本文为集思录帖子“3A银行转债的增强策略”的复现实验。
基本介绍
本文回测实验是一种股债轮动增强策略。操作对象是银行股及其3A级可转债。
因为大行PB一般都小于1，其可转债很难下调转股价。所以银行可转债受下调转股价影响较小。另一方面，从历史来看，3A转债无一不强赎成功，也就是一定会转股，或者可转债价格一定会大于130。
基于上述经验，可以采用“下跌靠债，上涨靠股”的轮动策略针对含可转债的银行股进行投资。
策略描述
策略的基本思想类似于配对交易，当股票净值偏离可转债净值达一定程度，则进行轮动换仓。具体策略如下：
（1）回测首日净值为1；
（2）转债净值-股票净值>5%，买入股票，卖出债券；
（3）股票净值-转债净值>0, 卖出股票，买入债券；
策略回测
实验数据在下方研究板块中，可转债行情数据可从Wind等终端获得。
光大银行股债轮动
光大银行股票及可转债收盘价选取2017-4-5到2019-8-1日线数据（股票价格前复权）。首先看看股票和可转债的净值曲线。
gd_stock_nets = [1]
for i in range(1, len(gd_stock_prices)):
gd_stock_nets.append(gd_stock_nets[i-1]*gd_stock_prices[i]/gd_stock_prices[i-1])
gd_kzz_nets = [1]
for i in range(1, len(gd_kzz_prices)):
gd_kzz_nets.append(gd_kzz_nets[i-1]*gd_kzz_prices[i]/gd_kzz_prices[i-1])
import matplotlib.pyplot as plt
fig = plt.figure(figsize=(12, 6))
ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])
offsets = [i for i in range(len(gd_dates))]
ax.plot(offsets, gd_stock_nets, color="blue", linewidth=1.5, linestyle="-", label="股票净值")
ax.plot(offsets, gd_kzz_nets, color="green", linewidth=1.5, linestyle="-", label="转债净值")
plt.legend(loc='upper left', frameon=False)
下面我们采用上述策略进行配对交易：
gd_position = [0] # 0代表持有可转债，1代表持有银行股票，初始持有可转债
gd_stgy_nets = [1]
gd_chng_count = 0
for i in range(1, len(gd_dates)):
if gd_kzz_nets[i] - gd_stock_nets[i] > 0.05:
gd_position.append(1)
if gd_position[i-1] != 1:
gd_chng_count = 1
elif gd_stock_nets[i] - gd_kzz_nets[i] > 0:
gd_position.append(0)
if gd_position[i-1] != 0:
gd_chng_count = 1
else:
gd_position.append(gd_position[i-1])
if gd_position[i-1] == 0:
gd_stgy_nets.append(gd_stgy_nets[i-1]*(gd_kzz_prices[i]/gd_kzz_prices[i-1]))
elif gd_position[i-1] == 1:
gd_stgy_nets.append(gd_stgy_nets[i-1]*(gd_stock_prices[i]/gd_stock_prices[i-1]))
print("调仓次数：%d" % gd_chng_count)
print("股票净值：%f" % gd_stock_nets[-1])
print("可转债净值：%f" % gd_kzz_nets[-1])
print("策略净值：%f" % gd_stgy_nets[-1])
fig = plt.figure(figsize=(12, 6))
ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])
offsets = [i for i in range(len(gd_dates))]
ax.plot(offsets, gd_stock_nets, color="blue", linewidth=1.5, linestyle="-", label="股票净值")
ax.plot(offsets, gd_kzz_nets, color="green", linewidth=1.5, linestyle="-", label="转债净值")
ax.plot(offsets, gd_stgy_nets, color="red", linewidth=1.5, linestyle="-", label="策略净值")
plt.legend(loc='upper left', frameon=False)
调仓次数：11
股票净值：1.069369
可转债净值：1.096699
策略净值：1.512695
可以看出明显的超额收益。
宁波银行股债轮动
宁波银行股票及可转债收盘价选取2018-1-12到2019-8-1日线数据（股票价格前复权）。实验代码如下：
nb_stock_nets = [1]
for i in range(1, len(nb_stock_prices)):
nb_stock_nets.append(nb_stock_nets[i-1]*nb_stock_prices[i]/nb_stock_prices[i-1])
nb_kzz_nets = [1]
for i in range(1, len(nb_kzz_prices)):
nb_kzz_nets.append(nb_kzz_nets[i-1]*nb_kzz_prices[i]/nb_kzz_prices[i-1])
nb_position = [0] # 0代表持有可转债，1代表持有银行股票，初始持有可转债
nb_stgy_nets = [1]
nb_chng_count = 0
for i in range(1, len(nb_dates)):
if nb_kzz_nets[i] - nb_stock_nets[i] > 0.05:
nb_position.append(1)
if nb_position[i-1] != 1:
nb_chng_count = 1
elif nb_stock_nets[i] - nb_kzz_nets[i] > 0:
