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Enter Long When the 90-Bar Return Turns Positive, Exit When It Turns Negative

A pure momentum rule on a single market's close: the signal is nothing but the return over the last 90 bars, and the position is long whenever that return is positive and flat whenever it is negative. The notebook defines the rule, shows it trading on a simulated series, measures it on ten years of real Binance data across a basket of liquid symbols and four timeframes, then replays it on a resampled history, ending in a verdict.

---

• Imports
• Config
• Strategy
• Metrics
• Visualization
• Run on Real Data
• Run on Resampled History
• Conclusion

Imports

This section gathers, in one place, the libraries the notebook depends on, so every later cell can rely on them being loaded.

import numpy as np
import pandas as pd
import plotly.graph_objects as go
from plotly.subplots import make_subplots

Config

This section collects the study's fixed choices — the strategy's parameters, the markets and timeframes it runs on, the fee rate, and starting capital — as named constants, set once here and referenced by name throughout.

FEE_PCT = 0.02 / 100  # binance futures taker, per side
INITIAL_CASH = 100

# Bars in the trailing window whose return sets the position.
MOMENTUM_LOOKBACK = 90

SYMBOLS = ["BTCUSDT", "ETHUSDT", "SOLUSDT", "BNBUSDT", "DOGEUSDT"]

# Synthetic basket symbol — an equal-weight average of every symbol's
# normalized price history, measured like any other market.
BASKET_SYMBOL = "ALL"

# Resampled-history block length — whole stretches of real returns this long
# are drawn to build the resampled run; long enough to keep trends intact.
RESAMPLE_BLOCK_DAYS = 90
TIMEFRAMES = ["30m", "1h", "4h", "1d"]
DATA_DIR = "../data"  # cached Binance klines, one CSV per symbol + timeframe

# Bars per year by timeframe — annualizes the Sharpe ratio.
BARS_PER_YEAR = {
    "30m": 365 * 24 * 2,
    "1h": 365 * 24,
    "4h": 365 * 6,
    "1d": 365,
}

# One colour per symbol, used for the overlaid lines in every chart.
SYMBOL_COLORS = {
    "BTCUSDT": "#f7931a",
    "ETHUSDT": "#627eea",
    "SOLUSDT": "#14b8a6",
    "BNBUSDT": "#f3ba2f",
    "DOGEUSDT": "#9b59b6",
    BASKET_SYMBOL: "#333333",
}

Strategy

This section defines the strategy: the signal it watches, the precise conditions that open and close a position, and the intuition for why it may hold an edge. A short example on simulated prices shows the entry and exit markers in isolation, so the mechanics are clear before any real data or performance is considered.

The strategy reads nothing but the market's own trailing return: the momentum at bar $t$ is the percentage change of the close over the prior 90 bars, $m_t = (p_t / p_{t-90} - 1)\cdot 100\%$. The position is long exactly while that return is positive — it opens the moment $m_t$ turns positive and closes the moment it turns negative:

$$\text{open at } t \iff m_{t-1} \le 0 \;\land\; m_t > 0, \qquad \text{close at } t \iff m_{t-1} > 0 \;\land\; m_t \le 0.$$

There is no smoothing, no envelope, and no oscillator — the raw return is the entire signal. It is long-only and always fully in or fully out, a bet on momentum in its purest form: a market that has risen over its recent past keeps rising more often than chance allows, and holding exactly while that is true is the most direct way to collect it.

def strategy(prices, lookback):
    momentum = np.full(prices.shape, np.nan)
    momentum[lookback:] = (prices[lookback:] / prices[:-lookback] - 1) * 100

    above = (momentum > 0).astype(np.int8)
    change = np.diff(above)
    opens = np.where(change == 1)[0] + 1
    closes = np.where(change == -1)[0] + 1
    return momentum, opens, closes

An illustrative example on a synthetic price path, drawn as candles around its closes, so the entries (green) and exits (red) on the price can be read against the momentum's sign flips below.

