Herron Topic 3 - Quantitative Value Investing

FINA 6333 for Spring 2025

Author

Richard Herron 

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import pandas_datareader as pdr
import statsmodels.api as sm
import yfinance as yf
%precision 4
pd.options.display.float_format = '{:.4f}'.format
# %config InlineBackend.figure_format = 'retina'

Introduction

This notebook adapts the portfolio formation approach from Fama and French (1993), who show that firms with high book-to-market equity ratios (value stocks) tend to outperform those with low ratios (growth stocks), forming the basis of the value factor in their three-factor model. This notebook relies on two large data files. You can find these files in our shared OneDrive folder or our Notebook and Syllabus folder on Canvas. These two files are:

  1. Firm-level market data (e.g., stock prices and share counts) from the Center for Research in Security Prices (CRSP) in crsp.csv
  2. Firm-level fundamentals (i.e., financial statement information) from Compustat in compustat.csv

This notebook walks you through the steps to test a quantitative value investing strategy based on the book-to-market equity ratio (B/M). I based this lecture notebook on Gray and Carlisle (2012, chap. 1 and 7), which presents much more on quantitative value investing.

Import the data from CRSP and Compustat

CRSP

The CRSP data provide the following variables:

  1. PERMNO is the stock identifier
  2. date is the last trading day of the month
  3. SHRCD indicates share class, and we can ignore it
  4. PRC is the share price in dollars, and negative prices indicate the price is the midpoint of the bid-ask spread instead of a transaction
  5. SHROUT is the number of shares outstanding in thousands

Read the CRSP data into a data frame named crsp. Be sure to parse dates. The codea A, B, and C indicate missing values.

crsp = (
    pd.read_csv(
        filepath_or_buffer='crsp.csv',
        parse_dates=['date'],
        na_values=list('ABC')
    )
    .query('date >= 1965')
    .sort_values(by=['PERMNO', 'date'])
    .assign(
        ME=lambda x: x['PRC'].abs() * x['SHROUT'] / 1000,
        date=lambda x: x['date'] + pd.offsets.MonthEnd(0)
    )
)
crsp.head()
PERMNO date SHRCD PRC RET SHROUT ME
0 10000 1986-01-31 10 -4.3750 NaN 3680.0000 16.1000
1 10000 1986-02-28 10 -3.2500 -0.2571 3680.0000 11.9600
2 10000 1986-03-31 10 -4.4375 0.3654 3680.0000 16.3300
3 10000 1986-04-30 10 -4.0000 -0.0986 3793.0000 15.1720
4 10000 1986-05-31 10 -3.1094 -0.2227 3793.0000 11.7939

Compustat

The Compustat data provide the following variables:

  1. GVKEY is the S&P firm identifier
  2. LPERMNO is the link between CRSP and Compustat
  3. datadate is the date of the filing, which is the last day of the fiscal year
  4. fyear is the fiscal year
  5. ceq is the book value of equity
  6. ib is income before extraordinary items
  7. We can ignore the other variables that Wharton Research Data Services (WRDS) adds to this data set

Read the Compustat data into a data frame named compustat. Be sure to parse dates.

compustat = (
    pd.read_csv(
        filepath_or_buffer='compustat.csv',
        parse_dates=['datadate']
    )
    .query('datadate >= 1965')
    .sort_values(['LPERMNO', 'fyear', 'datadate'])
    .drop_duplicates(subset=['LPERMNO', 'fyear'], keep='last')
)
compustat.head()
GVKEY LPERMNO datadate fyear indfmt consol popsrc datafmt curcd ceq ib costat
165681 13007 10000 1986-10-31 1986.0000 INDL C D STD USD 0.4180 -0.7300 I
165586 12994 10001 1986-06-30 1986.0000 INDL C D STD USD 5.4320 0.6690 I
165587 12994 10001 1987-06-30 1987.0000 INDL C D STD USD 5.3690 0.3120 I
165588 12994 10001 1988-06-30 1988.0000 INDL C D STD USD 5.5120 0.5420 I
165589 12994 10001 1989-06-30 1989.0000 INDL C D STD USD 6.3210 1.2080 I