nb_position.append(0)
if nb_position[i-1] != 0:
nb_chng_count = 1
else:
nb_position.append(nb_position[i-1])
if nb_position[i-1] == 0:
nb_stgy_nets.append(nb_stgy_nets[i-1]*(nb_kzz_prices[i]/nb_kzz_prices[i-1]))
elif nb_position[i-1] == 1:
nb_stgy_nets.append(nb_stgy_nets[i-1]*(nb_stock_prices[i]/nb_stock_prices[i-1]))
print("调仓次数：%d" % nb_chng_count)
print("股票净值：%f" % nb_stock_nets[-1])
print("可转债净值：%f" % nb_kzz_nets[-1])
print("策略净值：%f" % nb_stgy_nets[-1])
fig = plt.figure(figsize=(12, 6))
ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])
offsets = [i for i in range(len(nb_dates))]
ax.plot(offsets, nb_stock_nets, color="blue", linewidth=1.5, linestyle="-", label="股票净值")
ax.plot(offsets, nb_kzz_nets, color="green", linewidth=1.5, linestyle="-", label="转债净值")
ax.plot(offsets, nb_stgy_nets, color="red", linewidth=1.5, linestyle="-", label="策略净值")
plt.legend(loc='upper left', frameon=False)
调仓次数：4
股票净值：1.315276
可转债净值：1.171215
策略净值：1.335564
上述回测结果中，光大银行的股债配对交易有明显的超额收益，而宁波银行不太明显。原贴也分析了这个原因。其主要由于光大银行的股价波动周期明显，因而股债切换次数较为频繁，每一次股切债相当于避免了大回撤；而每一次债切股又抓股了高涨幅。相反，宁波银行股价偏向单边走势，切换次数也不多，所以超额收益不明显。
一个小优化
上面交易中的5%区间是一个主观值。我们可以通过统计股票净值与可转债净值的差值分布来获得一个统计值。
import numpy as np
gd_nets_diff_fit = np.array(gd_stock_nets) - np.array(gd_kzz_nets)
gd_diff_fit_mean = gd_nets_diff_fit.mean()
gd_diff_fit_std = np.std(gd_nets_diff_fit)
print(gd_diff_fit_mean, gd_diff_fit_std)
-0.03743553771100191 0.028274851087685723
光大银行的股债净值差的均值为-0.037，标准差为0.028。股票净值向下偏离一个标准差，净值差大概是-0.065，向上偏离一个标准差大概是-0.009。这个与主观值差不多。
再看看宁波银行：
nb_nets_diff_fit = np.array(nb_stock_nets) - np.array(nb_kzz_nets)
nb_diff_fit_mean = nb_nets_diff_fit.mean()
nb_diff_fit_std = np.std(nb_nets_diff_fit)
print(nb_diff_fit_mean, nb_diff_fit_std)
0.004643115736568061 0.07745156370857084
宁波银行的股债净值差的均值为0.0046，标准差为0.0775。股票净值向下偏离一个标准差，净值差大概是-0.0729，向上偏离一个标准差大概是0.0821。这个与主观值差的比较多。
下面我们用上面的统计值代入策略看看效果：
nb_position = [0] # 0代表持有可转债，1代表持有银行股票，初始持有可转债
nb_stgy_nets = [1]
nb_chng_count = 0
for i in range(1, len(nb_dates)):
if nb_kzz_nets[i] - nb_stock_nets[i] > 0.0729:
nb_position.append(1)
if nb_position[i-1] != 1:
nb_chng_count = 1
elif nb_stock_nets[i] - nb_kzz_nets[i] > 0.0821:
nb_position.append(0)
if nb_position[i-1] != 0:
nb_chng_count = 1
else:
nb_position.append(nb_position[i-1])
if nb_position[i-1] == 0:
nb_stgy_nets.append(nb_stgy_nets[i-1]*(nb_kzz_prices[i]/nb_kzz_prices[i-1]))
elif nb_position[i-1] == 1:
nb_stgy_nets.append(nb_stgy_nets[i-1]*(nb_stock_prices[i]/nb_stock_prices[i-1]))
print("调仓次数：%d" % nb_chng_count)
print("股票净值：%f" % nb_stock_nets[-1])
print("可转债净值：%f" % nb_kzz_nets[-1])
print("策略净值：%f" % nb_stgy_nets[-1])
fig = plt.figure(figsize=(12, 6))
ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])
offsets = [i for i in range(len(nb_dates))]
ax.plot(offsets, nb_stock_nets, color="blue", linewidth=1.5, linestyle="-", label="股票净值")
ax.plot(offsets, nb_kzz_nets, color="green", linewidth=1.5, linestyle="-", label="转债净值")
ax.plot(offsets, nb_stgy_nets, color="red", linewidth=1.5, linestyle="-", label="策略净值")
