Toraniko is a complete implementation of a risk model suitable for quantitative and systematic trading at institutional scale. In particular, it is a characteristic factor model in the same vein as Barra and Axioma (in fact, given the same datasets, it approximately reproduces Barra's estimated factor returns).
Using this library, you can create new custom factors and estimate their returns. Then you can estimate a factor covariance matrix suitable for portfolio optimization with factor exposure constraints (e.g. to main a market neutral portfolio).
The only dependencies are numpy and polars. It supports market, sector and style factors; three styles are included: value, size and momentum. The library also comes with generalizable math and data cleaning utility functions you'd want to have for constructing more style factors (or custom fundamental factors of any kind).
Using pip:
pip install toraniko
You'll need the following data to run a complete model estimation:
- Sector scores, used for estimating the market and sector factor returns. GICS level 1 is suitable for this. The sector scores consist of one row per asset, with 0s in each column except for the sector in which the asset is a member, which is filled with 1.
symbol Basic Materials Communication Services Consumer Cyclical Consumer Defensive Energy Financial Services Healthcare Industrials Real Estate Technology Utilities
str i64 i64 i64 i64 i64 i64 i64 i64 i64 i64 i64
"A" 0 0 0 0 0 0 1 0 0 0 0
"AA" 1 0 0 0 0 0 0 0 0 0 0
"AACI" 0 0 0 0 0 1 0 0 0 0 0
"AACT" 0 0 0 0 0 1 0 0 0 0 0
"AADI" 0 0 0 0 0 0 1 0 0 0 0
… … … … … … … … … … … …
"ZVRA" 0 0 0 0 0 0 1 0 0 0 0
"ZVSA" 0 0 0 0 0 0 1 0 0 0 0
"ZWS" 0 0 0 0 0 0 0 1 0 0 0
"ZYME" 0 0 0 0 0 0 1 0 0 0 0
"ZYXI" 0 0 0 0 0 0 1 0 0 0 0
- Symbol-by-symbol daily asset returns for a large universe of equities:
date symbol asset_returns
date str f64
2013-01-02 "A" 0.022962
2013-01-02 "AAMC" -0.073171
2013-01-02 "AAME" 0.035566
2013-01-02 "AAON" 0.019163
2013-01-02 "AAP" 0.001935
… … …
2024-02-23 "ZVRA" -0.025
2024-02-23 "ZVSA" 0.291311
2024-02-23 "ZWS" 0.006378
2024-02-23 "ZYME" 0.000838
2024-02-23 "ZYXI" 0.001552
- For the value factor: symbol-by-symbol daily market cap, cash flow, share count, revenue and book value estimates, so you can calculate book-price, sales-price and cash flow-price metrics:
date symbol book_price sales_price cf_price market_cap
date str f64 f64 f64 f64
2013-10-30 "AAPL" 0.343017 0.081994 0.007687 4.5701e11
2013-10-31 "AAPL" 0.342231 0.081763 0.007665 4.5830e11
2013-11-01 "AAPL" 0.341398 0.081521 0.007643 4.5966e11
2013-11-04 "AAPL" 0.340947 0.08137 0.007628 4.6051e11
2013-11-05 "AAPL" 0.340491 0.081219 0.007614 4.6137e11
… … … … … …
2024-02-16 "AAPL" 0.072243 0.040937 0.001972 2.9209e12
2024-02-20 "AAPL" 0.072405 0.040942 0.001972 2.9206e12
2024-02-21 "AAPL" 0.072614 0.040973 0.001974 2.9184e12
2024-02-22 "AAPL" 0.072792 0.040987 0.001974 2.9174e12
2024-02-23 "AAPL" 0.073007 0.041021 0.001976 2.9150e12
Taking the foregoing data together you'll have:
date symbol book_price sales_price cf_price market_cap asset_returns
date str f64 f64 f64 f64 f64
2013-02-12 "A" null null null 1.1080e10 0.00045
2013-02-12 "AAON" null null null 5.5410e8 0.006741
2013-02-12 "AAP" null null null 5.4212e9 0.002679
2013-02-12 "AAPL" 0.302543 0.1189 null 4.5847e11 -0.025069
2013-02-12 "AAT" null null null 1.1135e9 0.006764
… … … … … … …
2024-02-23 "ZS" 0.105832 0.016538 0.007052 3.5311e10 0.04015
2024-02-23 "ZTS" 0.125734 0.025145 -0.017418 8.8010e10 0.002797
2024-02-23 "ZUO" 0.424385 0.089243 0.073274 1.2309e9 0.002448
2024-02-23 "ZWS" 0.296327 0.067669 0.001916 5.2727e9 0.006378
2024-02-23 "ZYME" 0.363093 0.016538 -0.054523 7.3077e8 0.000838
Then to estimate the momentum factor, you can run
from toraniko.styles import factor_mom
mom_df = factor_mom(df.select("symbol", "date", "asset_returns"), trailing_days=252, winsor_factor=0.01).collect()
and you'll obtain scores roughly resembling this histogram:
Likewise for value, you can run:
from toraniko.styles import factor_val
value_df = factor_val(df.select("date", "symbol", "book_price", "sales_price", "cf_price")).collect()
Similarly:
Let's say you've estimated three style factors: value, momentum, size.
date symbol mom_score sze_score val_score
date str f64 f64 f64
2014-03-07 "A" 0.793009 -0.872847 0.265801
2014-03-07 "AAON" 1.128932 0.939116 -1.050307
2014-03-07 "AAP" 2.190209 0.0 0.351273
2014-03-07 "AAPL" -0.202091 -3.373659 -0.289713
2014-03-07 "AAT" -0.413211 0.805413 0.052482
… … … … …
2024-02-23 "ZS" 2.783905 -1.303952 -1.778753
2024-02-23 "ZTS" 0.030749 -1.905171 -1.619675
2024-02-23 "ZUO" 0.235533 0.905671 0.253427
2024-02-23 "ZWS" 0.594781 0.0 -0.520947
2024-02-23 "ZYME" -1.631452 1.248919 -1.451382
Merge these with the aforementioned GICS sector scores, and take the top N by market cap each day on a suitable universe. Here we'll do the Russell 3000:
from toraniko.utils import top_n_by_group
ddf = (
ret_df.join(cap_df.drop("book_value"), on=["date", "symbol"])
.join(sector_scores, on="symbol")
.join(style_scores, on=["date", "symbol"])
.drop_nulls()
)
ddf = (
top_n_by_group(
ddf.lazy(),
3000,
"market_cap",
("date",),
True
)
.collect()
.sort("date", "symbol")
)
returns_df = ddf.select("date", "symbol", "asset_returns")
mkt_cap_df = ddf.select("date", "symbol", "market_cap")
sector_df = ddf.select(["date"] + list(sector_scores.columns))
style_df = ddf.select(style_scores.columns)
Then simply:
from toraniko.model import estimate_factor_returns
fac_df, eps_df = estimate_factor_returns(returns_df, mkt_cap_df, sector_df, style_df, winsor_factor=0.1, residualize_styles=False)
On an M1 MacBook, this estimates 10+ years of daily market, sector and style factor returns in under a minute.
Here is a comparison of the model value factor out versus Barra's. Even on a relatively low quality data source (Yahoo Finance) and without significant effort in cleaning corporate actions, the results are comparable over a 10 year period:
