bonds, equities · United States · bonds, stocks · Monthly Free

Market Timing with Merton Rule for Earnings Yield

Academic paper

Man Doth Not Invest by Earnings Yield Alone

AuthorsJames White; Victor Haghani

Institute

Elm Partners

Paper linkhttps://papers.ssrn.com/sol3/papers.cfm?abstract_id=4025456

Strategy in a nutshell

Allocate between S&P 500 and TIPS using the Merton Rule. Equity allocation is proportional to the Excess Earnings Yield (Earnings Yield minus TIPS real yield) and inversely proportional to portfolio risk and investor risk aversion

Economic rationale

High CAPE predicts lower future stock returns due to investor overreaction. Incorporating risk and risk aversion refines allocation, while CAPE smooths earnings fluctuations, improving prediction and portfolio decisions.

Entry & exit

Entry

On each month, scan SPY, TIP. Long every name whose close is above its 200-day SMA, equal-weight. Skip names still below the average. An empty weight dict is 100% cash.

Exit

At the next rebalance, drop any name whose close has fallen back to or below the 200-day SMA. If the whole book is below trend, go fully to cash. Fills use 5 bps commission and 2 bps slippage.

Market data required

Needs at least 200 adjusted daily closes on SPY, TIP 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, TIP

Frequency

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

History needed

≥ 200 trading days per symbol (about 10 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 Market Timing with Merton Rule for Earnings Yield 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 · 40 lines

"""
Quant Buffet interactive lab — market-timing-with-merton-rule-for-earnings-yield
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', 'TIP']
SMA_DAYS = 200

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    sma = prices[cols].rolling(SMA_DAYS, min_periods=SMA_DAYS).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]
        ]
        w = {} if not long else {s: 1.0 / len(long) for s in long}
        engine.set_target_weights(dt, w)

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

"""
Quant Buffet interactive lab — market-timing-with-merton-rule-for-earnings-yield
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', 'TIP']
SMA_DAYS = 200

def make_on_day(prices: pd.DataFrame):
    cols = [c for c in ASSETS if c in prices.columns]
    sma = prices[cols].rolling(SMA_DAYS, min_periods=SMA_DAYS).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]
        ]
        w = {} if not long else {s: 1.0 / len(long) for s in long}
        engine.set_target_weights(dt, w)

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

5.13%

Sharpe

0.63

Max DD

-28.77%

Vol

8.45%

Sortino

0.95

Beta

0.22

Up days

71%

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: SMA trendAssets: SPY, TIP

# Generated from Quant Buffet → QuantConnect LEAN
# Strategy: Market Timing with Merton Rule for Earnings Yield
# Detected pattern: SMA trend
# 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", "TIP"]
        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 where close > SMA(200); equal-weight; monthly.

    def Rebalance(self):
        longs = []
        for symbol in self.symbols:
            hist = self.History(symbol, 200 + 5, Resolution.Daily)
            if hist.empty: continue
            close = hist["close"].unstack(level=0).iloc[:, 0] if hasattr(hist["close"], "unstack") else hist["close"]
            if len(close) < 200: continue
            if float(close.iloc[-1]) > float(close.iloc[-200:].mean()):
                longs.append(symbol)
        weight = 1.0 / len(longs) if longs else 0.0
        for symbol in self.symbols:
            self.SetHoldings(symbol, weight if symbol in longs 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.