plt.legend(loc='upper left', frameon=False)
调仓次数：2
股票净值：1.315276
可转债净值：1.171215
策略净值：1.374715
可以看到针对宁波银行的优化策略收益增加了4%，但是调仓频率反而降低了。因为这里用了一个标准差，使得调仓阈值更大。另外，这里其实用到了未来函数。在实盘中，我们应该针对历史数据计算统计值。
后期优化
上述策略其实是一种配对轮动交易，原始策略中的5%区间是人为定的，第二部分通过计算最简单的统计量确定交易阈值。
另一种优化方法是以“转股溢价率”为锚来找交易阈值。转股溢价率可以看作投资者对于某只可转债的估值。那么统计历史估值，找到溢价率分布的均值，然后用一个区间（比如上下一个标准差）做配对策略。这个以后有机会研究一下。
# 光大银行日期、股票收盘价、可转债数据
gd_dates = ['2017-4-5', '2017-4-6', '2017-4-7', '2017-4-10', '2017-4-11', '2017-4-12', '2017-4-13', '2017-4-14', '2017-4-17', '2017-4-18', '2017-4-19', '2017-4-20', '2017-4-21', '2017-4-24', '2017-4-25', '2017-4-26', '2017-4-27', '2017-4-28', '2017-5-2', '2017-5-3', '2017-5-4', '2017-5-5', '2017-5-8', '2017-5-9', '2017-5-10', '2017-5-11', '2017-5-12', '2017-5-15', '2017-5-16', '2017-5-17', '2017-5-18', '2017-5-19', '2017-5-22', '2017-5-23', '2017-5-24', '2017-5-25', '2017-5-26', '2017-5-31', '2017-6-1', '2017-6-2', '2017-6-5', '2017-6-6', '2017-6-7', '2017-6-8', '2017-6-9', '2017-6-12', '2017-6-13', '2017-6-14', '2017-6-15', '2017-6-16', '2017-6-19', '2017-6-20', '2017-6-21', '2017-6-22', '2017-6-23', '2017-6-26', '2017-6-27', '2017-6-28', '2017-6-29', '2017-6-30', '2017-7-3', '2017-7-4', '2017-7-5', '2017-7-6', '2017-7-7', '2017-7-10', '2017-7-11', '2017-7-12', '2017-7-13', '2017-7-14', '2017-7-17', '2017-7-18', '2017-7-19', '2017-7-20', '2017-7-21', '2017-7-24', '2017-7-25', '2017-7-26', '2017-7-27', '2017-7-28', '2017-7-31', '2017-8-1', '2017-8-2', '2017-8-3', '2017-8-4', '2017-8-7', '2017-8-8', '2017-8-9', '2017-8-10', '2017-8-11', '2017-8-14', '2017-8-15', '2017-8-16', '2017-8-17', '2017-8-18', '2017-8-21', '2017-8-22', '2017-8-23', '2017-8-24', '2017-8-25', '2017-8-28', '2017-8-29', '2017-8-30', '2017-8-31', '2017-9-1', '2017-9-4', '2017-9-5', '2017-9-6', '2017-9-7', '2017-9-8', '2017-9-11', '2017-9-12', '2017-9-13', '2017-9-14', '2017-9-15', '2017-9-18', '2017-9-19', '2017-9-20', '2017-9-21', '2017-9-22', '2017-9-25', '2017-9-26', '2017-9-27', '2017-9-28', '2017-9-29', '2017-10-9', '2017-10-10', '2017-10-11', '2017-10-12', '2017-10-13', '2017-10-16', '2017-10-17', '2017-10-18', '2017-10-19', '2017-10-20', '2017-10-23', '2017-10-24', '2017-10-25', '2017-10-26', '2017-10-27', '2017-10-30', '2017-10-31', '2017-11-1', '2017-11-2', '2017-11-3', '2017-11-6', '2017-11-7', '2017-11-8', '2017-11-9', '2017-11-10', '2017-11-13', '2017-11-14', '2017-11-15', '2017-11-16', '2017-11-17', '2017-11-20', '2017-11-21', '2017-11-22', '2017-11-23', '2017-11-24', '2017-11-27', '2017-11-28', '2017-11-29', '2017-11-30', '2017-12-1', '2017-12-4', '2017-12-5', '2017-12-6', '2017-12-7', '2017-12-8', '2017-12-11', '2017-12-12', '2017-12-13', '2017-12-14', '2017-12-15', '2017-12-18', '2017-12-19', '2017-12-20', '2017-12-21', '2017-12-22', '2017-12-25', '2017-12-26', '2017-12-27', '2017-12-28', '2017-12-29', '2018-1-2', '2018-1-3', '2018-1-4', '2018-1-5', '2018-1-8', '2018-1-9', '2018-1-10', '2018-1-11', '2018-1-12', '2018-1-15', '2018