Trend Following and Momentum Strategies › Combining Time-Series and Cross-Sectional Momentum

# Combined momentum strategy
def combined_momentum_strategy(prices, ts_lookback=252, xs_lookback=126):
    """
    Combine time-series and cross-sectional momentum.

    Time-series: Go long only when asset has positive momentum
    Cross-sectional: Overweight relative winners, underweight losers
    """
    returns = prices.pct_change()
    n_assets = prices.shape[1]

    # Time-series signals (1 for positive momentum, 0 otherwise)
    ts_signals = pd.DataFrame(index=prices.index, columns=prices.columns)
    for col in prices.columns:
        ts_momentum = prices[col] / prices[col].shift(ts_lookback) - 1
        ts_signals[col] = (ts_momentum > 0).astype(float)

    # Cross-sectional signals (rank-based weights)
    xs_signals = pd.DataFrame(
        index=prices.index, columns=prices.columns, dtype=float
    )
    xs_momentum = prices.pct_change(xs_lookback)

    for date in prices.index[xs_lookback:]:
        scores = xs_momentum.loc[date].dropna()
        if len(scores) > 0:
            ranks = scores.rank()
            # Normalize ranks to weights summing to 1
            xs_signals.loc[date] = (ranks - ranks.mean()) / ranks.sum()

    # Combined signal: time-series filter × cross-sectional weights
    combined_weights = ts_signals * xs_signals

    # Normalize to fully invested when possible
    combined_weights = combined_weights.div(
        combined_weights.abs().sum(axis=1), axis=0
    )
    combined_weights = combined_weights.fillna(0)

    # Portfolio returns
    portfolio_ret = (combined_weights.shift(1) * returns).sum(axis=1)

    return portfolio_ret, combined_weights


combined_returns, combined_weights = combined_momentum_strategy(stock_prices)

# Calculate pure strategies for comparison
# Re-calculate TS momentum on the stock universe for fair comparison
ts_lookback = 252
ts_mom_stocks = stock_prices / stock_prices.shift(ts_lookback) - 1
ts_sig_stocks = (ts_mom_stocks > 0).astype(float)
pure_ts_returns = (ts_sig_stocks.shift(1) * stock_returns).mean(axis=1)

# Calculate cumulative returns for plotting
cum_combined = (1 + combined_returns).cumprod()
cum_ts = (1 + pure_ts_returns).cumprod()