rng = np.random.default_rng(5)
example_prices = 100 * np.cumprod(1 + rng.normal(0, 0.01, size=500))
example_momentum, example_opens, example_closes = strategy(
    prices=example_prices,
    lookback=MOMENTUM_LOOKBACK,
)

# Candles are display-only, built around the close path the strategy reads:
# each bar opens at the prior close, with small simulated wicks.
candle_open_prices = np.concatenate(([example_prices[0]], example_prices[:-1]))
candle_high_prices = np.maximum(candle_open_prices, example_prices) * (
    1 + rng.uniform(0, 0.004, size=example_prices.size)
)
candle_low_prices = np.minimum(candle_open_prices, example_prices) * (
    1 - rng.uniform(0, 0.004, size=example_prices.size)
)

fig = make_subplots(rows=2, cols=1, shared_xaxes=True, vertical_spacing=0.06)
fig.add_trace(
    go.Candlestick(
        open=candle_open_prices,
        high=candle_high_prices,
        low=candle_low_prices,
        close=example_prices,
        name="Price",
        increasing=dict(line=dict(color="#8a9bab", width=1), fillcolor="#f6fafd"),
        decreasing=dict(line=dict(color="#8a9bab", width=1), fillcolor="#8a9bab"),
    ),
    row=1,
    col=1,
)
fig.add_trace(
    go.Scatter(
        x=example_opens,
        y=example_prices[example_opens],
        mode="markers",
        name="Entries",
        marker=dict(color="#00d4aa", size=9, symbol="triangle-up"),
    ),
    row=1,
    col=1,
)
fig.add_trace(
    go.Scatter(
        x=example_closes,
        y=example_prices[example_closes],
        mode="markers",
        name="Exits",
        marker=dict(color="#ff3b30", size=9, symbol="triangle-down"),
    ),
    row=1,
    col=1,
)
fig.add_trace(
    go.Scatter(
        y=example_momentum,
        mode="lines",
        name="Momentum",
        line=dict(color="#7b68ee", width=1),
    ),
    row=2,
    col=1,
)
threshold_x = [0, len(example_prices) - 1]
fig.add_trace(
    go.Scatter(
        x=threshold_x,
        y=[0, 0],
        mode="lines",
        name="Zero",
        line=dict(color="#888", width=1, dash="dot"),
    ),
    row=2,
    col=1,
)
fig.update_layout(
    template="plotly_white",
    height=500,
    width=1080,
    margin=dict(l=60, r=20, t=40, b=40),
    xaxis_rangeslider_visible=False,
)
fig.show()

Metrics

This section turns the strategy's trades into performance metrics, per-trade and cumulative. Each is defined with its formula below; equity is reported in both gross (before fees) and net (after fees) form, so the cost of trading is always visible.

• Symbol — the market this result belongs to (e.g. BTCUSDT); ALL is the equal-weight basket of every symbol, averaged from their normalized price histories over the common window.
• Price Change % — the close price as a percentage change from the start of the window (from the close series $p_0,\dots,p_T$); in the summary, the total change over the period — the buy-and-hold return.
• Momentum — the trailing 90-bar return of the close, $m_t = (p_t / p_{t-90} - 1)\cdot 100\%$, whose sign sets the position.
• Entries — bars where a position is opened.
• Exits — bars where a position is closed.
• Trade P&L % — per-trade net return, $\text{pnl}_i = (r_i - 1)\cdot 100\%$ with $r_i = (1 - f)^2\,p^{\text{exit}}_i / p^{\text{entry}}_i$ and $f$ the per-side fee.
• Cumulative Win Rate % — running share of winning trades, $\frac{1}{n}\sum_{i=1}^{n}\mathbf{1}\{\text{pnl}_i > 0\}\cdot 100\%$.
• Cumulative P&L % — the running sum of per-trade P&L.
• Equity — net equity curve, compounded all-in: $E_n = E_0 \prod_{i=1}^{n} r_i$; the gross variant drops the fee term.
• Cumulative Fees — the running total of fees paid, each proportional to capital at trade time.
• Rolling Sharpe — annualized Sharpe of net per-trade returns computed to-date after each trade, $S_n = \frac{\bar x}{\operatorname{std}(x)}\sqrt{T_\text{year}}$ over $x_1,\dots,x_n$, with $x_i = r_i - 1$ and $T_\text{year}$ the observed number of trades per year.