-1-16', '2018-1-17', '2018-1-18', '2018-1-19', '2018-1-22', '2018-1-23', '2018-1-24', '2018-1-25', '2018-1-26', '2018-1-29', '2018-1-30', '2018-1-31', '2018-2-1', '2018-2-2', '2018-2-5', '2018-2-6', '2018-2-7', '2018-2-8', '2018-2-9', '2018-2-12', '2018-2-13', '2018-2-14', '2018-2-22', '2018-2-23', '2018-2-26', '2018-2-27', '2018-2-28', '2018-3-1', '2018-3-2', '2018-3-5', '2018-3-6', '2018-3-7', '2018-3-8', '2018-3-9', '2018-3-12', '2018-3-13', '2018-3-14', '2018-3-15', '2018-3-16', '2018-3-19', '2018-3-20', '2018-3-21', '2018-3-22', '2018-3-23', '2018-3-26', '2018-3-27', '2018-3-28', '2018-3-29', '2018-3-30', '2018-4-2', '2018-4-3', '2018-4-4', '2018-4-9', '2018-4-10', '2018-4-11', '2018-4-12', '2018-4-13', '2018-4-16', '2018-4-17', '2018-4-18', '2018-4-19', '2018-4-20', '2018-4-23', '2018-4-24', '2018-4-25', '2018-4-26', '2018-4-27', '2018-5-2', '2018-5-3', '2018-5-4', '2018-5-7', '2018-5-8', '2018-5-9', '2018-5-10', '2018-5-11', '2018-5-14', '2018-5-15', '2018-5-16', '2018-5-17', '2018-5-18', '2018-5-21', '2018-5-22', '2018-5-23', '2018-5-24', '2018-5-25', '2018-5-28', '2018-5-29', '2018-5-30', '2018-5-31', '2018-6-1', '2018-6-4', '2018-6-5', '2018-6-6', '2018-6-7', '2018-6-8', '2018-6-11', '2018-6-12', '2018-6-13', '2018-6-14', '2018-6-15', '2018-6-19', '2018-6-20', '2018-6-21', '2018-6-22', '2018-6-25', '2018-6-26', '2018-6-27', '2018-6-28', '2018-6-29', '2018-7-2', '2018-7-3', '2018-7-4', '2018-7-5', '2018-7-6', '2018-7-9', '2018-7-10', '2018-7-11', '2018-7-12', '2018-7-13', '2018-7-16', '2018-7-17', '2018-7-18', '2018-7-19', '2018-7-20', '2018-7-23', '2018-7-24', '2018-7-25', '2018-7-26', '2018-7-27', '2018-7-30', '2018-7-31', '2018-8-1', '2018-8-2', '2018-8-3', '2018-8-6', '2018-8-7', '2018-8-8', '2018-8-9', '2018-8-10', '2018-8-13', '2018-8-14', '2018-8-15', '2018-8-16', '2018-8-17', '2018-8-20', '2018-8-21', '2018-8-22', '2018-8-23', '2018-8-24', '2018-8-27', '2018-8-28', '2018-8-29', '2018-8-30', '2018-8-31', '2018-9-3', '2018-9-4', '2018-9-5', '2018-9-6', '2018-9-7', '2018-9-10', '2018-9-11', '2018-9-12', '2018-9-13', '2018-9-14', '2018-9-17', '2018-9-18', '2018-9-19', '2018-9-20', '2018-9-21', '2018-9-25', '2018-9-26', '2018-9-27', '2018-9-28', '2018-10-8', '2018-10-9', '2018-10-10', '2018-10-11', '2018-10-12', '2018-10-15', '2018-10-16', '2018-10-17', '2018-10-18', '2018-10-19', '2018-10-22', '2018-10-23', '2018-10-24', '2018-10-25', '2018-10-26', '2018-10-29', '2018-10-30', '2018-10-31', '2018-11-1', '2018-11-2', '2018-11-5', '2018-11-6', '2018-11-7', '2018-11-8', '2018-11-9', '2018-11-12', '2018-11-13', '2018-11-14', '2018-11-15', '2018-11-16', '2018-11-19', '2018-11-20', '2018-11-21', '2018-11-22', '2018-11-23', '2018-11-26', '2018-11-27', '2018-11-28', '2018-11-29', '2018-11-30', '2018-12-3', '2018-12-4', '2018-12-5', '2018-12-6', '2018-12-7', '2018-12-10', '2018-12-11', '2018-12-12', '2018-12-13', '2018-12-14', '2018-12-17', '2018-12-18', '2018-12-19', '2018-12-20', '2018-12-21', '2018-12-24', '2018-12-25', '2018-12-26', '2018-12-27', '2018-12-28', '2019-1-2', '2019-1-3', '2019-1-4', '2019-1-7', '2019-1-8', '2019-1-9', '2019-1-10', '2019-1-11', '2019-1-14', '2019-1-15', '2019-1-16', '2019-1-17', '2019-1-18', '2019-1-21', '2019-1-22', '2019-1-23', '2019-1-24', '2019-1-25', '2019-1-28', '2019-1-29', '2019-1-30', '2019-1-31', '2019-2-1', '2019-2-11', '2019-2-12', '2019-2-13', '2019-2-14', '2019-2-15', '2019-2-18', '2019-2-19', '2019-2-20', 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gd_kzz_prices = [103.0, 103.61, 103.0, 103.44, 103.29, 103.12, 103.01, 102.31, 101.78, 101.7, 101.54, 101.53, 101.71, 101.48, 101.85, 101.6, 101.72, 101.5, 101.0, 100.95, 100.91, 100.6, 100.11, 100.19, 100.16, 100.29, 100.94, 100.94, 100.63, 100.38, 100.38, 100.49, 100.5, 100.57, 100.4, 101.5, 101.15, 101.5, 101.75, 101.93, 101.37, 101.61, 101.97, 102.0, 102.4, 102.59, 102.8, 102.35, 102.0, 102.15, 103.22, 103.89, 103.8, 104.0, 103.9, 105.4, 106.0, 105.71, 105.6, 105.12, 105.09, 104.8, 105.17, 105.2, 105.16, 104.96, 105.87, 106.3, 107.81, 109.23, 110.6, 110.04, 111.8, 112.79, 112.16, 113.29, 111.35, 111.99, 111.9, 112.14, 112.39, 113.71, 115.81, 115.2, 114.35, 113.87, 113.95, 112.8, 112.26, 111.19, 111.72, 112.65, 112.65, 113.16, 113.34, 112.63, 112.64, 112.7, 112.03, 114.29, 115.91, 116.22, 115.94, 115.29, 115.4, 115.85, 116.49, 116.32, 115.85, 116.3, 115.67, 113.95, 113.31, 113.0, 112.87, 112.73, 112.85, 112.75, 112.54, 112.3, 112.07, 110.7, 110.87, 110.69, 111.51, 111.83, 112.49, 112.93, 113.06, 112.95, 112.65, 112.79, 112.53, 111.39, 111.57, 110.73, 111.44, 110.88, 110.38, 111.3, 109.61, 109.74, 109.4, 109.32, 109.09, 108.34, 109.9, 110.01, 110.16, 110.12, 110.97, 110.3, 108.9, 108.62, 109.21, 108.74, 109.3, 109.5, 108.33, 108.66, 108.14, 107.63, 106.69, 106.5, 105.53, 105.47, 106.03, 106.04, 106.03, 107.5, 108.2, 106.6, 107.26, 106.1, 106.14, 105.6, 106.24, 105.7, 105.9, 105.78, 105.94, 105.7, 104.9, 104.41, 104.5, 105.8, 107.17, 107.2, 107.99, 107.84, 107.43, 108.0, 107.55, 107.8, 108.37, 109.1, 109.89, 111.6, 113.79, 115.25, 119.23, 120.63, 119.89, 120.14, 119.03, 117.1, 118.84, 118.2, 120.36, 123.78, 121.98, 119.9, 114.2, 111.92, 112.6, 113.25, 113.5, 115.68, 116.43, 116.06, 114.03, 113.51, 113.05, 112.5, 110.88, 112.9, 112.5, 113.24, 113.7, 113.0, 113.0, 112.3, 112.21, 112.18, 111.49, 111.09, 110.59, 110.21, 109.0, 108.7, 108.39, 107.91, 109.17, 108.5, 108.54, 108.4, 109.46, 109.8, 112.31, 112.89, 111.53, 110.45, 109.34, 109.08, 110.81, 110.12, 108.95, 108.26, 109.92, 109.5, 108.77, 109.8, 109.16, 109.04, 109.3, 109.99, 110.61, 110.6, 110.05, 109.97, 109.97, 110.0, 109.1, 109.3, 109.71, 110.3, 110.0, 109.1, 108.03, 107.8, 107.31, 105.91, 105.68, 106.12, 106.11, 106.6, 106.9, 106.3, 107.06, 105.76, 105.0, 105.15, 105.1, 105.0, 104.86, 103.13, 103.14, 103.25, 103.2, 102.82, 101.8, 100.31, 100.12, 101.6, 100.18, 100.86, 100.95, 101.41, 101.78, 103.48, 104.11, 103.79, 104.02, 104.01, 103.66, 103.7, 103.74, 104.65, 