equities · United States · ETFs · Monthly Free

Not All Factors Crowd Equally: Modeling, Measuring, and Trading on Alpha Decay

Academic paper

AuthorsChorok Lee

Paper linkhttps://arxiv.org/abs/2512.11913v2

Teaser

Enter when short-horizon z-score is deeply negative; exit near zero. Universe: SPY, BIL. Parameters: lookback=20; entry_z=-1.0; exit_z=0.0; rebalance=daily. Rebalanced on the engine's template schedule with 5 bps commission and 2 bps slippage.

Strategy in a nutshell

We derive a specific functional form for factor alpha decay -- hyperbolic decay alpha(t) = K/(1+lambda*t) -- from a game-theoretic equilibrium model, and test it against linear and exponential alternatives. Using eight Fama-French factors (1963--2024), we find: (1) Hyperbolic decay fits mechanical factors. Momentum exhibits clear hyperbolic decay (R^2 = 0.65), outperforming linear (0.51) and exponential (0.61) baselines -- validating the equilibrium foundation. (2) Not all factors crowd equally. Mechanical factors (momentum, reversal) fit the model; judgment-based factors (value, quality) do not -- consistent with a signal-ambiguity taxonomy paralleling Hua and Sun's "barriers to entry." (3) Crowding accelerated post-2015. Out-of-sample, the model over-predicts remaining alpha (0.30 vs. 0.

Economic rationale

Short-horizon overreaction produces temporary dislocations that reverse toward a local mean. Related evidence from “Not All Factors Crowd Equally: Modeling, Measuring, and Trading on Alpha Decay”: We derive a specific functional form for factor alpha decay -- hyperbolic decay alpha(t) = K/(1+lambda*t) -- from a game-theoretic equilibrium model, and test it against linear and exponential alternatives. Using eight Fama-French factors (1963--2024), we find: (1) Hyperbolic decay fits mechanical factors. Momentum exhibits clear hyperbolic decay (R^2 = 0.65), outperforming linear (0.51) and exponential (0.61) baselines -- validating the equilibrium foundation. (2) Not all factors crowd equally.

Entry & exit

Entry

Compute a 20-day z-score on each name in SPY, BIL. Enter when z ≤ -1 (stretched to the downside).

Exit

Exit when the z-score mean-reverts back to ≥ 0. Positions are not held through a full trend — only the snap-back.

Market data required

Needs at least 25 adjusted daily closes on SPY, BIL before the first signal is ready. ETF columns print on exchange sessions only. The lab loads Yahoo Finance via backtest.data.load_daily_prices.

Symbols

SPY, BIL

Frequency

Monthly · Daily adjusted close; signals rebalance on the month change (last available session)

History needed

≥ 25 trading days per symbol (about 2 months), plus a few extra bars so the first signal can fire.

Fields

Adjusted close (Yahoo auto_adjust)
Session date index

Credentials

None for paper and the onsite lab
Broker or exchange API keys only for live orders

APIs & providers

Quant Buffet Data API

The lab calls load_daily_prices for the ASSETS panel of adjusted closes, then caches CSV so backtests replay the same series.

Provider: backtest.data.load_daily_prices
Auth: None for paper / sandbox backtests
Endpoints: load_daily_prices(ASSETS, start="2000-01-01")

API / docs → /en/docs/data-api

Yahoo Finance via yfinance

US equities and ETFs, adjusted OHLCV, free for research (rate limits apply).

