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Buy and sell signals on weekly S&P 500 price data
Instead of predicting the market, I tested whether reacting to long term trends is enough to control risk.
The goal was to test a 12-month time-series momentum strategy on the US equity market and evaluate whether it can meaningfully reduce risk compared to buy and hold, without relying on prediction, frequent trading, or complex models.
Using weekly data, a long-term momentum filter, and volatility targeting, the strategy aims to stay invested during sustained uptrends and step aside during prolonged market weakness.
The focus is not on maximizing returns, but on improving risk-adjusted performance and reducing drawdowns.
The results are measured directly against buy and hold.
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The Core Idea Behind the Strategy
Time-series momentum is based on a simple observation. Markets tend to continue moving in the same direction over longer horizons.
Instead of asking whether the market is cheap or expensive, this strategy asks whether the market has shown enough positive momentum over the past 12 months to justify being invested. If the answer is yes, the strategy takes exposure. If the answer is no, it stays out.
To avoid taking the same amount of risk in all market conditions, volatility targeting is added. Position size is adjusted so that overall risk remains relatively stable even when market volatility changes.
This combination creates a slow, rules-based system that trades infrequently and reacts only to sustained changes in market behavior.
Tools, Data, and Assumptions
The strategy is implemented in Python using historical data from Yahoo Finance accessed through the yfinance library. SPY(S&P 500 ETF) is used as a proxy for the US equity market. Prices are adjusted for dividends and splits.
Weekly data is used instead of daily data to reduce noise and align the system with a long-term investment horizon. All calculations are done using information that would have been available at the time to avoid lookahead bias.
Strategy Implementation in Python
Installing and Importing Dependencies
The environment is set up by installing yfinance and importing the required data analysis and visualization libraries.
%pip install yfinance --quietimport yfinance as yf
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams["figure.figsize"] = (14, 6)
plt.rcParams["axes.grid"] = TrueDownloading and Preparing Market Data
SPY data is downloaded starting from 2000. Prices are adjusted automatically, and the data is resampled to weekly frequency using Friday closes.
ticker = "SPY" # S&P 500 ETF
start_date = "2000-01-01"
data = yf.download(ticker, start=start_date, auto_adjust=True)
weekly = data.resample("W-FRI").last()
weekly.head()Establishing a Price Baseline
Before applying indicators, it is important to understand the underlying price behavior of the market.
plt.plot(weekly.index, weekly["Close"], label="Price")
plt.title(f"{ticker} Weekly Price")
plt.xlabel("Date")
plt.ylabel("Price")
plt.legend()
plt.savefig("spy_weekly_price.png")
plt.show()
Weekly SPY price from 2000
Calculating 12-Month Momentum
Momentum is defined as the percentage return over the previous 52 weeks. This serves as the trend filter for the strategy.
lookback = 52
weekly["Momentum"] = weekly["Close"].pct_change(lookback)
weekly[["Close", "Momentum"]].dropna().head()Generating the Trading Signal
When momentum is positive, the strategy allows long exposure. When momentum is negative, it stays out of the market. The signal is shifted forward to avoid lookahead bias.
weekly["Signal"] = np.where(weekly["Momentum"] > 0, 1, 0)
weekly["Signal"] = weekly["Signal"].shift(1) # avoid lookahead biasApplying Volatility Targeting
Volatility targeting adjusts position size based on recent market volatility. The goal is to target a consistent level of annual risk rather than a fixed allocation.
target_vol = 0.10 # 10% annual volatility
weekly["Returns"] = weekly["Close"].pct_change()
rolling_vol = weekly["Returns"].rolling(52).std() * np.sqrt(52)
weekly["Position"] = (target_vol / rolling_vol) * weekly["Signal"]
weekly["Position"] = weekly["Position"].clip(0, 1)
weekly[["Signal", "Position"]].dropna().head()Calculating Strategy and Benchmark Returns
Strategy returns are calculated using the dynamic position size. Buy and hold returns are calculated for comparison.
