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波动率分解与共同基金收益

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学术论文

共同基金业绩与组合波动率的来源

作者Nima Vafai; David A. Rakowski

机构

The University of Texas of the Permian Basin
The university of Texas Permian Basin
The University of Texas at Arlington
University of Texas at Arlington

论文链接https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4005351

导读

投资标的：SPY、BIL。再平衡：每月。Universe: SPY, BIL. Parameters: rebalance=monthly.

策略概要

该策略投资于CRSP共同基金数据库中的全部基金。剔除当期及上一年股票持仓不足80%（且股票须被CRSP覆盖）的基金。多份额基金按份额汇总资产，其余属性（含收益）按滞后资产加权。

每月对每只基金k计算总收益方差σ2，并用成分资产的加权协方差将其分解为持仓平均方差ν与持仓平均协方差ψ。ν用各证券日收益计算，再由ψ = σ2 − ν得到。

基金每月按σ2、ν和ψ分成等权十分位。策略将50%配置给方差σ2最低的十分位，50%配置给平均持仓协方差ψ最低的十分位。组合等权，每月再平衡。

经济逻辑

金融理论认为更高预期收益对应更高风险。实践中投资者常为高风险资产支付过高价格，使高波动资产被高估、低波动资产被低估，随后收益分别偏低和偏高。

按Markowitz（1952、1959），组合总风险σ2可分解为持仓方差ν与持仓协方差ψ。分散化可使ν趋向于零，但无法消除ψ。因此，波动率相关的收益模式主要由协方差成分ψ驱动，而非整体组合方差σ2。

入场与出场

入场

每月计算 252 日收益。只持有收益为正的标的（SPY, BIL），等权。

出场

滚动收益转负则卖出该标的；全部为负则空仓，避免逆势持仓。

所需行情数据

需要 SPY, BIL 至少 252 根复权收盘价，才能形成第一个有效信号。ETF 仅交易日有行情。实验室通过 backtest.data.load_daily_prices 读取 Yahoo Finance。

标的

SPY, BIL

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 252 根交易日 K 线（约 12 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）

美股 / ETF 复权 OHLCV，免费研究接口，有速率限制。

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 波动率分解与共同基金收益 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 · 50 lines

"""
Quant Buffet interactive lab — 波动率分解与共同基金收益
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 = 252
CASH = 'BIL'

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    if CASH not in cols and CASH in prices.columns:
        cols = cols + [CASH]
    risky = [c for c in cols if c != CASH]
    rets = prices[cols].pct_change(LOOKBACK)
    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
        scores = {
            s: float(rets.at[dt, s])
            for s in risky
            if s in rets.columns and pd.notna(rets.at[dt, s])
        }
        if not scores:
            engine.set_target_weights(dt, {CASH: 1.0} if CASH in cols else {})
            return
        best = max(scores, key=scores.get)
        if scores[best] > 0:
            engine.set_target_weights(dt, {best: 1.0})
        elif CASH in cols:
            engine.set_target_weights(dt, {CASH: 1.0})
        else:
            engine.set_target_weights(dt, {})

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

"""
Quant Buffet interactive lab — 波动率分解与共同基金收益
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 = 252
CASH = 'BIL'

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    if CASH not in cols and CASH in prices.columns:
        cols = cols + [CASH]
    risky = [c for c in cols if c != CASH]
    rets = prices[cols].pct_change(LOOKBACK)
    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
        scores = {
            s: float(rets.at[dt, s])
            for s in risky
            if s in rets.columns and pd.notna(rets.at[dt, s])
        }
        if not scores:
            engine.set_target_weights(dt, {CASH: 1.0} if CASH in cols else {})
            return
        best = max(scores, key=scores.get)
        if scores[best] > 0:
            engine.set_target_weights(dt, {best: 1.0})
        elif CASH in cols:
            engine.set_target_weights(dt, {CASH: 1.0})
        else:
            engine.set_target_weights(dt, {})

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

7.89%

Sharpe

0.63

Max DD

-33.72%

Vol

13.60%

Sortino

0.93

Beta

0.51

Up days

59%

Run the backtest to populate charts.

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: Absolute momentumAssets: SPY, BIL

# Generated from Quant Buffet → QuantConnect LEAN
# Strategy: 波动率分解与共同基金收益
# Detected pattern: Absolute momentum
# 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: Long assets with positive 252-day return; equal-weight; monthly.

    def Rebalance(self):
        # Pattern: abs_momentum — Long assets with positive 252-day return; equal-weight; monthly.
        # 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。