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Enter Long When MACD Crosses Above Its Signal Line, Exit When It Crosses Back Down

A trend-following rule on a single market's close: ride the move while the MACD line sits above its signal line, and step aside when it falls back. 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.

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• Imports
• Config
• Strategy
• Metrics
• Visualization
• Run on Real Data
• Run on Resampled History
• Scoring
• 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
import talib
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

MACD_FAST_PERIOD = 12
MACD_SLOW_PERIOD = 26
MACD_SIGNAL_PERIOD = 9

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

# 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",
    "XRPUSDT": "#0085c0",
    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 the moving-average convergence/divergence of the close. The MACD line is the gap between two exponential moving averages — a fast one over 12 bars and a slow one over 26 — and the signal line is a 9-bar exponential moving average of that gap:

$$\mathrm{MACD}_t = \mathrm{EMA}_{12}(t) - \mathrm{EMA}_{26}(t), \qquad \mathrm{Signal}_t = \mathrm{EMA}_9(\mathrm{MACD})_t.$$

The MACD line climbs when the fast average pulls away above the slow — momentum building — and the signal line is its smoothed trail. A long position opens the moment the MACD line crosses above its signal, and closes when it crosses back below:

$$\text{open at } t \iff \mathrm{MACD}_{t-1} \le \mathrm{Signal}_{t-1} \;\land\; \mathrm{MACD}_t > \mathrm{Signal}_t, \qquad \text{close at } t \iff \mathrm{MACD}_{t-1} \ge \mathrm{Signal}_{t-1} \;\land\; \mathrm{MACD}_t < \mathrm{Signal}_t.$$

It is long-only and always fully in or fully out — a bet that the fast average accelerating above the slow marks the start of an up-move worth riding until that acceleration fades.

def strategy(prices, fast, slow, signal):
    macd_line, signal_line, _ = talib.MACD(
        prices, fastperiod=fast, slowperiod=slow, signalperiod=signal
    )
    macd = {"macd": macd_line, "signal": signal_line}

    above = (macd_line > signal_line).astype(np.int8)
    change = np.diff(above)
    opens = np.where(change == 1)[0] + 1
    closes = np.where(change == -1)[0] + 1
    return macd, 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 MACD line crossing its signal below.

rng = np.random.default_rng(5)
example_prices = 100 * np.cumprod(1 + rng.normal(0, 0.01, size=300))
example_macd, example_opens, example_closes = strategy(
    prices=example_prices,
    fast=MACD_FAST_PERIOD,
    slow=MACD_SLOW_PERIOD,
    signal=MACD_SIGNAL_PERIOD,
)

# 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_macd["macd"],
        mode="lines",
        name="MACD",
        line=dict(color="#7b68ee", width=1),
    ),
    row=2,
    col=1,
)
fig.add_trace(
    go.Scatter(
        y=example_macd["signal"],
        mode="lines",
        name="Signal",
        line=dict(color="#d4a017", 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.
• MACD — the MACD line, the 12-bar exponential moving average of the close minus the 26-bar one, with its signal line, a 9-bar exponential moving average of the MACD line, whose crossover sets the signals.
• Entries — bars where a position is opened.
• Exits — bars where a position is closed.
• Cumulative Win Rate % — running share of winning trades, $\frac{1}{n}\sum_{i=1}^{n}\mathbf{1}\{r_i > 1\}\cdot 100\%$, where $r_i = (1 - f)^2\,p^{\text{exit}}_i / p^{\text{entry}}_i$ and $f$ the per-side fee.
• Cumulative P&L % — the running sum of per-trade net returns, $\sum_{i=1}^{n}(r_i - 1)\cdot 100\%$.
• 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 the daily returns of the net (after-fee) equity curve, to-date: $S = \frac{\bar r}{\operatorname{std}(r)}\sqrt{365}$ over daily returns $r_t$ of the mark-to-market equity (the open position marked each bar, cash when flat); reported at each trade's close.