weekly["Strategy_Returns"] = weekly["Position"] * weekly["Returns"]
weekly["Cumulative_Strategy"] = (1 + weekly["Strategy_Returns"]).cumprod()
weekly["Cumulative_BuyHold"] = (1 + weekly["Returns"]).cumprod()Removing Warm-Up Periods
Rows affected by indicator warm-up periods are removed before analysis and visualization.
weekly_clean = weekly.dropna().copy()Comparing Long-Term Growth
This chart compares the cumulative performance of the momentum strategy with buy and hold.
plt.plot(
weekly_clean.index,
weekly_clean["Cumulative_Strategy"],
label="Strategy"
)
plt.plot(
weekly_clean.index,
weekly_clean["Cumulative_BuyHold"],
label="Buy & Hold",
alpha=0.7
)
plt.title("Cumulative Returns Comparison")
plt.ylabel("Growth of $1")
plt.legend()
plt.savefig("cumulative_returns_comparison.png")
plt.show()
Cumulative returns of the momentum strategy versus buy and hold
Visualizing Entry and Exit Points
This visualization shows how the strategy enters and exits the market based on long-term momentum changes.
buy_signals = weekly_clean[
(weekly_clean["Signal"] == 1) &
(weekly_clean["Signal"].shift(1) == 0)
]
sell_signals = weekly_clean[
(weekly_clean["Signal"] == 0) &
(weekly_clean["Signal"].shift(1) == 1)
]
plt.plot(
weekly_clean.index,
weekly_clean["Close"],
label="Price",
alpha=0.8
)
plt.scatter(
buy_signals.index,
buy_signals["Close"],
marker="^",
color="green",
label="Buy",
zorder=3
)
plt.scatter(
sell_signals.index,
sell_signals["Close"],
marker="v",
color="red",
label="Sell",
zorder=3
)
plt.title("Buy and Sell Signals")
plt.legend()
plt.savefig("buy_sell_signals.png")
plt.show()
Buy and sell signals on weekly price data
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Evaluating Drawdowns
Drawdowns show how much capital is lost from peak to trough. Reducing drawdowns is a primary objective of this strategy.
rolling_max = weekly_clean["Cumulative_Strategy"].cummax()
drawdown = weekly_clean["Cumulative_Strategy"] / rolling_max - 1
plt.fill_between(drawdown.index, drawdown, 0)
plt.title("Strategy Drawdowns")
plt.ylabel("Drawdown")
plt.savefig("strategy_drawdowns.png")
plt.show()
Drawdowns of the momentum strategy over time
Final Performance Comparison
The table below summarizes the performance of buy and hold versus the 12-month time-series momentum strategy.
def performance_metrics(returns):
ann_return = (1 + returns.mean()) ** 52 - 1
ann_vol = returns.std() * np.sqrt(52)
sharpe = ann_return / ann_vol
cumulative = (1 + returns).cumprod()
rolling_max = cumulative.cummax()
max_dd = (cumulative / rolling_max - 1).min()
return ann_return, ann_vol, sharpe, max_dd
metrics = pd.DataFrame(
[
performance_metrics(weekly_clean["Returns"]),
performance_metrics(weekly_clean["Strategy_Returns"])
],
columns=["Annual Return", "Annual Volatility", "Sharpe Ratio", "Max Drawdown"],
index=["Buy & Hold", "Strategy"]
)
metrics Annual Return Annual Volatility Sharpe Ratio Max Drawdown
Buy & Hold 0.103782 0.176047 0.589514 -0.546130
Strategy 0.064627 0.085261 0.757993 -0.135246What the Results Show
The momentum strategy produces lower annual returns than buy and hold. However, it does so with significantly lower volatility and much smaller drawdowns.
The maximum drawdown is reduced from more than 50% to around 13%, and the risk-adjusted return improves meaningfully.
This outcome reflects the core trade-off of trend following. Some upside is sacrificed in strong bull markets in exchange for protection during prolonged market declines.
A More Practical Way to Stay Invested
This strategy is not designed to outperform the market in every environment. It is designed to make long-term participation more manageable.
By reducing drawdowns and smoothing returns, the strategy increases the likelihood that an investor can remain disciplined through different market regimes. For many, that may be more valuable than chasing the highest possible return.
The 12-month time-series momentum approach offers a structured way to respect market trends while keeping risk under control.
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