1
$\begingroup$

I am sure I am missing something simple, but I would expect my portfolio beta when regressed against the market to match my individual component betas multiplied by the portfolio weights. I have created a simple example below. Any help in explaining where I have gone wrong would be much appreciated.

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?
Improve this question
$\endgroup$
5
  • $\begingroup$ But why exactly do you expect that to be the case ? Have you verified by the beta formula that the sum of betas is the beta of the sum ? I haven’t but given the definition of beta, I highly doubt it. This is the place to start. $\endgroup$
    – Ivan
    Commented Oct 8, 2019 at 15:03
  • $\begingroup$ I was basing my understanding on this StackExchange post: quant.stackexchange.com/questions/22002/… which suggests they should be the same. That is why I was asking the question. $\endgroup$
    – dsugasa
    Commented Oct 8, 2019 at 17:47
  • $\begingroup$ how off are they? $\endgroup$
    – Chris
    Commented Oct 8, 2019 at 21:27
  • $\begingroup$ quite different, which makes me think I am doing something wrong or my understanding is incorrect. I tried to provide a complete simple example of what I am doing to illustrate the problem. $\endgroup$
    – dsugasa
    Commented Oct 8, 2019 at 22:51
  • $\begingroup$ Nicely answered at stackoverflow.com/questions/58284469/why-dont-these-betas-match $\endgroup$
    – dsugasa
    Commented Oct 9, 2019 at 13:29

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.