Provider: yfinance → Yahoo Finance
Auth: None for public history
Endpoints: Ticker.history / yf.download(auto_adjust=True)

API / docs → github.com/ranaroussi/yfinance

Onsite backtest IDE

Quant Buffet native backtest IDE

Edit and run Quant Buffet Python for Not All Factors Crowd Equally: Modeling, Measuring, and Trading on Alpha Decay in the browser. Results update live with equity, drawdown, and metrics charts. Allowed: backtest.data, backtest.engine, backtest.metrics, numpy, pandas. Define ASSETS and make_on_day(prices). Shortcut: Ctrl+Enter. API docs →

IDE · 44 lines

"""
Quant Buffet interactive lab — not-all-factors-crowd-equally-modeling-measuring-and-trading-on-alpha-decay
Allowed: backtest.data / backtest.engine / backtest.metrics, numpy, pandas.
Required: a module-level ASSETS list, and def make_on_day(prices) returning (on_day, ready)
"""
from __future__ import annotations

import numpy as np
import pandas as pd

from backtest.data import load_daily_prices
from backtest.engine import EngineConfig, PortfolioEngine
from backtest.metrics import compute_metrics

ASSETS = ['SPY', 'BIL']
LOOKBACK = 20
ENTRY_Z = -1.0
EXIT_Z = 0.0

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    mu = prices[cols].rolling(LOOKBACK, min_periods=LOOKBACK).mean()
    sd = prices[cols].rolling(LOOKBACK, min_periods=LOOKBACK).std(ddof=0)
    z = (prices[cols] - mu) / sd.replace(0, np.nan)
    held = {s: False for s in cols}

    def on_day(engine: PortfolioEngine, dt: pd.Timestamp) -> None:
        long = []
        for s in cols:
            zv = z.at[dt, s]
            if pd.isna(zv):
                continue
            if not held[s] and zv <= ENTRY_Z:
                held[s] = True
            elif held[s] and zv >= EXIT_Z:
                held[s] = False
            if held[s]:
                long.append(s)
        w = {} if not long else {s: 1.0 / len(long) for s in long}
        engine.set_target_weights(dt, w)

    ready = z.dropna(how="all").index.min() if z.notna().any().any() else None
    return on_day, ready

"""
Quant Buffet interactive lab — not-all-factors-crowd-equally-modeling-measuring-and-trading-on-alpha-decay
Allowed: backtest.data / backtest.engine / backtest.metrics, numpy, pandas.
Required: a module-level ASSETS list, and def make_on_day(prices) returning (on_day, ready)
"""
from __future__ import annotations

import numpy as np
import pandas as pd

from backtest.data import load_daily_prices
from backtest.engine import EngineConfig, PortfolioEngine
from backtest.metrics import compute_metrics

ASSETS = ['SPY', 'BIL']
LOOKBACK = 20
ENTRY_Z = -1.0
EXIT_Z = 0.0

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    mu = prices[cols].rolling(LOOKBACK, min_periods=LOOKBACK).mean()
    sd = prices[cols].rolling(LOOKBACK, min_periods=LOOKBACK).std(ddof=0)
    z = (prices[cols] - mu) / sd.replace(0, np.nan)
    held = {s: False for s in cols}

def on_day(engine: PortfolioEngine, dt: pd.Timestamp) -> None:
        long = []
        for s in cols:
            zv = z.at[dt, s]
            if pd.isna(zv):
                continue
            if not held[s] and zv <= ENTRY_Z:
                held[s] = True
            elif held[s] and zv >= EXIT_Z:
                held[s] = False
            if held[s]:
                long.append(s)
        w = {} if not long else {s: 1.0 / len(long) for s in long}
        engine.set_target_weights(dt, w)

ready = z.dropna(how="all").index.min() if z.notna().any().any() else None
    return on_day, ready

Quant Buffet syntax cheat sheet (copy / insert)

Paste these fragments into the editor. The sandbox rejects QuantConnect, os, and network libraries.

Required imports

Only these libraries are allowed in the sandbox.

from __future__ import annotations

import numpy as np
import pandas as pd

from backtest.data import load_daily_prices
from backtest.engine import EngineConfig, PortfolioEngine
from backtest.metrics import compute_metrics

ASSETS list (whitelisted ETFs)

Module-level list. Tickers must be in the Quant Buffet whitelist.

ASSETS = ["SPY", "QQQ", "TLT", "GLD", "BIL"]

make_on_day contract

Must return (on_day, ready). on_day calls engine.set_target_weights.