107.09, 108.29, 107.53, 106.91, 105.55, 105.89, 106.26, 106.9, 105.76, 105.41, 105.4, 105.4, 106.9, 106.13, 106.41, 105.99, 105.33, 105.05, 104.88, 104.78, 104.3, 104.36, 105.0, 105.2, 105.42, 105.8, 106.39, 106.05, 105.84, 105.51, 105.43, 105.26, 105.82, 105.37, 105.66, 105.58, 105.45, 105.1, 105.11, 105.51, 105.73, 105.46, 106.09, 106.67, 107.37, 108.5, 108.25, 108.34, 107.9, 108.57, 107.2, 107.17, 107.75, 106.52, 107.3, 106.64, 106.6, 107.44, 106.65, 107.86, 108.48, 107.53, 108.71, 109.01, 109.46, 109.27, 108.95, 108.68, 108.65, 109.2, 108.86, 108.67, 108.47, 108.57, 107.14, 107.56, 107.9, 107.76, 108.45, 108.89, 108.91, 108.0, 108.01, 107.7, 107.37, 107.94, 107.92, 108.38, 107.8, 107.91, 108.3, 107.92, 108.02, 107.86, 107.8, 107.41, 107.16, 107.3, 107.84, 107.6, 107.23, 105.8, 105.65, 104.47, 103.91, 104.8, 105.05, 104.88, 104.7, 105.43, 103.78, 104.8, 106.55, 106.83, 106.79, 107.38, 107.85, 108.03, 107.51, 108.32, 108.61, 108.0, 109.01, 109.06, 108.57, 108.2, 109.0, 111.53, 111.02, 111.26, 111.79, 112.24, 113.5, 113.5, 113.12, 113.4, 113.5, 112.66, 114.07, 113.95, 113.44, 113.35, 113.56, 118.0, 115.5, 115.18, 114.12, 116.81, 118.17, 119.0, 118.93, 116.31, 113.98, 113.87, 114.7, 113.77, 113.73, 113.64, 114.96, 115.25, 115.3, 115.74, 115.7, 114.26, 113.59, 113.5, 112.81, 114.9, 117.31, 117.21, 117.28, 117.71, 117.58, 116.36, 114.35, 113.68, 113.23, 114.09, 114.88, 116.1, 115.03, 114.7, 113.39, 112.28, 111.75, 110.97, 110.24, 111.29, 112.05, 108.73, 109.3, 109.2, 109.1, 110.02, 109.91, 110.04, 110.6, 110.9, 110.88, 110.99, 110.57, 109.79, 109.06, 109.0, 108.4, 108.78, 108.66, 107.77, 107.48, 107.22, 106.55, 106.85, 107.1, 107.7, 109.3, 108.9, 108.66, 108.07, 108.07, 108.05, 108.75, 110.85, 110.95, 110.52, 109.49, 109.31, 109.43, 108.63, 108.88, 109.15, 109.27, 109.04, 109.1, 108.88, 108.8, 108.8, 108.9, 109.89, 109.86, 109.9, 110.02, 109.68, 110.53, 110.55, 110.4, 110.39, 110.85, 112.24, 112.96, 113.0, 112.5, 112.96]
# 宁波银行日期、股票收盘价、可转债数据
nb_dates = ['2018-1-12', '2018-1-15', '2018-1-16', '2018-1-17', '2018-1-18', '2018-1-19', '2018-1-22', '2018-1-23', '2018-1-24', '2018-1-25', '2018-1-26', '2018-1-29', '2018-1-30', '2018-1-31', '2018-2-1', '2018-2-2', '2018-2-5', '2018-2-6', '2018-2-7', '2018-2-8', '2018-2-9', '2018-2-12', '2018-2-13', '2018-2-14', '2018-2-22', '2018-2-23', '2018-2-26', '2018-2-27', '2018-2-28', '2018-3-1', '2018-3-2', '2018-3-5', '2018-3-6', '2018-3-7', '2018-3-8', '2018-3-9', '2018-3-12', '2018-3-13', '2018-3-14', '2018-3-15', '2018-3-16', '2018-3-19', '2018-3-20', '2018-3-21', '2018-3-22', '2018-3-23', '2018-3-26', '2018-3-27', '2018-3-28', '2018-3-29', '2018-3-30', '2018-4-2', '2018-4-3', '2018-4-4', '2018-4-9', '2018-4-10', '2018-4-11', '2018-4-12', '2018-4-13', '2018-4-16', '2018-4-17', '2018-4-18', '2018-4-19', '2018-4-20', '2018-4-23', '2018-4-24', '2018-4-25', '2018-4-26', '2018-4-27', '2018-5-2', '2018-5-3', '2018-5-4', '2018-5-7', '2018-5-8', '2018-5-9', '2018-5-10', '2018-5-11', '2018