def analytics(symbol, prices, bars_per_year):
    momentum, opens, closes = strategy(prices=prices, lookback=MOMENTUM_LOOKBACK)

    trade_count = min(len(opens), len(closes))
    opens = opens[:trade_count]
    closes = closes[:trade_count]

    entry_prices = prices[opens]
    exit_prices = prices[closes]

    # Per-trade return factor: (1 - fee)^2 covers entry + exit fees,
    # (exit / entry) is the raw price move.
    factor = (1 - FEE_PCT) ** 2 * (exit_prices / entry_prices)

    # Equity compounded with all-in sizing.
    equity = INITIAL_CASH * np.cumprod(factor)
    equity_no_fee = INITIAL_CASH * np.cumprod(exit_prices / entry_prices)
    entry_capital = np.concatenate(([INITIAL_CASH], equity[:-1]))

    # Fees in dollars — proportional to capital at trade time.
    entry_fees = entry_capital * FEE_PCT
    exit_fees = entry_capital * (1 - FEE_PCT) * (exit_prices / entry_prices) * FEE_PCT
    fees = entry_fees + exit_fees
    cum_fees = np.cumsum(fees)

    pnls = equity - entry_capital
    pnl_pct = (factor - 1) * 100

    total_trades = pnls.size
    cum_winrate = np.cumsum(pnls > 0) / np.arange(1, total_trades + 1) * 100
    pct_cum_pnl = np.cumsum(pnl_pct)

    # Rolling (to-date) Sharpe after each trade: per-trade fractional returns,
    # annualized by the observed trade frequency.
    returns = factor - 1
    with np.errstate(invalid="ignore", divide="ignore"):
        cum_mean = np.cumsum(returns) / np.arange(1, total_trades + 1)
        cum_var = (np.cumsum(returns**2) / np.arange(1, total_trades + 1)) - cum_mean**2
        cum_std = np.sqrt(np.clip(cum_var, 0, None))
        cum_sharpe_per_trade = np.where(cum_std > 0, cum_mean / cum_std, 0.0)
    cum_sharpe = cum_sharpe_per_trade * np.sqrt(
        np.arange(1, total_trades + 1) * bars_per_year / max(len(prices), 1)
    )

    return {
        "symbol": symbol,
        "prices": prices,
        "momentum": momentum,
        "opens": opens,
        "closes": closes,
        "pnl_pct": pnl_pct,
        "cum_winrate": cum_winrate,
        "pct_cum_pnl": pct_cum_pnl,
        "equity": equity,
        "equity_no_fee": equity_no_fee,
        "cum_fees": cum_fees,
        "cum_sharpe": cum_sharpe,
    }

Visualization

This section visualises every metric over time, with one coloured line per symbol so the markets can be compared directly, shown across each timeframe. Each summary table below is also drawn as grouped bars — one panel per metric, one bar per symbol and timeframe — so the final results compare at a glance.

def charts(results):
    symbols = list(dict.fromkeys(symbol for symbol, _ in results))
    metrics = [
        ("Price Change %", "pct_prices", None),
        ("Trade P&L %", "pnl_pct", None),
        ("Cumulative Win Rate %", "cum_winrate", None),
        ("Cumulative P&L %", "pct_cum_pnl", None),
        ("Equity", "equity", "equity_no_fee"),
        ("Cumulative Fees", "cum_fees", None),
        ("Rolling Sharpe", "cum_sharpe", None),
    ]
    n_rows = len(metrics)
    n_cols = len(TIMEFRAMES)

    col_width = 600
    row_height = 280
    gap_px = 60
    total_w = col_width * n_cols + gap_px * max(n_cols - 1, 0)
    total_h = row_height * n_rows
    h_spacing = gap_px / total_w if n_cols > 1 else 0

