为什么这些贝塔不匹配？

Question

我也在 Quant Finance 上问过，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在对市场进行回归时与我的单个成分贝塔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。任何帮助解释我哪里出错的地方都将不胜感激。

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。因为您的投资组合成分的价值每天都在变化，所以权重也是如此。 port_beta 是您的投资组合价值到 market 的 beta，而 calc_beta 是投资组合成分的 beta 加权和。产生差异的主要原因是 calc_beta 是使用当前权重计算的，而 port_beta 是根据历史权重计算的。

为什么这些贝塔不匹配？

Why don't these betas match?

python

python-3.x

linear-regression

statsmodels

quantitative-finance