9.2. Estimating beta via CAPM, using Yahoo Finance

Let’s estimate, for each firm, for each year, the alpha and beta of a stock, using CAPM as our asset pricing model.

So we want a dataset that looks like this:

Firm

Year

alpha

beta

GM

2000

0.01

1.04

GM

2001

-0.005

0.98

…but it will do this for every firm, every year!

The psuedo code is relatively simple:

  1. Load the data on stock returns.

  2. Load the market return premium and the risk free rate (the “factors” in CAPM).

    • Note: Make sure your returns are scaled like your factors (e.g., below, I convert stock returns to percentages to match the convention in the FF dataset)

    • Make sure your stock returns and market returns are both excess returns

  3. Merge the stock and factors returns

  4. For each firm and time period you’re interested in, estimate the CAPM model to get the stock’s alpha and beta for that period.

Note

  1. This page assumes you are familiar with CAPM, the capital asset pricing model.

  2. This page uses Yahoo finance for stock returns. Yahoo Finance is more of a “quick and dirty” way to get return data. CRSP is the industry standard data provider for stock returns, and you can access via WRDS.

  3. This file can estimate CAPM for any firms that Yahoo has ticker data for.

  4. As written, it will estimate beta separately for each calendar year in the date range you give it. But you can adjust that.

9.2.1. Getting started

#!pip install pandas_datareader # uncomment and run this ONE TIME ONLY to install pandas data reader
import pandas as pd
import numpy as np
import pandas_datareader as pdr # you might need to install this (see above)
from datetime import datetime

9.2.2. Load asset return data

Load your stock returns. This file uses yahoo finance. The returns don’t even have to be firms! They can be any asset. (Portfolios, mutual funds, crypto, …)

# choose your firms and years 
stocks = ['SBUX','AAPL','MSFT']
start  = datetime(2016, 1, 1)
end    = datetime(2016, 12, 31)

Tip

The code in the next block is explained more thoroughly in handouts/factor_loading_simple.ipynb in the textbook repo, because that file prints the status of the data throughout. Looking at this might help.

# download stock prices 
# here, from yahoo: not my fav source, but quick. 
# we need to do some data manipulation to get the data ready 
stock_prices = pdr.get_data_yahoo(stocks, start=start, end=end)
stock_prices = stock_prices.filter(like='Adj Close') # reduce to just columns with this in the name
stock_prices.columns = stocks # put their tickers as column names

# refmt from wide to long
stock_prices = stock_prices.stack().swaplevel().sort_index().reset_index()
stock_prices.columns = ['Firm','Date','Adj Close']

# add return var = pct_change() function compares to prior row
# EXCEPT: don't compare for first row of one firm with last row of prior firm!
# MAKE SURE YOU CREATE THE VARIABLES WITHIN EACH FIRM - use groupby
stock_prices['ret'] = stock_prices.groupby('Firm')['Adj Close'].pct_change()
stock_prices['ret'] = stock_prices['ret'] *100 # convert to p.p. to match FF's convention on scaling (daily % rets)
stock_prices.head(15)
Firm Date Adj Close ret
0 AAPL 2016-01-04 24.220573 NaN
1 AAPL 2016-01-05 23.613630 -2.505899
2 AAPL 2016-01-06 23.151514 -1.956989
3 AAPL 2016-01-07 22.174414 -4.220460
4 AAPL 2016-01-08 22.291668 0.528782
5 AAPL 2016-01-11 22.652626 1.619251
6 AAPL 2016-01-12 22.981384 1.451303
7 AAPL 2016-01-13 22.390528 -2.571022
8 AAPL 2016-01-14 22.880220 2.187053
9 AAPL 2016-01-15 22.330753 -2.401494
10 AAPL 2016-01-19 22.222696 -0.483893
11 AAPL 2016-01-20 22.252586 0.134502
12 AAPL 2016-01-21 22.139933 -0.506250
13 AAPL 2016-01-22 23.317051 5.316720
14 AAPL 2016-01-25 22.861835 -1.952286

9.2.3. Get the factor returns

Above, we got the asset returns, \(r_i\) (called “ret” in the dataframe).

To estimate \(\alpha\) and \(\beta\) in \(r_i-r_f = \alpha + \beta (r_m-r_f)\), we need \((r_m-r_f)\) and \(r_f\). Let’s download those now.

Note: \((r_m-r_f)\) is the excess return on the market, which is one “factor”. Hedge funds typically use 5 factors in tests.