    fig = make_subplots(
        rows=n_rows,
        cols=n_cols,
        shared_xaxes=True,
        vertical_spacing=0.025,
        horizontal_spacing=h_spacing,
        column_titles=list(TIMEFRAMES),
    )

    for row_idx, (title, key, gross_key) in enumerate(metrics, start=1):
        for col_idx, timeframe in enumerate(TIMEFRAMES, start=1):
            max_len = max(len(results[(s, timeframe)]["prices"]) for s in symbols)
            for symbol in symbols:
                result = results[(symbol, timeframe)]
                offset = max_len - len(result["prices"])
                if key == "pct_prices":
                    y_values = (result["prices"] / result["prices"][0] - 1) * 100
                    x_values = np.arange(offset, offset + len(y_values))
                else:
                    y_values = result[key]
                    x_values = result["opens"] + offset
                fig.add_trace(
                    go.Scatter(
                        x=x_values,
                        y=y_values,
                        mode="lines",
                        name=symbol,
                        legendgroup=symbol,
                        line=dict(color=SYMBOL_COLORS[symbol], width=1),
                        showlegend=False,
                        hovertemplate="%{fullData.name}: %{y}<extra></extra>",
                    ),
                    row=row_idx,
                    col=col_idx,
                )
                if gross_key:
                    fig.add_trace(
                        go.Scatter(
                            x=result["opens"] + offset,
                            y=result[gross_key],
                            mode="lines",
                            name=symbol,
                            legendgroup=symbol,
                            line=dict(color=SYMBOL_COLORS[symbol], width=1, dash="dot"),
                            showlegend=False,
                            hoverinfo="skip",
                        ),
                        row=row_idx,
                        col=col_idx,
                    )
        fig.update_yaxes(title_text=title, title_font=dict(size=13), row=row_idx, col=1)

    # Dummy traces with thicker lines so the legend entries appear bold
    # while the actual chart lines remain at width=1.
    for symbol in symbols:
        fig.add_trace(
            go.Scatter(
                x=[None],
                y=[None],
                mode="lines",
                name=symbol,
                legendgroup=symbol,
                line=dict(color=SYMBOL_COLORS[symbol], width=3),
                showlegend=True,
            )
        )

    # Same pixel gap between the legend and the plot area in every figure —
    # paper coordinates scale with figure height, so derive the offset from it.
    legend_y = 1 + 75 / (total_h - 110)  # 110 = top + bottom margins
    fig.update_layout(
        template="plotly_white",
        height=total_h,
        width=total_w,
        font=dict(size=11),
        hovermode="x unified",
        hoverlabel=dict(bgcolor="white"),
        legend=dict(
            orientation="h",
            yanchor="bottom",
            y=legend_y,
            xanchor="left",
            x=0,
        ),
        margin=dict(l=90, r=20, t=70, b=40),
    )
    fig.update_annotations(font=dict(size=13))
    fig.update_xaxes(showgrid=True)
    fig.update_yaxes(showgrid=True, zeroline=True)
    fig.update_yaxes(range=[-3, 3], row=n_rows)  # clamp Rolling Sharpe
    fig.show()


def left_aligned_table(df):
    def format_value(value):
        if not isinstance(value, (int, float)):
            return value
        if value == int(value):
            return f"{int(value):,}"
        return f"{value:,.2f}".rstrip("0").rstrip(".")

    return (
        df.style.format(format_value)
        .hide(axis="index")
        .set_properties(**{"text-align": "left", "white-space": "nowrap"})
        .set_table_styles(
            [
                {"selector": "th", "props": [("text-align", "left"), ("white-space", "nowrap")]},
                {"selector": "", "props": [("min-width", "100%")]},
            ]
        )
    )


