u98ce\u9669\u8861\u91cf-\u6807\u51c6\u5dee$\\overline{\\sigma_p}$\u4e3a\uff1a
\n$$ \\overline{\\sigma_p} = \\sqrt{\\sum_{i=1}^{n}{\\sum_{j=1}^n{w_i*w_j*\\sigma_{ij}}}} $$\n\u5176\u4e2d\uff0c$\\sigma_{ij}$\u4e3a\u4e2a\u80a1i\u4e0e\u4e2a\u80a1j\u7684\u534f\u65b9\u5dee\u3002
\n\u4ee5\u4e0a\u5f0f\u5b50\u4e5f\u53ef\u4ee5\u5199\u4e3a$\\overline{\\sigma_p}^2 = W^T\\Sigma W$\uff0c\u5176\u4e2dW\u662f\u4e2a\u80a1\u8d44\u91d1\u5360\u6bd4\u7684\u5411\u91cf\uff0c$\\Sigma$\u662f\u534f\u65b9\u5dee\u77e9\u9635\u3002
\n\u5747\u503c-\u65b9\u5dee\u6a21\u578b\u5c31\u662f\u8981\u505a\u5230\u6700\u5927\u5316\u6536\u76ca\uff0c\u6700\u5c0f\u5316\u98ce\u9669\uff0c\u56e0\u6b64\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a
\n$$ \\begin{cases}\nmin& \\overline{\\sigma_p}^2 = W^T\\Sigma W \\\\\nmax& \\overline{R_p} = W^T * R \\\\\ns.t.& \\sum_{i=1}^n{w_i} = 1\n\\end{cases}$$\n\u8fd9\u662f\u4e00\u4e2a\u51f8\u4f18\u5316\u95ee\u9898\uff0c\u7ed9\u5b9a\u9884\u671f\u6536\u76ca\u7387$\\overline{R_p}$\u6211\u4eec\u53ef\u4ee5\u5199\u6210\u4e8c\u6b21\u89c4\u5212\u6a21\u578b\uff1a\n$$ min\\qquad \\overline{\\sigma_p}^2 = W^T\\Sigma W $$\n$$ s.t. \\qquad \\begin{cases}\n& W^TR \\geqslant \\overline{R_p} \\\\\n& w_i \\geqslant 0 \\\\\n& w_i \\leqslant 1 \\\\\n& \\sum_{i=1}^n{w_i} = 1 \\\\\n& ...\n\\end{cases}\n$$",
"cell_type": "markdown",
"metadata": {}
},
{
"source": "\u51f8\u4f18\u5316\u7b97\u6cd5\u6211\u4eec\u4f7f\u7528CPLEX\u6765\u89e3\u51b3\u3002",
"cell_type": "markdown",
"metadata": {
"collapsed": true
}
},
{
"execution_count": 51,
"cell_type": "code",
"metadata": {},
"outputs": [
{
"execution_count": 51,
"metadata": {},
"data": {
"text/plain": "['meidi', 'icbc', '5liang', 'pingan']"
},
"output_type": "execute_result"
}
],
"source": "return_label"
},
{
"execution_count": 52,
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": "returns = log_return[return_label]"
},
{
"execution_count": 53,
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": "returns.columns = return_label\nsec = return_label"
},
{
"source": "### 3.2 \u51c6\u5907\u8c03\u7528cplex\u670d\u52a1",
"cell_type": "markdown",
"metadata": {}
},
{
"source": "\u5728DO Optimization\u670d\u52a1\u4e2d\u67e5\u770b\u670d\u52a1\u51ed\u8bc1\uff0c\u590d\u5236url\u548cclient_id\u7684\u503c\u5206\u522b\u5230\u4e0b\u9762SVC_URL\u548cSVC_KEY\u53d8\u91cf\u8d4b\u503c\u57df\u3002",
"cell_type": "markdown",
"metadata": {}
},
{
"execution_count": 55,
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": "# The code was removed by DSX for sharing.\nSVC_URL = \"\"\nSVC_KEY = \"\""
},
{
"execution_count": 56,
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": "import sys\ntry:\n import docplex.mp\nexcept:\n if hasattr(sys, 'real_prefix'):\n #we are in a virtual env.\n !pip install docplex\n else:\n !pip install --user docplex"
},
{
"execution_count": 57,
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": "from docplex.mp.advmodel import AdvModel as Model"
},
{
"execution_count": 58,
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": "df_s = pd.DataFrame(columns=['stock', 'return'])\ndf_s['stock'] = return_label\ndf_s['return'] = log_return[return_label].mean().values"
