Small Cap Value and Momentum¶

MGMT 638: Data-Driven Investments: Equity¶

Kerry Back, Rice University¶

Alternate Code to Access SQL Server¶

  • Hopefully, "pip3 install" has solved the Mac problems (on a Mac always use pip3 instead of pip).
  • If there continues to be a problem with pymssql, it is possible to use pyodbc instead.
  • On a Mac,
    • Install Microsoft's ODBC Server
    • Then pip3 install pyodbc
    • Then create a connection with the following code.
  • If this still doesn't work, we can install and use any SQL client, for example Azure Data Studio.
In [5]:
"""
from sqlalchemy import create_engine

server = 'fs.rice.edu'
database = 'stocks'
username = 'stocks'
password = '6LAZH1'
driver = 'SQL+Server'
string = "mssql+pyodbc://" + username + ":" + password + "@" + server + "/" + database + "?driver=" + driver
conn = create_engine(string).connect()
"""
Out[5]:
'\nfrom sqlalchemy import create_engine\n\nserver = \'fs.rice.edu\'\ndatabase = \'stocks\'\nusername = \'stocks\'\npassword = \'6LAZH1\'\ndriver = \'SQL+Server\'\nstring = "mssql+pyodbc://" + username + ":" + password + "@" + server + "/" + database + "?driver=" + driver\nconn = create_engine(string).connect()\n'

Why Long and Short?¶

  • Can do long and short and index ETF
    • earn index return + long return - short return - short borrowing fee
    • except cannot use short proceeds to buy index or long
  • to get 100 index + 100 long - 100 short, must invest 200 or borrow 100
    • earn index return + long return - short return - short borrowing fee - margin loan rate
  • or buy index futures
    • implicit interest rate in futures (spot-futures parity) will be less than margin loan rate
    • but maybe bad tax consequences (40% short-term gains $\approx$ ordinary income)

Small Cap Value and Growth¶

  • small cap $\approx$ Russell 2000
  • value usually measured by PB or PE
  • some academic work (Fama-French) found PB is a better predictor of returns
  • low PB = value, high PB = growth
  • academics usually use BP instead of PB and call it book-to-market
  • high BP = value, low BP = growth
  • small-cap growth has historically had very poor returns

Value and Momentum Portfolios I¶

  • get marketcap data in addition to prices
  • calculate momentum
  • keep stocks between 1,001 and 3,000 in market cap
  • create 5x5 sort on value and momentum
  • compute equally weighted portfolio returns

Value and Momentum Portfolios II¶

  • rank each stock between 1,001 and 3,000 on value
    • low rank = best (low pb)
  • rank each stock also on momentum
    • low rank = best (high momentum)
  • add ranks to get a single combined rank
    • low combined rank = best
  • go long best n and short worst n (e.g., n=50)

Value and Momentum Portfolios III¶

  • For long only portfolio, choose best stocks in each sector and match sector weights to benchmark (e.g., Russell 2000).
  • For long-short portfolio, match shorts and longs in each sector to get market-neutral and sector-neutral portfolio.

Value and Momentum Portfolios IV¶

  • Use machine learning to find the optimal way to combine value and momentum
  • And add other predictors (ROE, investment rate, short-term reversal, ...)

Data and Procedure¶

  • Get sectors from tickers table
  • Get marketcap and pb from weekly table
  • Get closeadj and closeunadj from sep_weekly as before
  • Calculate momentum as before
  • Filter to 1,001-3,000 on marketcap each week
  • Form portfolios

Create connection¶

Get data¶

Calculate momentum¶

Merge marketcap and pb¶

Save this week's data¶

In [12]:
today = df[df.date==df.date.max()]
today.head(3)
Out[12]:
ticker date ret mom closeunadj marketcap pb sector
668 A 2023-10-27 -0.059141 -0.188863 102.77 30069.2 5.4 Healthcare
981 AA 2023-10-27 -0.020825 -0.256682 23.51 4195.9 0.9 Basic Materials
1644 AADI 2023-10-27 0.039120 -0.626255 4.25 104.2 0.8 Healthcare

Shift predictors and shift filtering variables to backtest¶

In [13]:
df = df.set_index(["ticker", "date"])
variables = ["mom", "pb", "marketcap", "closeunadj"]
df[variables] = df.groupby("ticker", group_keys=False)[variables].shift()
df = df.dropna()
df.head(3)
Out[13]:
ret mom closeunadj marketcap pb sector
ticker date
A 2011-01-14 0.008130 0.199287 41.88 14557.7 4.5 Healthcare
2011-01-21 0.050456 0.270914 42.22 14675.8 4.5 Healthcare
2011-01-28 -0.075973 0.337839 44.35 15416.2 4.8 Healthcare

Filter out penny stocks and filter to small caps¶

In [14]:
df = df[df.closeunadj>5]
df["rnk"] = df.groupby("date").marketcap.rank(
    ascending=False, 
    method="first"
)
df = df[(df.rnk>1000) & (df.rnk<=3000)]
df.reset_index().groupby("date").ticker.count()
Out[14]:
date
2011-01-14    2000
2011-01-21    2000
2011-01-28    2000
2011-02-04    2000
2011-02-11    2000
              ... 
2023-09-29    1865
2023-10-06    1853
2023-10-13    1837
2023-10-20    1829
2023-10-27    1802
Name: ticker, Length: 668, dtype: int64

Value and Momentum Portfolios I¶

In [15]:
df["value_group"] = df.groupby("date", group_keys=False).pb.apply(
    lambda x: pd.qcut(x, 5, labels=range(1, 6))
)
df["mom_group"] = df.groupby("date", group_keys=False).mom.apply(
    lambda x: pd.qcut(x, 5, labels=range(1, 6))
)
rets = df.groupby(["date", "value_group", "mom_group"]).ret.mean()
rets = rets.unstack().unstack()
rets.head(3)
Out[15]:
mom_group 1 2 ... 4 5
value_group 1 2 3 4 5 1 2 3 4 5 ... 1 2 3 4 5 1 2 3 4 5
date
2011-01-14 -0.004985 -0.014070 -0.008452 -0.006321 -0.009538 -0.006124 -0.011125 -0.008001 -0.010104 -0.015608 ... -0.000915 -0.011512 -0.004276 -0.002012 0.002801 -0.002485 -0.012314 -0.001888 0.001080 0.012422
2011-01-21 0.018622 0.018095 0.020878 0.013126 0.003709 0.013191 0.016730 0.016485 0.010804 0.009455 ... 0.010303 0.011679 0.018304 0.011691 0.020454 0.002941 0.019437 0.018831 0.023021 0.009367
2011-01-28 -0.026927 -0.021369 -0.030210 -0.027047 -0.030028 -0.010046 -0.016295 -0.016319 -0.029533 -0.041064 ... -0.015679 -0.018504 -0.017971 -0.019429 -0.024112 -0.015446 -0.025357 -0.016465 -0.039987 -0.043814

3 rows × 25 columns

In [16]:
(52*rets.mean()).unstack().round(3)
Out[16]:
value_group 1 2 3 4 5
mom_group
1 0.040 0.039 0.061 0.053 -0.004
2 0.114 0.087 0.076 0.079 0.067
3 0.129 0.093 0.094 0.101 0.098
4 0.145 0.095 0.094 0.117 0.078
5 0.176 0.125 0.113 0.104 0.138

How many stocks are in the groups?¶

In [17]:
counts = df.groupby(["date", "value_group", "mom_group"]).ret.count()
counts = counts.unstack().unstack()
counts.tail(3)
Out[17]:
mom_group 1 2 ... 4 5
value_group 1 2 3 4 5 1 2 3 4 5 ... 1 2 3 4 5 1 2 3 4 5
date
2023-10-13 131 74 61 57 45 103 94 57 53 60 ... 50 75 87 79 76 32 38 76 94 128
2023-10-20 138 75 57 50 46 108 94 59 47 58 ... 58 71 80 66 91 28 41 85 95 117
2023-10-27 144 63 54 52 48 107 94 52 57 50 ... 62 80 55 79 84 36 36 74 98 117