def summarize(results):
    rows = []
    for (symbol, timeframe), result in results.items():
        equity = result["equity"]
        equity_no_fee = result["equity_no_fee"]
        prices = result["prices"]
        has_trades = len(equity) > 0
        rows.append(
            {
                "Symbol": symbol,
                "Timeframe": timeframe,
                "Price Change %": round(float(prices[-1] / prices[0] - 1) * 100, 1),
                "Cumulative Win Rate %": (
                    round(float(result["cum_winrate"][-1]), 1) if has_trades else 0.0
                ),
                "Cumulative P&L %": (
                    round(float(result["pct_cum_pnl"][-1]), 1) if has_trades else 0.0
                ),
                "Equity Net": (round(float(equity[-1]), 2) if has_trades else float(INITIAL_CASH)),
                "Equity Gross": (
                    round(float(equity_no_fee[-1]), 2) if has_trades else float(INITIAL_CASH)
                ),
                "Cumulative Fees": (round(float(result["cum_fees"][-1]), 2) if has_trades else 0.0),
                "Rolling Sharpe": (
                    round(float(result["cum_sharpe"][-1]), 2) if has_trades else 0.0
                ),
            }
        )
    return pd.DataFrame(rows)


def summary_charts(summary):
    symbols = list(dict.fromkeys(summary["Symbol"]))
    metrics = [column for column in summary.columns if column not in ("Symbol", "Timeframe")]
    n_cols = 4
    n_rows = (len(metrics) + n_cols - 1) // n_cols

    col_width = 600
    row_height = 280
    gap_px = 60
    total_w = col_width * n_cols + gap_px * max(n_cols - 1, 0)
    total_h = row_height * n_rows
    h_spacing = gap_px / total_w if n_cols > 1 else 0
    v_spacing = gap_px / total_h if n_rows > 1 else 0

    fig = make_subplots(
        rows=n_rows,
        cols=n_cols,
        vertical_spacing=v_spacing,
        horizontal_spacing=h_spacing,
        subplot_titles=metrics,
    )

    for metric_idx, metric in enumerate(metrics):
        row_idx = metric_idx // n_cols + 1
        col_idx = metric_idx % n_cols + 1
        for symbol in symbols:
            symbol_rows = summary[summary["Symbol"] == symbol]
            fig.add_trace(
                go.Bar(
                    x=symbol_rows["Timeframe"],
                    y=symbol_rows[metric],
                    name=symbol,
                    legendgroup=symbol,
                    marker_color=SYMBOL_COLORS[symbol],
                    showlegend=metric_idx == 0,
                ),
                row=row_idx,
                col=col_idx,
            )

    # Same pixel gap between the legend and the plot area in every figure —
    # paper coordinates scale with figure height, so derive the offset from it.
    legend_y = 1 + 75 / (total_h - 110)  # 110 = top + bottom margins
    fig.update_layout(
        template="plotly_white",
        height=total_h,
        width=total_w,
        font=dict(size=11),
        barmode="group",
        hovermode="x unified",
        hoverlabel=dict(bgcolor="white"),
        legend=dict(
            orientation="h",
            yanchor="bottom",
            y=legend_y,
            xanchor="left",
            x=0,
        ),
        margin=dict(l=90, r=20, t=70, b=40),
    )
    fig.update_annotations(font=dict(size=13))
    fig.update_xaxes(showgrid=True)
    fig.update_yaxes(showgrid=True, zeroline=True)
    # Hide the axes of grid slots past the last metric so they stay blank.
    for slot_idx in range(len(metrics), n_rows * n_cols):
        row_idx = slot_idx // n_cols + 1
        col_idx = slot_idx % n_cols + 1
        fig.update_xaxes(visible=False, row=row_idx, col=col_idx)
        fig.update_yaxes(visible=False, row=row_idx, col=col_idx)
    fig.show()

Run on Real Data

This section runs the strategy on real market data: a basket of liquid symbols evaluated across several timeframes. Every metric is charted with one coloured line per symbol, so the markets can be compared directly.