Create interim data frames

To test the book/market investing strategy, we need to match the following data:

  1. Book value of equity for year \(t-1\)
  2. Market value of equity from December of year \(t-1\)
  3. Portfolios for year \(t\) based on book and market values of equity in year \(t-1\)
  4. Returns from July of year \(t\) through June of year \(t+1\)

We will form portfolios once a year because the book value of equity updates once a year. Fama and French (1993) wait until June of year \(t\) to form portfolios, ensuring financial data from year \(t-1\) is public, then track returns from July in year \(t\) through June in year \(t+1\). The simplest and clearest way to match these data is to create one data frame for each of these three data sets.

Market value of equity from December of year \(t-1\)

Then create a new data frame mve that contains the latest market value of equity as of December.

mve = (
    crsp
    .query('ME > 0')
    .groupby(['PERMNO', pd.Grouper(key='date', freq='YE-DEC')])
    [['ME']]
    .last()
)
crsp.query('PERMNO == 10001').head(12)
PERMNO date SHRCD PRC RET SHROUT ME
18 10001 1986-01-31 11 -6.1250 NaN 985.0000 6.0331
19 10001 1986-02-28 11 -6.2500 0.0204 985.0000 6.1562
20 10001 1986-03-31 11 -6.3125 0.0252 985.0000 6.2178
21 10001 1986-04-30 11 -6.3750 0.0099 985.0000 6.2794
22 10001 1986-05-31 11 -6.3125 -0.0098 985.0000 6.2178
23 10001 1986-06-30 11 -6.1250 -0.0131 985.0000 6.0331
24 10001 1986-07-31 11 -6.0625 -0.0102 985.0000 5.9716
25 10001 1986-08-31 11 -6.5000 0.0722 985.0000 6.4025
26 10001 1986-09-30 11 6.3750 -0.0031 991.0000 6.3176
27 10001 1986-10-31 11 6.6250 0.0392 991.0000 6.5654
28 10001 1986-11-30 11 7.0000 0.0566 991.0000 6.9370
29 10001 1986-12-31 11 7.0000 0.0150 991.0000 6.9370 
mve.head()
ME
PERMNO date
10000 1986-12-31 1.9816
1987-12-31 0.8516
10001 1986-12-31 6.9370
1987-12-31 5.8280
1988-12-31 6.3623

Book value of equity for year \(t-1\)

Create a new data frame bve that contains the latest book value of equity as of December. Because some firms have fiscal years that do not end in December, use .groupby(), pd.Grouper() with YE-DEC, and .last() to roll forward earlier fiscal year ends.

bve = (
    compustat
    .query('ceq > 0')
    .groupby(by=['LPERMNO', pd.Grouper(key='datadate', freq='YE-DEC')])
    [['ceq']]
    .last()
)
compustat.query('LPERMNO == 10001').head()
GVKEY LPERMNO datadate fyear indfmt consol popsrc datafmt curcd ceq ib costat
165586 12994 10001 1986-06-30 1986.0000 INDL C D STD USD 5.4320 0.6690 I
165587 12994 10001 1987-06-30 1987.0000 INDL C D STD USD 5.3690 0.3120 I
165588 12994 10001 1988-06-30 1988.0000 INDL C D STD USD 5.5120 0.5420 I
165589 12994 10001 1989-06-30 1989.0000 INDL C D STD USD 6.3210 1.2080 I
165590 12994 10001 1990-06-30 1990.0000 INDL C D STD USD 7.1790 1.1310 I 
bve.head()
ceq
LPERMNO datadate
10000 1986-12-31 0.4180
10001 1986-12-31 5.4320
1987-12-31 5.3690
1988-12-31 5.5120
1989-12-31 6.3210

Portfolios for year \(t\)