3 rows × 25 columns

Value and Momentum Portfolios II¶

  • Rank stocks on momentum each week: 1=best, 2=next best, etc. (best=high momentum)
  • Rank stocks on pb each week: 1=best, 2=next best, etc. (best=low pb)
  • Add momentum and pb ranks: lowest combined ranks are best stocks
  • Test A: sort into deciles on combined ranks and compute equally weighted returns
  • Test B: go long best 50 stocks and short worst 50 stocks and compute returns
In [18]:
df["mom_rnk"] = df.groupby("date", group_keys=False).mom.rank(
    ascending=False, 
    method="first"
)
df["pb_rnk"] = df.groupby("date", group_keys=False).pb.rank(
    ascending=True, 
    method="first"
)
df["combined_rnk"] = df.mom_rnk + df.pb_rnk

Test A: Deciles¶

In [19]:
df["decile"] = df.groupby("date", group_keys=False).combined_rnk.apply(
    lambda x: pd.qcut(x, 10, labels=range(1, 11))
)
rets = df.groupby(["date", "decile"]).ret.mean()
rets = rets.unstack()
52*rets.mean()
Out[19]:
decile
1     0.140992
2     0.111454
3     0.109872
4     0.106887
5     0.096466
6     0.102888
7     0.092114
8     0.057470
9     0.075204
10    0.034701
dtype: float64

Test B: Top 44 and Bottom 44¶

  • rank at each date on combined_rnk
  • put best 44 in long portfolio at each date
  • put worst 44 in short portfolio at each date
  • compute equally weighted returns in each portfolio
  • calculate long minus short return
In [21]:
print(f"annualized mean long return is {52*long_rets.mean():.2%}")
print(f"annualized mean short return is {52*short_rets.mean():.2%}")

annualized mean long return is 18.68%
annualized mean short return is 0.47%
In [22]:
(1+long_rets-short_rets).cumprod().plot(logy=True)
Out[22]:
<AxesSubplot: xlabel='date'>