The basket symbol ALL is an equal-weight portfolio of the whole set: every symbol's price history is normalized to its starting value over the common window, then averaged. It runs through the same strategy and metrics as any single market.

def basket_prices(symbol_prices):
    common_len = min(len(prices) for prices in symbol_prices)
    aligned = [prices[-common_len:] for prices in symbol_prices]
    normalized = [prices / prices[0] for prices in aligned]
    return np.mean(normalized, axis=0)

prices = {
    (symbol, timeframe): pd.read_csv(f"{DATA_DIR}/{symbol}_{timeframe}.csv")["close"].to_numpy()
    for symbol in SYMBOLS
    for timeframe in TIMEFRAMES
}

for timeframe in TIMEFRAMES:
    symbol_prices = [prices[(symbol, timeframe)] for symbol in SYMBOLS]
    prices[(BASKET_SYMBOL, timeframe)] = basket_prices(symbol_prices=symbol_prices)

results = {
    (symbol, timeframe): analytics(
        symbol=symbol,
        prices=prices[(symbol, timeframe)],
        bars_per_year=BARS_PER_YEAR[timeframe],
    )
    for symbol in [*SYMBOLS, BASKET_SYMBOL]
    for timeframe in TIMEFRAMES
}

charts(results=results)

summary = summarize(results=results)
left_aligned_table(df=summary)

Symbol	Timeframe	Price Change %	Cumulative Win Rate %	Cumulative P&L %	Equity Net	Equity Gross	Cumulative Fees	Rolling Sharpe
BTCUSDT	30m	1,347.9	28.1	236.7	410.25	1,954.17	551.81	0.55
BTCUSDT	1h	1,331.8	29	348.7	1,037.75	2,142.4	589.28	0.73
BTCUSDT	4h	1,318	29.5	531.7	3,492.07	4,109.54	270.01	0.82
BTCUSDT	1d	1,339.4	37.3	661.3	1,216.89	1,245.95	11.71	0.47
ETHUSDT	30m	444.3	29.6	390.7	1,069.65	5,154.6	949.98	0.71
ETHUSDT	1h	440.1	31.9	494.2	2,135.16	4,315.49	1,126.01	0.79
ETHUSDT	4h	429.1	34.6	569.7	3,535.65	4,157.5	303.28	0.83
ETHUSDT	1d	439.5	33.3	625.5	1,200.54	1,226.76	13.22	0.47
SOLUSDT	30m	1,957.1	31.3	505.3	1,797.45	4,738.25	1,425.64	0.93
SOLUSDT	1h	2,086.3	31	630.1	2,937.47	4,772.14	1,392.49	0.92
SOLUSDT	4h	2,107.4	35.8	1,038.1	6,412.22	7,115.08	432.12	0.8
SOLUSDT	1d	1,856.3	26.7	1,279.2	2,805.73	2,856.7	43.75	0.6
BNBUSDT	30m	34,845.9	30.7	534.8	1,547.88	7,453.18	2,644.27	0.68
BNBUSDT	1h	34,877.6	30.8	892.1	24,403.41	48,598.45	10,561.23	0.92
BNBUSDT	4h	34,864.7	36.1	1,512.9	48,766.71	57,458.58	4,209.91	0.62
BNBUSDT	1d	37,733.2	33.9	1,108.5	3,623.69	3,705.78	45.35	0.47
DOGEUSDT	30m	2,106.6	27.3	579.6	326.45	1,240.42	295.64	0.54
DOGEUSDT	1h	2,041.5	29.6	1,065.1	3,449.76	6,558.54	1,724.28	0.67
DOGEUSDT	4h	2,148.9	31.6	1,474.2	18,245.76	20,945.97	1,473.96	0.69
DOGEUSDT	1d	2,071.8	20	5,510.5	1,560.74	1,598.65	36.73	0.38
ALL	30m	1,511.3	36.6	747.1	31,610.3	69,405.19	6,687.74	1.46
ALL	1h	1,540.6	37	909.9	68,715.36	100,004	10,395.17	1.29
ALL	4h	1,544.9	32.9	753	4,873.98	5,445.14	308.9	0.79
ALL	1d	1,539.7	34.8	1,668.8	2,379.93	2,424.13	33.43	0.45

summary_charts(summary=summary)

Run on Resampled History

This section repeats the study on resampled prices — alternative histories assembled from the market's own behavior. Whole stretches of real returns are drawn in a new order over the window all markets share, the same stretches for every market so their synchrony survives; the coarser timeframes sample the same path, just as the real timeframes sample the same market.