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    sma = prices[cols].rolling(200, min_periods=200).mean()
    state = {"last": None}

    def on_day(engine: PortfolioEngine, dt: pd.Timestamp) -> None:
        if sma.loc[dt].isna().all():
            return
        key = (dt.year, dt.month)
        if state["last"] == key:
            return
        state["last"] = key
        long = [
            s for s in cols
            if pd.notna(prices.at[dt, s]) and pd.notna(sma.at[dt, s])
            and prices.at[dt, s] > sma.at[dt, s]
        ]
        weights = {} if not long else {s: 1.0 / len(long) for s in long}
        engine.set_target_weights(dt, weights)

    ready = sma.dropna(how="all").index.min() if sma.notna().any().any() else None
    return on_day, ready

Set target weights

Weights should sum to about 1.0. Empty dict = 100% cash.

engine.set_target_weights(dt, {"SPY": 0.60, "BIL": 0.40})

Live backtest performance

CAGR

1.44%

Sharpe

0.17

Max DD

-36.97%

Vol

14.04%

Sortino

0.26

Beta

0.55

Stored preview only. Run backtest to simulate every daily session from Yahoo Finance adjusted closes.

Run the backtest to load orders, then mark them on the equity chart.

Equity curve (indexed = 100)

Accent = strategy · dashed grey = buy-and-hold benchmark. Hover or tap any point for its date and values.

Drawdown

Metrics bar chart

Monthly returns

Order records

Run the backtest to load every order fill alongside performance.

Export to your platform

Transform Quant Buffet lab code (ASSETS + make_on_day / PortfolioEngine) into native classes for a third-party IDE — then copy and paste.

Target platform

Run in: QuantConnect Cloud or LEAN CLI · QCAlgorithm with Equity securities and monthly rebalance.

Detected pattern: Mean reversionAssets: SPY, BIL

# Generated from Quant Buffet → QuantConnect LEAN
# Strategy: Not All Factors Crowd Equally: Modeling, Measuring, and Trading on Alpha Decay
# Detected pattern: Mean reversion
# Source uses Quant Buffet lab APIs (ASSETS + make_on_day / PortfolioEngine).
# Review fees, data, and risk before live trading — educational export only.

from AlgorithmImports import *


class QuantBuffetExport(QCAlgorithm):
    def Initialize(self):
        self.SetStartDate(2010, 1, 1)
        self.SetCash(100000)
        tickers = ["SPY", "BIL"]
        self.symbols = []
        for t in tickers:
            if "-" in t:  # crypto proxy e.g. BTC-USD
                self.symbols.append(self.AddCrypto(t.replace("-USD", ""), Resolution.Daily).Symbol)
            else:
                self.symbols.append(self.AddEquity(t, Resolution.Daily).Symbol)
        self.Schedule.On(
            self.DateRules.MonthStart(self.symbols[0]),
            self.TimeRules.AfterMarketOpen(self.symbols[0], 30),
            self.Rebalance,
        )
        # Logic: Buy when return z-score < -1 over 20 days.

    def Rebalance(self):
        import numpy as np
        picks = []
        for symbol in self.symbols:
            hist = self.History(symbol, 20 + 5, Resolution.Daily)
            if hist.empty: continue
            close = hist["close"]
            if hasattr(close, "unstack"):
                close = close.unstack(level=0).iloc[:, 0]
            rets = close.pct_change().dropna()
            if len(rets) < 20: continue
            window = rets.iloc[-20:]
            z = (window.iloc[-1] - window.mean()) / (window.std() or 1e-9)
            if z < -1:
                picks.append(symbol)
        w = 1.0 / len(picks) if picks else 0.0
        for symbol in self.symbols:
            self.SetHoldings(symbol, w if symbol in picks else 0.0)

Exported code uses the platform’s native classes and libraries. Install dependencies in your third-party IDE, then run. Validate before live trading.