-5-14', '2018-5-15', '2018-5-16', '2018-5-17', '2018-5-18', '2018-5-21', '2018-5-22', '2018-5-23', '2018-5-24', '2018-5-25', '2018-5-28', '2018-5-29', '2018-5-30', '2018-5-31', '2018-6-1', '2018-6-4', '2018-6-5', '2018-6-6', '2018-6-7', '2018-6-8', '2018-6-11', '2018-6-12', '2018-6-13', '2018-6-14', '2018-6-15', '2018-6-19', '2018-6-20', '2018-6-21', '2018-6-22', '2018-6-25', '2018-6-26', '2018-6-27', '2018-6-28', '2018-6-29', '2018-7-2', '2018-7-3', '2018-7-4', '2018-7-5', '2018-7-6', '2018-7-9', '2018-7-10', '2018-7-11', '2018-7-12', '2018-7-13', '2018-7-16', '2018-7-17', '2018-7-18', '2018-7-19', '2018-7-20', '2018-7-23', '2018-7-24', '2018-7-25', '2018-7-26', '2018-7-27', '2018-7-30', '2018-7-31', '2018-8-1', '2018-8-2', '2018-8-3', '2018-8-6', '2018-8-7', '2018-8-8', '2018-8-9', '2018-8-10', '2018-8-13', '2018-8-14', '2018-8-15', '2018-8-16', '2018-8-17', '2018-8-20', '2018-8-21', '2018-8-22', '2018-8-23', '2018-8-24', '2018-8-27', '2018-8-28', '2018-8-29', '2018-8-30', '2018-8-31', '2018-9-3', '2018-9-4', '2018-9-5', '2018-9-6', '2018-9-7', '2018-9-10', '2018-9-11', '2018-9-12', '2018-9-13', '2018-9-14', '2018-9-17', '2018-9-18', '2018-9-19', '2018-9-20', '2018-9-21', '2018-9-25', '2018-9-26', '2018-9-27', '2018-9-28', '2018-10-8', '2018-10-9', '2018-10-10', '2018-10-11', '2018-10-12', '2018-10-15', '2018-10-16', '2018-10-17', '2018-10-18', '2018-10-19', '2018-10-22', '2018-10-23', '2018-10-24', '2018-10-25', '2018-10-26', '2018-10-29', '2018-10-30', '2018-10-31', '2018-11-1', '2018-11-2', '2018-11-5', '2018-11-6', '2018-11-7', '2018-11-8', '2018-11-9', '2018-11-12', '2018-11-13', '2018-11-14', '2018-11-15', '2018-11-16', '2018-11-19', '2018-11-20', '2018-11-21', '2018-11-22', '2018-11-23', '2018-11-26', '2018-11-27', '2018-11-28', '2018-11-29', '2018-11-30', '2018-12-3', '2018-12-4', '2018-12-5', '2018-12-6', '2018-12-7', '2018-12-10', '2018-12-11', '2018-12-12', '2018-12-13', '2018-12-14', '2018-12-17', '2018-12-18', '2018-12-19', '2018-12-20', '2018-12-21', '2018-12-24', '2018-12-25', '2018-12-26', '2018-12-27', '2018-12-28', '2019-1-2', '2019-1-3', '2019-1-4', '2019-1-7', '2019-1-8', '2019-1-9', '2019-1-10', '2019-1-11', '2019-1-14', '2019-1-15', '2019-1-16', '2019-1-17', '2019-1-18', '2019-1-21', '2019-1-22', '2019-1-23', '2019-1-24', '2019-1-25', '2019-1-28', '2019-1-29', '2019-1-30', '2019-1-31', '2019-2-1', '2019-2-11', '2019-2-12', '2019-2-13', '2019-2-14', '2019-2-15', '2019-2-18', '2019-2-19', '2019-2-20', '2019-2-21', '2019-2-22', '2019-2-25', '2019-2-26', '2019-2-27', '2019-2-28', '2019-3-1', '2019-3-4', '2019-3-5', '2019-3-6', '2019-3-7', '2019-3-8', '2019-3-11', '2019-3-12', '2019-3-13', '2019-3-14', '2019-3-15', '2019-3-18', '2019-3-19', '2019-3-20', '2019-3-21', '2019-3-22', '2019-3-25', '2019-3-26', '2019-3-27', '2019-3-28', '2019-3-29', '2019-4-1', '2019-4-2', '2019-4-3', '2019-4-4', '2019-4-8', '2019-4-9', '2019-4-10', '2019-4-11', '2019-4-12', '2019-4-15', '2019-4-16', '2019-4-17', '2019