What are the top 44 and bottom 44 today?¶

  • Apply penny stock and size filters to today dataframe
  • Rank on momentum (low rank = high momentum = best)
  • Rank on value (low rank = low pb = best)
  • Add ranks
  • Find best 44 and worst 44 stocks today
In [25]:
long
Out[25]:
ticker sector mom_rnk pb_rnk combined_rnk closeunadj
772871 EHTH Financial Services 26 32 58 7.860
427948 CBUS Healthcare 30 69 99 10.270
2367118 TRML Healthcare 78 53 131 14.000
1429651 LSEA Real Estate 97 39 136 7.240
2197648 SPHR Communication Services 100 51 151 33.470
387833 BZH Consumer Cyclical 48 221 269 23.430
2449388 USAP Basic Materials 102 197 299 14.020
1761051 OPRT Financial Services 272 44 316 5.510
1597522 MUX Basic Materials 99 267 366 7.090
1488461 MDV Real Estate 125 260 385 15.210
1139786 HOV Consumer Cyclical 29 362 391 66.360
1593141 MTW Industrials 128 266 394 12.320
2200559 SPNT Financial Services 129 294 423 9.610
950535 FRD Basic Materials 276 147 423 9.710
1041933 GNW Financial Services 392 33 425 5.810
2178802 SNFCA Financial Services 325 103 428 7.050
1706041 NWLI Financial Services 46 390 436 478.460
488571 CION Financial Services 322 126 448 9.700
2149533 SKYW Industrials 36 413 449 42.270
925188 FLXS Consumer Cyclical 239 241 480 19.750
1013867 GHLD Financial Services 406 80 486 10.650
1148943 HRTG Financial Services 6 490 496 5.850
1763361 OPY Financial Services 457 45 502 33.710
1738882 OIS Energy 232 272 504 7.990
306996 BH Consumer Cyclical 442 65 507 144.660
32796 ACOR Healthcare 513 3 516 9.560
941111 FOR Real Estate 41 480 521 23.390
438831 CCS Consumer Cyclical 195 328 523 60.850
2300744 TDS Communication Services 504 24 528 17.800
1309749 KELYA Industrials 445 86 531 17.580
2639665 ZIMV Healthcare 508 27 535 7.020
2097818 SCX Industrials 356 194 550 10.390
1700409 NVRI Industrials 162 389 551 5.730
429145 CCAP Financial Services 227 327 554 15.445
1026237 GLRE Financial Services 308 247 555 10.750
256238 AXR Real Estate 243 313 556 16.700
574003 CPSS Financial Services 225 332 557 9.390
1297858 JXN Financial Services 525 38 563 37.190
1515142 MHO Consumer Cyclical 68 502 570 81.320
988986 GBLI Financial Services 220 353 573 36.480
2354021 TPH Consumer Cyclical 152 423 575 24.440
1157233 HT Real Estate 426 157 583 9.890
2503950 VRA Consumer Cyclical 57 536 593 7.190
286492 BCSF Financial Services 286 317 603 14.690
In [26]:
short
Out[26]:
ticker sector mom_rnk pb_rnk combined_rnk closeunadj
291701 BE Industrials 1409 1654 3063 9.780
1903132 PRCT Healthcare 1393 1678 3071 26.090
260770 AYX Technology 1304 1767 3071 31.460
244448 AVXL Healthcare 1685 1399 3084 5.200
1447625 LYFT Technology 1387 1701 3088 9.260
1217100 IMXI Technology 1566 1524 3090 16.200
1253736 IRTC Healthcare 1378 1716 3094 78.190
2107199 SEMR Technology 1463 1635 3098 8.050
2418352 UDMY Consumer Defensive 1551 1551 3102 8.770
2375532 TRUP Financial Services 1665 1438 3103 20.690
804166 ENVX Industrials 1494 1628 3122 8.770
1569788 MRTX Healthcare 1557 1579 3136 55.370
2630788 YOU Technology 1433 1704 3137 16.520
1298662 JYNT Healthcare 1690 1471 3161 7.890
2227119 SSTI Technology 1722 1449 3171 14.790
2339832 TMCI Healthcare 1678 1539 3217 9.500
220283 ATOM Technology 1560 1665 3225 6.320
2388282 TTGT Communication Services 1732 1497 3229 25.260
2298608 TCX Technology 1734 1496 3230 16.690
1374556 LEE Consumer Cyclical 1658 1578 3236 8.960
350200 BOWL Consumer Cyclical 1518 1718 3236 10.340
2524170 VVI Industrials 1484 1759 3243 23.050
1549618 MODN Technology 1552 1692 3244 23.770
1550287 MODV Healthcare 1769 1493 3262 40.130
1694815 NVCR Healthcare 1777 1487 3264 12.640
312569 BIGC Technology 1513 1754 3267 8.925
2345995 TNDM Healthcare 1759 1508 3267 17.990
356528 BRDG Financial Services 1565 1706 3271 7.120
794073 ENFN Technology 1524 1750 3274 8.250
2229642 STAA Healthcare 1660 1619 3279 38.550
1544665 MNTK Utilities 1657 1644 3301 9.750
1011292 GH Healthcare 1592 1710 3302 24.960
507828 CLPT Healthcare 1715 1589 3304 5.180
806691 EP Energy 1618 1707 3325 8.020
97708 ALHC Healthcare 1686 1640 3326 6.840
2395412 TVTX Healthcare 1750 1577 3327 6.800
2077665 SAVA Healthcare 1736 1593 3329 19.890
2514031 VSCO Consumer Cyclical 1741 1611 3352 18.520
1458847 MARPS Energy 1662 1713 3375 5.030
1056027 GRND Technology 1674 1769 3443 5.870
2379344 TSE Basic Materials 1735 1708 3443 5.990
38102 ACXP Healthcare 1733 1719 3452 5.380
2056469 RVNC Healthcare 1697 1756 3453 7.980
1856242 PI Technology 1724 1768 3492 61.660

Sector weights¶

In [27]:
long.groupby("sector").ticker.count()
Out[27]:
sector
Basic Materials            3
Communication Services     2
Consumer Cyclical          8
Energy                     1
Financial Services        16
Healthcare                 4
Industrials                5
Real Estate                5
Name: ticker, dtype: int64
In [28]:
short.groupby("sector").ticker.count()
Out[28]:
sector
Basic Materials            1
Communication Services     1
Consumer Cyclical          3
Consumer Defensive         1
Energy                     2
Financial Services         2
Healthcare                17
Industrials                3
Technology                13
Utilities                  1
Name: ticker, dtype: int64

