python - 为什么这些测试版不匹配？

Question

我也在Quant Finance上询问过，但我认为这里也有人可以提供帮助: https://quant.stackexchange.com/questions/49099/why-dont-these-betas-match

我希望我的投资组合贝塔值在对市场进行回归时能够与我的各个组成部分贝塔值乘以投资组合权重相匹配。我在下面创建了一个简单的示例。任何帮助解释我出错的地方将不胜感激。

import pandas as pd
    import numpy as np
    import statsmodels.api as sm
    from statsmodels import regression

    def beta(x, y):
        x = sm.add_constant(x)
        model = regression.linear_model.OLS(y, x).fit()
        # Remove the constant now that we're done
        x = x[:, 1]
        return model.params[1]


    bond_one = [100, 96, 102, 88, 96, 101, 120, 110, 105, 107, 106]
    bond_two = [98, 102, 88, 95, 105, 100, 101, 99, 104, 108, 112]
    mkt = [1000, 1004, 1000, 1010, 1020, 1000, 990, 995, 1005, 1025, 1035]

    df_mkt = pd.DataFrame(mkt, columns = ['mkt'])
    df_mkt = df_mkt.pct_change().dropna()
    df = pd.DataFrame(bond_one, columns = ['bond_one'])
    df['bond_two'] = bond_two

    df_price = df.copy()
    df = df.pct_change().dropna()

    notionals = {'bond_one': 2500000,
                    'bond_two': 6500000}

    mkt_values = {key: value*(df_price[key].iloc[-1]/100)
                  for (key, value) in notionals.items()}

    #create portfolio market value
    tot_port = sum(list(mkt_values.values()))
    #generate weights
    wts = {key: value/tot_port for (key, value) in mkt_values.items()}

    #create portfolio returns
    df_port = df.copy()*0
    df_port = df.mul(list(wts.values()), axis=1)
    df_port['port'] = df_port.sum(axis=1)

    #add port and market into original dataframe
    df['port'] = df_port['port'].copy()
    df['mkt'] = df_mkt['mkt'].copy()

    #run OLS on individuals and portfolio
    b1_beta = regression.linear_model.OLS(x = df['bond_one'].values, y=df['mkt'].values).fit()
    b2_beta = beta(x=df['bond_two'].values, y=df['mkt'].values)
    port_beta = beta(x=df['port'].values, y=df['mkt'].values)

    calc_beta = wts['bond_one']*b1_beta + wts['bond_two']*b2_beta
    ###why don't calc_beta and port_beta match?

Answer 1

差异与回归中投资组合权重的存在(或缺乏)有关。由于投资组合成分的值(value)每天都在变化，因此权重也会变化。 port_beta是您的投资组合值(value)随时间的贝塔值 market而calc_beta是投资组合成分的贝塔系数的加权和。差异的产生主要是由于 calc_beta使用当前权重计算，而 port_beta根据历史权重计算。