multi-asset · Global · Monthly Free

Risk budget portfolios with convex Non-negative Matrix Factorization

Academic paper

AuthorsBruno Spilak; Wolfgang Karl Härdle

Paper linkhttps://arxiv.org/abs/2204.02757v2

Teaser

Scale exposure inversely to realized volatility toward a target annual vol. Universe: BTC-USD, ETH-USD. Parameters: target_vol=0.1; vol_lookback=63; rebalance=monthly. Rebalanced on the engine's template schedule with 5 bps commission and 2 bps slippage.

Strategy in a nutshell

We propose a portfolio allocation method based on risk factor budgeting using convex Nonnegative Matrix Factorization (NMF). Unlike classical factor analysis, PCA, or ICA, NMF ensures positive factor loadings to obtain interpretable long-only portfolios. As the NMF factors represent separate sources of risk, they have a quasi-diagonal correlation matrix, promoting diversified portfolio allocations. We evaluate our method in the context of volatility targeting on two long-only global portfolios of cryptocurrencies and traditional assets. Our method outperforms classical portfolio allocations regarding diversification and presents a better risk profile than hierarchical risk parity (HRP). We assess the robustness of our findings using Monte Carlo simulation.

Economic rationale

Volatility is more forecastable than expected returns; scaling down when vol is high improves risk-adjusted outcomes (volatility-managed portfolios). Related evidence from “Risk budget portfolios with convex Non-negative Matrix Factorization”: We propose a portfolio allocation method based on risk factor budgeting using convex Nonnegative Matrix Factorization (NMF). Unlike classical factor analysis, PCA, or ICA, NMF ensures positive factor loadings to obtain interpretable long-only portfolios. As the NMF factors represent separate sources of risk, they have a quasi-diagonal correlation matrix, promoting diversified portfolio allocations. We evaluate our method in the context of volatility targeting on two long-only global portfolios o

Entry & exit

Entry

Scale exposure on BTC-USD, ETH-USD so trailing 63-day realized vol maps toward a 10% annual target. Calm markets get more risk; noisy markets get less.

Exit

Cut size automatically when realized vol runs hot. This is a volatility budget, not a price stop.

Market data required

Needs at least 63 adjusted daily closes on BTC-USD, ETH-USD before the first signal is ready. Crypto columns include weekend rows. The lab loads Yahoo Finance via backtest.data.load_daily_prices.

Symbols

BTC-USD, ETH-USD

Frequency

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

History needed

≥ 63 trading days per symbol (about 3 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

ETFs and crypto proxies such as BTC-USD / ETH-USD share Yahoo daily bars (auto_adjust=True).

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 Risk budget portfolios with convex Non-negative Matrix Factorization 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 · 43 lines

"""
Quant Buffet interactive lab — risk-budget-portfolios-with-convex-non-negative-matrix-factorization
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 = ['BTC-USD', 'ETH-USD']
TARGET_VOL = 0.1
VOL_LOOKBACK = 63

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    rets = prices[cols].pct_change()
    vol = rets.rolling(VOL_LOOKBACK, min_periods=VOL_LOOKBACK).std() * np.sqrt(252)
    state = {"last": None}

    def on_day(engine: PortfolioEngine, dt: pd.Timestamp) -> None:
        key = (dt.year, dt.month)
        if state["last"] == key:
            return
        state["last"] = key
        weights = {}
        for s in cols:
            v = vol.at[dt, s]
            if pd.isna(v) or v <= 1e-8:
                continue
            weights[s] = min(1.0, TARGET_VOL / float(v))
        total = sum(weights.values())
        if total > 1.0:
            weights = {k: v / total for k, v in weights.items()}
        engine.set_target_weights(dt, weights)

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

"""
Quant Buffet interactive lab — risk-budget-portfolios-with-convex-non-negative-matrix-factorization
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 = ['BTC-USD', 'ETH-USD']
TARGET_VOL = 0.1
VOL_LOOKBACK = 63

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    rets = prices[cols].pct_change()
    vol = rets.rolling(VOL_LOOKBACK, min_periods=VOL_LOOKBACK).std() * np.sqrt(252)
    state = {"last": None}

def on_day(engine: PortfolioEngine, dt: pd.Timestamp) -> None:
        key = (dt.year, dt.month)
        if state["last"] == key:
            return
        state["last"] = key
        weights = {}
        for s in cols:
            v = vol.at[dt, s]
            if pd.isna(v) or v <= 1e-8:
                continue
            weights[s] = min(1.0, TARGET_VOL / float(v))
        total = sum(weights.values())
        if total > 1.0:
            weights = {k: v / total for k, v in weights.items()}
        engine.set_target_weights(dt, weights)

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

18.20%

Sharpe

0.84

Max DD

-42.02%

Vol

23.10%

Sortino

1.35

Beta

0.33

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: Volatility targetingAssets: BTC-USD, ETH-USD

# Generated from Quant Buffet → QuantConnect LEAN
# Strategy: Risk budget portfolios with convex Non-negative Matrix Factorization
# Detected pattern: Volatility targeting
# 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 = ["BTC-USD", "ETH-USD"]
        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: Scale weights to target vol 0.1 using 63-day vol.

    def Rebalance(self):
        # Pattern: vol_target — Scale weights to target vol 0.1 using 63-day vol.
        # Default: equal-weight. Port your make_on_day weights here via SetHoldings.
        w = 1.0 / len(self.symbols) if self.symbols else 0.0
        for symbol in self.symbols:
            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.