-4-18', '2019-4-19', '2019-4-22', '2019-4-23', '2019-4-24', '2019-4-25', '2019-4-26', '2019-4-29', '2019-4-30', '2019-5-6', '2019-5-7', '2019-5-8', '2019-5-9', '2019-5-10', '2019-5-13', '2019-5-14', '2019-5-15', '2019-5-16', '2019-5-17', '2019-5-20', '2019-5-21', '2019-5-22', '2019-5-23', '2019-5-24', '2019-5-27', '2019-5-28', '2019-5-29', '2019-5-30', '2019-5-31', '2019-6-3', '2019-6-4', '2019-6-5', '2019-6-6', '2019-6-10', '2019-6-11', '2019-6-12', '2019-6-13', '2019-6-14', '2019-6-17', '2019-6-18', '2019-6-19', '2019-6-20', '2019-6-21', '2019-6-24', '2019-6-25', '2019-6-26', '2019-6-27', '2019-6-28', '2019-7-1', '2019-7-2', '2019-7-3', '2019-7-4', '2019-7-5', '2019-7-8', '2019-7-9', '2019-7-10', '2019-7-11', '2019-7-12', '2019-7-15', '2019-7-16', '2019-7-17', '2019-7-18', '2019-7-19', '2019-7-22', '2019-7-23', '2019-7-24', '2019-7-25', '2019-7-26', '2019-7-29', '2019-7-30', '2019-7-31', '2019-8-1']
nb_stock_prices = [17.752929230544783, 18.385934810888358, 18.712028594701714, 18.990167410307222, 19.181987283138607, 19.16280529585547, 18.99975840394879, 19.814992863482182, 19.373807155969995, 19.1532143022139, 18.980576416665652, 18.702437601060144, 18.4338897790962, 19.229942251346454, 19.32585218776215, 19.25871523227116, 20.735728253072836, 20.591863348449294, 19.34503417504529, 19.172396289497037, 18.06943202071657, 18.472253753662482, 19.229942251346454, 19.095668340364483, 19.834174850765322, 19.834174850765322, 20.131495653653968, 19.33544318140372, 19.45053510510255, 19.795810876199045, 19.383398149611565, 18.89425747389153, 19.076486353081346, 19.642354977933934, 19.738264914349628, 19.45053510510255, 19.114850327647623, 19.105259334006057, 18.89425747389153, 18.9038484675331, 18.86548449296682, 19.047713372156636, 19.047713372156636, 19.28748821319587, 18.836711512042115, 18.62570965192759, 18.002295065225585, 17.407653459448287, 17.62824631320438, 18.558572696436606, 18.251660899906387, 18.280433880831094, 17.935158109734598, 17.877612147885184, 17.50356339586398, 18.33797984268051, 18.61611865828602, 18.33797984268051, 18.155750963490693, 17.13910563748435, 16.860966821878836, 17.225424580258473, 17.23501557390004, 17.158287624767485, 16.995240732860807, 17.599473332279675, 17.35010749759887, 17.292561535749456, 17.36928948488201, 17.0911506692765, 16.736283904538436, 16.506100057140774, 16.82260284731256, 17.0911506692765, 17.2158335866169, 17.2158335866169, 17.417244453089857, 17.359698491240444, 17.417244453089857, 17.11033265655964, 17.024013713785514, 17.263788554824746, 17.311743523032593, 16.995240732860807, 16.784238872746283, 16.54446403170705, 16.467736082574497, 16.582828006273328, 16.362235152517233, 15.882685470438767, 16.323871177950956, 16.563646018990188, 16.717101917255295, 16.678737942689022, 16.458145088932927, 16.573237012631758, 16.458145088932927, 16.55405502534862, 16.669146949047448, 16.68832893633059, 16.669146949047448, 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