Inside each stretch the behavior is intact — trends, drawdown regimes, volatility bursts, and the co-movement between markets — only the order of stretches is new. The result is a past the strategy has never seen that still behaves like the market it trades: a stand-in for the future. Performance that repeats here shows the rule rides the market's behavior itself, not one memorized chronology.

def resample_history(real_prices, block_starts, block_bars):
    returns = np.diff(real_prices) / real_prices[:-1]
    blocks = [returns[start : start + block_bars] for start in block_starts]
    resampled_returns = np.concatenate(blocks)[: returns.size]
    growth = np.concatenate(([1.0], np.cumprod(1 + resampled_returns)))
    return real_prices[0] * growth

rng = np.random.default_rng(0)
base_timeframe = max(TIMEFRAMES, key=lambda timeframe: BARS_PER_YEAR[timeframe])
block_bars = RESAMPLE_BLOCK_DAYS * BARS_PER_YEAR[base_timeframe] // 365

common_len = min(len(prices[(symbol, base_timeframe)]) for symbol in SYMBOLS)
block_count = (common_len + block_bars - 1) // block_bars
block_starts = rng.integers(0, common_len - block_bars, size=block_count)

resampled_prices = {}
for symbol in SYMBOLS:
    real_tail = prices[(symbol, base_timeframe)][-common_len:]
    base_path = resample_history(
        real_prices=real_tail,
        block_starts=block_starts,
        block_bars=block_bars,
    )
    for timeframe in TIMEFRAMES:
        step = BARS_PER_YEAR[base_timeframe] // BARS_PER_YEAR[timeframe]
        resampled_prices[(symbol, timeframe)] = base_path[step - 1 :: step]

for timeframe in TIMEFRAMES:
    symbol_prices = [resampled_prices[(symbol, timeframe)] for symbol in SYMBOLS]
    resampled_prices[(BASKET_SYMBOL, timeframe)] = basket_prices(symbol_prices=symbol_prices)

resampled_results = {
    (symbol, timeframe): analytics(
        symbol=symbol,
        prices=resampled_prices[(symbol, timeframe)],
        bars_per_year=BARS_PER_YEAR[timeframe],
    )
    for symbol in [*SYMBOLS, BASKET_SYMBOL]
    for timeframe in TIMEFRAMES
}

charts(results=resampled_results)

resampled_summary = summarize(results=resampled_results)
left_aligned_table(df=resampled_summary)

Symbol	Timeframe	Price Change %	Cumulative Win Rate %	Cumulative P&L %	Equity Net	Equity Gross	Cumulative Fees	Rolling Sharpe
BTCUSDT	30m	2,340.1	28.9	103	179.47	502.54	176.54	0.44
BTCUSDT	1h	2,336.9	29.7	338.2	1,650.88	2,661.67	335.2	1.23
BTCUSDT	4h	2,348.9	36.5	479.8	4,320.62	4,794.21	118.38	1.23
BTCUSDT	1d	2,340.7	25.6	1,024	1,623.12	1,648.64	11.4	0.46
ETHUSDT	30m	832	29.3	186.6	264.64	760.87	318.68	0.55
ETHUSDT	1h	825	31	281.3	693.7	1,130.57	189.99	0.83
ETHUSDT	4h	833.2	36	570.1	5,886.73	6,505.91	210.26	1.11
ETHUSDT	1d	779.2	28.6	1,054.1	654.01	663.23	7.32	0.4
SOLUSDT	30m	15,210.4	31.3	635.5	6,080.44	16,137.96	3,527.16	1.14
SOLUSDT	1h	15,289	33	754	9,069.84	14,705.22	1,716.91	1.08
SOLUSDT	4h	15,463.4	34.3	1,364.7	53,629.7	59,223.18	2,693.23	0.86
SOLUSDT	1d	15,594.7	32.6	2,430.4	11,561.14	11,775.86	91.25	0.59
BNBUSDT	30m	5,780.4	29.8	257.1	440.03	1,327.88	634.61	0.64
BNBUSDT	1h	5,761.4	31.4	459.1	1,363.91	2,231.79	474.05	0.72
BNBUSDT	4h	5,540.5	35.6	661.3	2,235.15	2,549.56	188.13	0.61
BNBUSDT	1d	5,641.4	39.6	1,990	5,490.99	5,597.44	62.12	0.46
DOGEUSDT	30m	15,851.6	29.1	645.3	2,723.72	7,768.69	3,553.07	0.86
DOGEUSDT	1h	15,731.9	31	975.2	7,730.21	13,029.13	3,010.82	0.83
DOGEUSDT	4h	15,847.8	32.7	1,345.6	15,813.85	17,873.13	852.16	0.73
DOGEUSDT	1d	13,838.4	35.7	11,132.4	27,387.75	27,851.8	292.82	0.44
ALL	30m	8,002.9	34.8	807.2	77,970.86	175,215.42	16,871.11	1.8
ALL	1h	7,988.8	33.6	765.3	18,837.89	29,157.55	3,873.02	1.16
ALL	4h	8,006.8	40.2	985.5	31,524.26	35,345.42	1,296.63	0.9
ALL	1d	7,638.9	36.4	4,783.4	24,459.76	24,784.8	112.28	0.46