# We need (r_mkt - rf), and rf
# the Fama French data library is a benchmark asset pricing dataset 
ff = pdr.get_data_famafrench('F-F_Research_Data_5_Factors_2x3_daily',start=start,end=end)[0] # the [0] is because the imported obect is a dictionary, and key=0 is the dataframe
ff = ff.reset_index().rename(columns={"Mkt-RF":"mkt_excess"})
ff
Date mkt_excess SMB HML RMW CMA RF
0 2016-01-04 -1.59 -0.76 0.52 0.35 0.40 0.000
1 2016-01-05 0.12 -0.24 0.01 0.07 0.31 0.000
2 2016-01-06 -1.35 -0.22 0.00 0.16 0.05 0.000
3 2016-01-07 -2.44 -0.28 0.09 0.52 0.36 0.000
4 2016-01-08 -1.11 -0.51 -0.04 0.25 0.06 0.000
... ... ... ... ... ... ... ...
247 2016-12-23 0.19 0.52 -0.50 -0.40 -0.15 0.001
248 2016-12-27 0.27 0.23 0.14 0.14 0.04 0.001
249 2016-12-28 -0.87 -0.29 0.09 0.19 -0.15 0.001
250 2016-12-29 -0.04 0.10 -0.33 0.27 0.02 0.001
251 2016-12-30 -0.52 -0.06 0.20 -0.09 0.03 0.001

252 rows × 7 columns

9.2.4. Merge the asset and factor returns

assets_and_factors = pd.merge(
    left=stock_prices,
    right=ff,
    on="Date",
    how="inner",
    indicator=True,
    validate="many_to_one",
)
assets_and_factors
Firm Date Adj Close ret mkt_excess SMB HML RMW CMA RF _merge
0 AAPL 2016-01-04 24.220573 NaN -1.59 -0.76 0.52 0.35 0.40 0.000 both
1 MSFT 2016-01-04 49.591057 NaN -1.59 -0.76 0.52 0.35 0.40 0.000 both
2 SBUX 2016-01-04 52.108959 NaN -1.59 -0.76 0.52 0.35 0.40 0.000 both
3 AAPL 2016-01-05 23.613630 -2.505899 0.12 -0.24 0.01 0.07 0.31 0.000 both
4 MSFT 2016-01-05 49.817291 0.456200 0.12 -0.24 0.01 0.07 0.31 0.000 both
... ... ... ... ... ... ... ... ... ... ... ...
751 MSFT 2016-12-29 58.483051 -0.142872 -0.04 0.10 -0.33 0.27 0.02 0.001 both
752 SBUX 2016-12-29 51.127605 -0.053199 -0.04 0.10 -0.33 0.27 0.02 0.001 both
753 AAPL 2016-12-30 27.220133 -0.779584 -0.52 -0.06 0.20 -0.09 0.03 0.001 both
754 MSFT 2016-12-30 57.776413 -1.208279 -0.52 -0.06 0.20 -0.09 0.03 0.001 both
755 SBUX 2016-12-30 50.401356 -1.420465 -0.52 -0.06 0.20 -0.09 0.03 0.001 both

756 rows × 11 columns

9.2.5. Estimate CAPM

So the data’s basically ready. (We need to do two quick things below.)

Again, the goal is to estimate, for each firm, for each year, alpha and beta, from the CAPM formula.

Well, as we’ve said, if you are doing a “for each” on a dataframe, that means you want to use groupby!

So, I have a dataframe, and for each firm, and for each year, I want to <do stuff> (run regressions).

That almost directly translates to the code we need: assets_and_factors.groupby([firm,year]).runregression(). Except there is no “runregression” function that applies to pandas groupby objects. But we can write such a function and then apply() it. Meaning, our plan is to basically use this code: assets_and_factors.groupby([firm,year]).apply(<our own reg fcn>).

We just need to write a reg function that works on groupby objects.

import statsmodels.api as sm


def reg_in_groupby(df, formula="ret_excess ~ mkt_excess + SMB + HML"):
    """
    Want to run regressions after groupby? E.g., repeat the regression 
    for each firm-year?
    
    This will do it! 
    
    Note: This defaults to a FF3 model assuming specific variable names. If you
    want to run any other regression, just specify your model.
    
    Usage: 
        df.groupby(<whatever>).apply(reg_in_groupby)
        df.groupby(<whatever>).apply(reg_in_groupby,formula=<whatever>)
    """
    return pd.Series(sm.formula.ols(formula, data=df).fit().params)
(
    assets_and_factors # grab the data
    
    # Two things before the regressions:
    # 1. need a year variable (to group on)
    # 2. the market returns in FF are excess returns, so 
    #    our stock returns need to be excess as well
    .assign(year = assets_and_factors.Date.dt.year,
            ret_excess = assets_and_factors.ret - assets_and_factors.RF)
    
    # ok, run the regs, so easy!
    .groupby(['Firm','year']).apply(reg_in_groupby,formula='ret_excess ~ mkt_excess')
    
    # and clean up - with better var names
    .rename(columns={'Intercept':'alpha','mkt_excess':'beta'})
    .reset_index()
)
Firm year alpha beta
0 AAPL 2016 -0.001081 0.965622
1 MSFT 2016 0.000690 1.166076
2 SBUX 2016 -0.056862 0.848162