equities · United States · ETFs · Monthly Free

Trend Momentum II: Driving Forces of Low Volatility and Momentum

Academic paper

AuthorsWilhelm Berghorn; Martin T. Schulz; Markus Vogl; Sascha Otto

Institute

Aschaffenburg University of Applied Sciences

Paper linkhttps://doi.org/10.5430/ijfr.v12n3p300

Teaser

Rank the book by trailing return and hold the top-N names equal-weight. Universe: SPY, EFA, EEM, VNQ, DBC, GLD, TLT, IEF, HYG. Parameters: lookback=126; top_n=1; rebalance=monthly. Rebalanced on the engine's template schedule with 5 bps commission and 2 bps slippage.

Strategy in a nutshell

In discussions and critiques on the validity of the Efficient Market Hypothesis, there are two important research focuses: statistical analyses showing that the basic assumption of statistical independence in price series is violated and empirical findings that show that significant market anomalies exist. In this paper, we combine both viewpoints by analyzing two important mathematical factor anomalies: low volatility and momentum. By applying an explicit trend model, we show that both anomalies require trending. Additionally, we show that the trend model exhibits lognormal trend characteristics. Furthermore, the model allows us to describe how low volatility uses implicitly asymmetric trend characteristics while momentum directly exploits trends. Using Mandelbrot’s model of fractional Br

Economic rationale

Assets with stronger recent relative performance tend to continue outperforming over intermediate horizons; rotating into leaders harvests that premium. Related evidence from “Trend Momentum II: Driving Forces of Low Volatility and Momentum”: In discussions and critiques on the validity of the Efficient Market Hypothesis, there are two important research focuses: statistical analyses showing that the basic assumption of statistical independence in price series is violated and empirical findings that show that significant market anomalies exist. In this paper, we combine both viewpoints by analyzing two important mathematical factor anomalies: low volatility and momentum. By applying an explicit trend model, we show that both anomalie

Entry & exit

Entry

On each month, rank SPY, EFA, EEM, VNQ, DBC, GLD, TLT, IEF, HYG by 126-day return and equal-weight the strongest 1 name(s).

Exit

Sell any holding that falls out of the top 1 at the next rebalance and rotate into the new leaders.

Market data required

Needs at least 126 adjusted daily closes on SPY, EFA, EEM, VNQ, DBC, GLD (+3 more) 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, EFA, EEM, VNQ, DBC, GLD, TLT, IEF, HYG

Frequency

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

History needed

≥ 126 trading days per symbol (about 6 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 Trend Momentum II: Driving Forces of Low Volatility and Momentum 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 · 42 lines

"""
Quant Buffet interactive lab — trend-momentum-ii-driving-forces-of-low-volatility-and-momentum
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', 'EFA', 'EEM', 'VNQ', 'DBC', 'GLD', 'TLT', 'IEF', 'HYG']
LOOKBACK = 126
TOP_N = 1
INVERT = False  # True = short-term reversal (rank ascending)

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    rets = prices[cols].pct_change(LOOKBACK)
    state = {"last": None}

    def on_day(engine: PortfolioEngine, dt: pd.Timestamp) -> None:
        row = rets.loc[dt]
        if row.isna().all():
            return
        key = (dt.year, dt.month)
        if state["last"] == key:
            return
        state["last"] = key
        ranked = row.dropna().sort_values(ascending=INVERT)
        picks = list(ranked.head(TOP_N).index)
        if not INVERT:
            picks = [s for s in picks if ranked[s] > 0] or picks[:1]
        w = {} if not picks else {s: 1.0 / len(picks) for s in picks}
        engine.set_target_weights(dt, w)

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

"""
Quant Buffet interactive lab — trend-momentum-ii-driving-forces-of-low-volatility-and-momentum
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', 'EFA', 'EEM', 'VNQ', 'DBC', 'GLD', 'TLT', 'IEF', 'HYG']
LOOKBACK = 126
TOP_N = 1
INVERT = False  # True = short-term reversal (rank ascending)

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    rets = prices[cols].pct_change(LOOKBACK)
    state = {"last": None}

def on_day(engine: PortfolioEngine, dt: pd.Timestamp) -> None:
        row = rets.loc[dt]
        if row.isna().all():
            return
        key = (dt.year, dt.month)
        if state["last"] == key:
            return
        state["last"] = key
        ranked = row.dropna().sort_values(ascending=INVERT)
        picks = list(ranked.head(TOP_N).index)
        if not INVERT:
            picks = [s for s in picks if ranked[s] > 0] or picks[:1]
        w = {} if not picks else {s: 1.0 / len(picks) for s in picks}
        engine.set_target_weights(dt, w)

ready = rets.dropna(how="all").index.min() if rets.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

3.86%

Sharpe

0.29

Max DD

-49.56%

Vol

20.97%

Sortino

0.45

Beta

0.38

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: Momentum rotationAssets: SPY, EFA, EEM, VNQ, DBC, GLD, TLT, IEF, HYG

# Generated from Quant Buffet → QuantConnect LEAN
# Strategy: Trend Momentum II: Driving Forces of Low Volatility and Momentum
# Detected pattern: Momentum rotation
# 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", "EFA", "EEM", "VNQ", "DBC", "GLD", "TLT", "IEF", "HYG"]
        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: Hold top 1 by 126-day return; monthly.

    def Rebalance(self):
        scores = {}
        for symbol in self.symbols:
            hist = self.History(symbol, 126 + 5, Resolution.Daily)
            if hist.empty: continue
            close = hist["close"]
            if hasattr(close, "unstack"):
                close = close.unstack(level=0).iloc[:, 0]
            if len(close) < 126 + 1: continue
            scores[symbol] = float(close.iloc[-1] / close.iloc[-126 - 1] - 1)
        ranked = sorted(scores.items(), key=lambda kv: kv[1], reverse=True)[:1]
        for symbol in self.symbols:
            self.SetHoldings(symbol, 0)
        if ranked:
            w = 1.0 / len(ranked)
            for symbol, _ in ranked:
                self.SetHoldings(symbol, w)

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