1 + pd.qcut(x=np.arange(10), q=5, labels=False)
array([1, 1, 2, 2, 3, 3, 4, 4, 5, 5])
portfolios = (
    bve
    [['ceq']]
    .dropna()
    .rename_axis(index=['PERMNO', 'Date'])
    .join(
        other=(
            mve
            [['ME']]
            .dropna()
            .rename_axis(index=['PERMNO', 'Date'])
        ),
        how='inner'
    )
    .assign(BM=lambda x: x['ceq'] / x['ME'])
    .reset_index()
    .assign(
        Portfolio=lambda x: x.groupby('Date')['BM'].transform(lambda x: 1 + pd.qcut(x=x, q=10, labels=False)),
        Date=lambda x: x['Date'] + pd.DateOffset(months=7)
    )
    [['PERMNO', 'Date', 'Portfolio', 'BM']]
)
portfolios.head()
PERMNO Date Portfolio BM
0 10000 1987-07-31 2 0.2109
1 10001 1987-07-31 7 0.7830
2 10001 1988-07-31 7 0.9212
3 10001 1989-07-31 7 0.8664
4 10001 1990-07-31 5 0.6109 
(
    portfolios
    .groupby(by=['Portfolio', 'Date'])
    ['BM']
    .mean()
    .groupby(by=['Portfolio'])
    .mean()
    .plot(kind='bar')
)
plt.ylabel('Mean B/M')
plt.xlabel('Portfolio (1 = Low B/M, 10 = High B/M)')
plt.title('Mean B/M for Ten Portfolios Formed on B/M')
plt.show()

Returns from July of year \(t\) to June of year \(t+1\)

Now we assign returns to each of these ten portfolios.

returns = (
    pd.merge_asof(
        left=crsp.sort_values(by=['date', 'PERMNO']),
        right=portfolios.sort_values(by=['Date', 'PERMNO']),
        left_on='date',
        right_on='Date',
        by='PERMNO',
        tolerance=pd.Timedelta('366 days')
    )
    [['PERMNO', 'date', 'RET', 'Portfolio']]
    .dropna()
    .assign(Portfolio=lambda x: x['Portfolio'].astype(int))
    .rename(columns={'date': 'Date'})
)
returns
PERMNO Date RET Portfolio
37636 10006 1966-07-31 -0.0149 6
37640 10102 1966-07-31 -0.0545 6
37641 10137 1966-07-31 0.0105 4
37642 10145 1966-07-31 -0.0129 6
37643 10153 1966-07-31 -0.0788 9
... ... ... ... ...
3457680 93397 2024-12-31 -0.1174 5
3457681 93426 2024-12-31 0.0218 7
3457682 93429 2024-12-31 -0.0947 3
3457683 93434 2024-12-31 0.1333 10
3457684 93436 2024-12-31 0.1700 1

2690626 rows × 4 columns

Performance of Portfolios Formed on B/M

(
    returns
    .groupby(['Portfolio', 'Date'])
    ['RET']
    .mean()
    .groupby(['Portfolio'])
    .mean()
    .mul(100)
    .plot(kind='bar')
)
plt.ylabel('Mean Monthly Return (%)')
plt.xlabel('Portfolio (1 = Low B/M, 10 = High B/M)')
plt.title('Mean Monthly Returns for Equal-Weighted Portfolios Formed on B/M')
plt.show()

(
    returns
    .groupby(['Portfolio', 'Date'])
    ['RET']
    .mean()
    .unstack('Portfolio')
    .add(1)
    .cumprod()
    .plot()
)
plt.semilogy()
plt.ylabel('Value of $1 Investment')
plt.title('Values of $1 Investments in Equal-Weighted Portfolios Formed on B/M')
plt.show()

(
    returns
    .groupby(['Portfolio', 'Date'])
    ['RET']
    .mean()
    .unstack('Portfolio')
    .assign(Diff=lambda x: x[10] - x[1])
    ['Diff']
    .rolling(12*10)
    .mean()
    .mul(100)
    .plot()
)
plt.ylabel('10-year Rolling Mean of Monthly Spread (%)')
plt.title('10-year Rolling Mean of Monthly Spread\n Between Value and Growth Portfolios')
plt.show()

References

Fama, Eugene F., and Kenneth R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33 (1): 3–56.
Gray, Wesley R., and Tobias E. Carlisle. 2012. Quantitative Value: A Practitioner’s Guide to Automating Intelligent Investment and Eliminating Behavioral Errors. John Wiley & Sons.