},
{
"execution_count": 59,
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": "df_s.set_index(['stock'], inplace=True)"
},
{
"source": "### 3.3 \u8ba1\u7b97\u534f\u65b9\u5dee\u77e9\u9635",
"cell_type": "markdown",
"metadata": {}
},
{
"execution_count": 60,
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": "dfv = pd.DataFrame(np.cov(np.asmatrix(returns).transpose()), index = sec, columns=sec)"
},
{
"execution_count": 61,
"cell_type": "code",
"metadata": {},
"outputs": [
{
"execution_count": 61,
"metadata": {},
"data": {
"text/html": "\n\n
\n \n \n | \n meidi | \n icbc | \n 5liang | \n pingan | \n
\n \n \n \n | meidi | \n 0.000389 | \n 0.000026 | \n 0.000260 | \n 0.000147 | \n
\n \n | icbc | \n 0.000026 | \n 0.000164 | \n 0.000014 | \n 0.000068 | \n
\n \n | 5liang | \n 0.000260 | \n 0.000014 | \n 0.000469 | \n 0.000157 | \n
\n \n | pingan | \n 0.000147 | \n 0.000068 | \n 0.000157 | \n 0.000311 | \n
\n \n
\n
\n - \u76ee\u6807\uff1a\u7ed9\u5b9a\u6536\u76ca\u7387\u4e0b\u98ce\u9669\u6700\u5c0f
\n - \u7ea6\u675f\uff1a
\n \n - \u6240\u6709\u90fd\u8981\u6295\u8d44\uff0c\u56e0\u6b64\u4e2a\u80a1\u6bd4\u4f8b\u5408\u8ba1\u4e3a100%
\n - \u6240\u6709\u4e2a\u80a1\u4e0d\u80fd\u5356\u7a7a\uff0c\u6bd4\u4f8b>=0
\n - \u6bcf\u652f\u4e2a\u80a1\u6bd4\u4f8b\u4e0d\u8d85\u8fc750%
\n
\n
",
"cell_type": "markdown",
"metadata": {}
},
{
"execution_count": 62,
"cell_type": "code",
"metadata": {},
"outputs": [],
"source": "def init_model(df_secs, target):\n sec = df_secs.index\n mdl = Model(name='portfolio_miqp')\n df_secs['frac'] = mdl.continuous_var_list(sec, name='frac', ub=1)\n # max fraction\n # every stock fraction must great than 0\n frac_max = 0.95\n for row in df_secs.itertuples():\n mdl.add_constraint(row.frac <= frac_max)\n mdl.add_constraint(row.frac >= 0.0)\n\n # sum of fractions equal 100%\n mdl.add_constraint(mdl.sum(df_secs.frac) == 1);\n # north america constraint:\n # - add a 1-0 column equal to 1 \n # compute the scalar product of frac variables and the 1-0 'is_na' column and set a minimum\n # mdl.add_constraint(mdl.dot(df_secs.frac, df_secs.is_na) >= .4);\n\n # again we use scalar product to compute compound return rate\n # keep the expression to use as a kpi.\n actual_return = mdl.dot(df_secs.frac, df_secs['return'])\n mdl.add_kpi(actual_return, 'ROI')\n\n # KPIs\n fracs = df_secs.frac\n variance = mdl.sum(float(dfv[sec1][sec2]) * fracs[sec1] * fracs[sec2] for sec1 in sec for sec2 in sec)\n mdl.add_kpi(variance, 'Variance')\n\n # finally the objective\n mdl.minimize(variance)\n target_return = target # return data is expressed in percents\n # keep the constraint for later use (more on this later)\n ct_return = mdl.add_constraint(actual_return >= target_return);\n return mdl, ct_return, variance"
},
{
"execution_count": 63,
"cell_type": "code",
"metadata": {},
"outputs": [
{
"execution_count": 63,
"metadata": {},
"data": {
"text/html": "\n\n
\n \n \n | \n return | \n
\n \n | stock | \n | \n
\n \n \n \n | icbc | \n 0.001244 | \n
\n \n | pingan | \n 0.002332 | \n
\n \n | meidi | \n 0.002458 | \n
\n \n | 5liang | \n 0.002728 | \n
\n \n
\n