9.4. 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 psuedocode is relatively simple:

Load the data on stock returns.
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
Merge the stock and factors returns
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

This page assumes you are familiar with CAPM, the capital asset pricing model.
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.
This file can estimate CAPM for any firms that Yahoo has ticker data for.
As written, it will estimate beta separately for each calendar year in the date range you give it. But you can adjust that.

9.4.1. Getting started¶

Note

The code below might need to be modified to work as of Feb 2023. The fix is here.

#!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

9.4.2. 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

9.4.3. 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

9.4.4. 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

9.4.5. 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

LeDataSciFi-2023