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凸非负矩阵分解下的风险预算组合

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学术论文

凸非负矩阵分解下的风险预算组合

作者Bruno Spilak; Wolfgang Karl Härdle

论文链接https://arxiv.org/abs/2204.02757v2

导读

投资标的：BTC-USD、ETH-USD。再平衡：每月。Universe: BTC-USD, ETH-USD. Parameters: rebalance=monthly.

策略概要

该策略投资于 BTC-USD、ETH-USD，按 63 日已实现波动率的倒数缩放仓位，瞄准 10% 目标年化波动，并按月再平衡。论文用凸非负矩阵分解做风险因子预算，保证因子载荷为正，从而得到可解释的纯多头组合，并在加密与传统资产上做波动目标配置。

经济逻辑

波动率比预期收益更可预测；波动升高时降低仓位，有助于改善风险调整后表现（波动率管理组合）。相关证据来自“凸非负矩阵分解下的风险预算组合”：NMF 因子近似不相关，有利于分散；相对 PCA/ICA，正载荷更符合纯多头约束，风险轮廓优于分层风险平价。

入场与出场

入场

按过去 63 日已实现波动，把风险资产仓位缩放到年化目标波动 10%（BTC-USD, ETH-USD）。波动低则加仓，波动高则减仓。

出场

已实现波动升破目标时自动降杠杆；不是点位止损，而是波动预算约束。

所需行情数据

需要 BTC-USD, ETH-USD 至少 63 根复权收盘价，才能形成第一个有效信号。加密货币列为日历日（含周末）。实验室通过 backtest.data.load_daily_prices 读取 Yahoo Finance。

标的

BTC-USD, ETH-USD

频率

每月 · 日频复权收盘价；信号按月再平衡（用当月最后一个有效交易日）

所需历史

每个标的至少 63 根交易日 K 线（约 3 个交易月），外加数根缓冲才能发出第一个信号。

字段

复权收盘价（Adj Close / auto_adjust Close）
交易日日期索引

凭证

回测与实验室：无需密钥
实盘下单才需要券商 / 交易所 API

API 与数据源

Quant Buffet 数据 API

实验室用 load_daily_prices 拉取 ASSETS 的复权收盘价面板，磁盘缓存后回测可复现。

提供方: backtest.data.load_daily_prices
鉴权: 回测无需密钥
接口: load_daily_prices(ASSETS, start="2000-01-01")

API / docs → /zh/docs/data-api

Yahoo Finance（yfinance）

ETF 与 BTC-USD / ETH-USD 等加密代理共用 Yahoo 日线（auto_adjust=True）。

提供方: yfinance → Yahoo Finance
鉴权: 公开历史无需密钥
接口: Ticker.history / yf.download(auto_adjust=True)

API / docs → github.com/ranaroussi/yfinance

Onsite backtest IDE

Quant Buffet 原生回测 IDE

Edit and run Quant Buffet Python for 凸非负矩阵分解下的风险预算组合 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 — 凸非负矩阵分解下的风险预算组合
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 — 凸非负矩阵分解下的风险预算组合
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: 凸非负矩阵分解下的风险预算组合
# 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)

导出代码使用目标平台的原生类与库。请在第三方 IDE 中安装依赖后运行；实盘前请自行验证。