summary_charts(summary=resampled_summary)

Conclusion

This section judges the strategy. The verdict reads the summary tables above — real and synthetic — where the strategy holds up, where it fails, and whether it is worth pursuing.

Over each symbol's full available Binance history, the bare sign of the 90-bar return is profitable after fees in all 24 symbol × timeframe cells — every Equity Net ends above its starting capital, from DOGE at 30m (326) to BNB at 4h (48,767).

Versus buy-and-hold it wins 15 of 24 cells, and the wins have structure. The whole 4h column wins, the whole ETH row wins, and the whole basket row wins; the losses sit where one market's own drift was unbeatable (BNB outside 4h) or where fast noise whipsaws the raw signal (BTC, SOL, DOGE at 30m).

The basket is again the strategy's best market. ALL turns 100 into 68,715 at 1h (Rolling Sharpe 1.29) and 31,610 at 30m (1.46) — far ahead of any single market at those speeds. Averaging the symbols cancels their idiosyncratic noise, so when the smoothed basket's trailing return changes sign, the flip marks a genuine shift in the shared trend rather than one market's flutter.

Cumulative Win Rate % is the lowest of any respectable system — 20–37%. A raw sign rule re-enters on every wobble around zero (several thousand trades at 30m), and almost all of those probes lose a little; the rare ones that catch a real trend pay for everything. Fees tax that style heavily: at 1h, BNB pays 10,561 in Cumulative Fees against a 48,598 gross result, and the basket pays 10,395 against 100,004 — roughly a third to a half of gross at speed — yet every cell still ends profitable.

On resampled history the edge repeats. All 24 cells end profitable again, buy-and-hold falls in 8 of them — including the entire basket row, with ALL at 30m reaching 77,971 at a Rolling Sharpe of 1.80 — and the 4h column stays the strongest single-market column. The rule rides the market's behavior itself, not one memorized chronology.

Caveats. Results come from one historical window with a fixed 90-bar lookback; the basket is five liquid survivors (and ALL inherits that); the strategy is long-only over a window in which every symbol rose; the large terminal figures come from compounding all-in over roughly a decade; the resampled run is a single draw — one alternative history — not a distribution; and prices are spot klines while the fee rate models the futures taker rate.

Call: pursue. The plainest possible momentum signal — the sign of the market's own trailing return, with no indicator machinery at all — is profitable everywhere, beats buy-and-hold across a structured majority of cells, and repeats on resampled history. Its weakness is mechanical, not statistical: a raw sign flip is the noisiest possible trigger, so the natural next steps are a confirmation band around zero to cut the whipsaw count, fee-aware execution, and walking the lookback forward out of sample.

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