Value and Momentum Portfolios III¶

  • Rank on combined rank separately in each sector
  • Do that by grouping by date and sector instead of just date
  • Go long best 4 and short worst 4 in each sector to get sector neutrality
  • Compute equally weighted returns for long and short portfolios
  • Compute long minus short return
In [30]:
print(f"annualized mean long return is {52*long_rets.mean():.2%}")
print(f"annualized mean short return is {52*short_rets.mean():.2%}")

annualized mean long return is 15.32%
annualized mean short return is 1.54%
In [31]:
(1+long_rets-short_rets).cumprod().plot(logy=True)
Out[31]:
<AxesSubplot: xlabel='date'>

Best and worst stocks today in sector-neutral strategy¶

  • Just group by sector when ranking
  • Choose best 4 and worst 4 in each sector
In [33]:
long_neutral
Out[33]:
ticker sector mom_rnk pb_rnk combined_rnk closeunadj
2449388 USAP Basic Materials 102 197 299 14.020
1597522 MUX Basic Materials 99 267 366 7.090
950535 FRD Basic Materials 276 147 423 9.710
2638060 ZEUS Basic Materials 47 636 683 49.430
2197648 SPHR Communication Services 100 51 151 33.470
2300744 TDS Communication Services 504 24 528 17.800
2455127 USM Communication Services 274 430 704 41.390
1177442 IAC Communication Services 704 159 863 41.840
387833 BZH Consumer Cyclical 48 221 269 23.430
1139786 HOV Consumer Cyclical 29 362 391 66.360
925188 FLXS Consumer Cyclical 239 241 480 19.750
306996 BH Consumer Cyclical 442 65 507 144.660
2193812 SPB Consumer Defensive 106 620 726 75.250
889276 FDP Consumer Defensive 727 140 867 25.010
2601835 WVVI Consumer Defensive 856 59 915 5.242
142373 ANDE Consumer Defensive 197 854 1051 49.310
1738882 OIS Energy 232 272 504 7.990
1123116 HLX Energy 116 584 700 9.870
1641108 NGS Energy 315 385 700 14.220
538462 CNX Energy 268 458 726 21.200
772871 EHTH Financial Services 26 32 58 7.860
1761051 OPRT Financial Services 272 44 316 5.510
2200559 SPNT Financial Services 129 294 423 9.610
1041933 GNW Financial Services 392 33 425 5.810
427948 CBUS Healthcare 30 69 99 10.270
2367118 TRML Healthcare 78 53 131 14.000
32796 ACOR Healthcare 513 3 516 9.560
2639665 ZIMV Healthcare 508 27 535 7.020
1593141 MTW Industrials 128 266 394 12.320
2149533 SKYW Industrials 36 413 449 42.270
1309749 KELYA Industrials 445 86 531 17.580
2097818 SCX Industrials 356 194 550 10.390
1429651 LSEA Real Estate 97 39 136 7.240
1488461 MDV Real Estate 125 260 385 15.210
941111 FOR Real Estate 41 480 521 23.390
256238 AXR Real Estate 243 313 556 16.700
2038182 RPAY Technology 413 286 699 5.890
29775 ACMR Technology 21 724 745 13.710
3791 AAOI Technology 10 850 860 7.040
2373620 TRT Technology 250 630 880 6.870
1035432 GNE Utilities 167 1310 1477 19.180
94400 ALE Utilities 838 642 1480 52.590
644205 CWCO Utilities 124 1359 1483 29.030
1703602 NWE Utilities 903 604 1507 46.550
In [34]:
short_neutral
Out[34]:
ticker sector mom_rnk pb_rnk combined_rnk closeunadj
1573351 MSB Basic Materials 950 1725 2675 20.170
2165284 SMID Basic Materials 1242 1447 2689 19.366
1555752 MP Basic Materials 1572 1207 2779 16.500
2379344 TSE Basic Materials 1735 1708 3443 5.990
1755960 OOMA Communication Services 1203 1535 2738 10.740
934187 FNGR Communication Services 1019 1749 2768 5.650
1042555 GOGO Communication Services 1113 1776 2889 10.650
2388282 TTGT Communication Services 1732 1497 3229 25.260
1492207 MED Consumer Cyclical 1480 1561 3041 69.580
350200 BOWL Consumer Cyclical 1518 1718 3236 10.340
1374556 LEE Consumer Cyclical 1658 1578 3236 8.960
2514031 VSCO Consumer Cyclical 1741 1611 3352 18.520
2359074 TR Consumer Defensive 1293 1381 2674 30.300
1836328 PETS Consumer Defensive 1700 1048 2748 9.360
2425203 UG Consumer Defensive 1664 1382 3046 6.180
2418352 UDMY Consumer Defensive 1551 1551 3102 8.770
1617424 NBR Energy 1388 1389 2777 102.830
362958 BROG Energy 1510 1529 3039 5.125
806691 EP Energy 1618 1707 3325 8.020
1458847 MARPS Energy 1662 1713 3375 5.030
2468353 VALU Financial Services 1414 1568 2982 34.500
1869626 PLMR Financial Services 1625 1433 3058 49.360
2375532 TRUP Financial Services 1665 1438 3103 20.690
356528 BRDG Financial Services 1565 1706 3271 7.120
2395412 TVTX Healthcare 1750 1577 3327 6.800
2077665 SAVA Healthcare 1736 1593 3329 19.890
38102 ACXP Healthcare 1733 1719 3452 5.380
2056469 RVNC Healthcare 1697 1756 3453 7.980
845359 EVEX Industrials 1261 1690 2951 7.480
291701 BE Industrials 1409 1654 3063 9.780
804166 ENVX Industrials 1494 1628 3122 8.770
2524170 VVI Industrials 1484 1759 3243 23.050
2428020 UHT Real Estate 1050 1297 2347 38.040
113290 ALX Real Estate 1102 1477 2579 179.250
1043620 GOOD Real Estate 1328 1311 2639 11.640
1781891 OUT Real Estate 1610 1208 2818 9.620
312569 BIGC Technology 1513 1754 3267 8.925
794073 ENFN Technology 1524 1750 3274 8.250
1056027 GRND Technology 1674 1769 3443 5.870
1856242 PI Technology 1724 1768 3492 61.660
1575731 MSEX Utilities 1264 1371 2635 63.500
1076808 GWRS Utilities 1130 1605 2735 9.970
757849 EE Utilities 1547 1466 3013 15.060
1544665 MNTK Utilities 1657 1644 3301 9.750
In [35]:
long_neutral.groupby("sector").ticker.count()
Out[35]:
sector
Basic Materials           4
Communication Services    4
Consumer Cyclical         4
Consumer Defensive        4
Energy                    4
Financial Services        4
Healthcare                4
Industrials               4
Real Estate               4
Technology                4
Utilities                 4
Name: ticker, dtype: int64
In [36]:
short_neutral.groupby("sector").ticker.count()
Out[36]:
sector
Basic Materials           4
Communication Services    4
Consumer Cyclical         4
Consumer Defensive        4
Energy                    4
Financial Services        4
Healthcare                4
Industrials               4
Real Estate               4
Technology                4
Utilities                 4
Name: ticker, dtype: int64

How many shares to buy/sell?¶

  • Can do this either for long and short or long_neutral and short_neutral
  • $1,000,000 to invest long and short
  • Divide by number of stocks to get $ per stock
  • Divide by price to get shares per stock

Long side¶

In [38]:
long_neutral["shares"] = (1000000/long_neutral.shape[0])/long_neutral.closeunadj
long_neutral["shares"] = long_neutral.shares.round(0).astype(int)

long["shares"] = (1000000/long.shape[0])/long.closeunadj
long["shares"] = long.shares.round(0).astype(int)

Short side¶

In [39]:
short_neutral["shares"] = (1000000/short_neutral.shape[0])/short_neutral.closeunadj
short_neutral["shares"] = short_neutral.shares.round(0).astype(int)

short["shares"] = (1000000/short.shape[0])/short.closeunadj
short["shares"] = short.shares.round(0).astype(int)
In [ ]:
with pd.ExcelWriter("portfolios 2023-11-02.xlsx") as writer:
    long.to_excel(writer, "long", index=False)
    short.to_excel(writer, "short", index=False)
    long_neutral.to_excel(writer, "long neutral", index=False)
    short_neutral.to_excel(writer, "short neutral", index=False)
    today.to_excel(writer, "today", index=False)