def analytics(symbol, prices, bars_per_year):
    macd, opens, closes = strategy(
        prices=prices,
        fast=MACD_FAST_PERIOD,
        slow=MACD_SLOW_PERIOD,
        signal=MACD_SIGNAL_PERIOD,
    )

    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

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

    # Rolling daily-equity Sharpe: mark the open position to market each bar,
    # resample to daily, and take the annualized (times sqrt(365)) Sharpe of the
    # daily returns to-date. Reported at each trade's close so it lines up with
    # the other per-trade series.
    bars_per_day = max(int(bars_per_year // 365), 1)
    if total_trades:
        bar_index = np.arange(len(prices))
        trade_of_bar = np.searchsorted(opens, bar_index, side="right") - 1
        held_trade = np.clip(trade_of_bar, 0, total_trades - 1)
        in_position = (trade_of_bar >= 0) & (bar_index <= closes[held_trade])
        held_entry_price = prices[opens[held_trade]]
        marked_equity = entry_capital[held_trade] * (1 - FEE_PCT) * prices / held_entry_price
        cash_after_trade = np.concatenate(([float(INITIAL_CASH)], equity))
        bar_equity = np.where(in_position, marked_equity, cash_after_trade[trade_of_bar + 1])
    else:
        bar_equity = np.full(len(prices), float(INITIAL_CASH))

    daily_equity = bar_equity[bars_per_day - 1 :: bars_per_day]
    daily_returns = np.diff(daily_equity) / daily_equity[:-1]
    day_count = np.arange(1, daily_returns.size + 1)
    with np.errstate(invalid="ignore", divide="ignore"):
        daily_mean = np.cumsum(daily_returns) / day_count
        daily_population_var = np.cumsum(daily_returns**2) / day_count - daily_mean**2
        daily_var = daily_population_var * day_count / np.maximum(day_count - 1, 1)
        daily_std = np.sqrt(np.clip(daily_var, 0, None))
        daily_sharpe = np.where(daily_std > 0, daily_mean / daily_std, 0.0) * np.sqrt(365)

    if daily_sharpe.size and total_trades:
        close_day = np.clip(closes // bars_per_day - 1, 0, daily_sharpe.size - 1)
        cum_sharpe = daily_sharpe[close_day]
    else:
        cum_sharpe = np.zeros(total_trades)

    return {
        "symbol": symbol,
        "prices": prices,
        "macd": macd,
        "opens": opens,
        "closes": closes,
        "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.

CHART_MAX_POINTS = 1500  # cap points per line so pages stay light; LTTB keeps the shape


def downsample(x_values, y_values, max_points):
    total_points = len(x_values)
    if total_points <= max_points or max_points < 3:
        return x_values, y_values
    x_values = np.asarray(x_values, dtype=float)
    y_values = np.asarray(y_values, dtype=float)
    bucket_size = (total_points - 2) / (max_points - 2)
    sampled_x = np.empty(max_points)
    sampled_y = np.empty(max_points)
    sampled_x[0] = x_values[0]
    sampled_y[0] = y_values[0]
    sampled_x[-1] = x_values[-1]
    sampled_y[-1] = y_values[-1]
    previous = 0
    for i in range(max_points - 2):
        next_start = int((i + 1) * bucket_size) + 1
        next_end = min(int((i + 2) * bucket_size) + 1, total_points)
        average_x = x_values[next_start:next_end].mean()
        average_y = y_values[next_start:next_end].mean()
        bucket_start = int(i * bucket_size) + 1
        bucket_end = int((i + 1) * bucket_size) + 1
        anchor_x = x_values[previous]
        anchor_y = y_values[previous]
        triangle_areas = np.abs(
            (anchor_x - average_x) * (y_values[bucket_start:bucket_end] - anchor_y)
            - (anchor_x - x_values[bucket_start:bucket_end]) * (average_y - anchor_y)
        )
        chosen = bucket_start + int(np.argmax(triangle_areas))
        sampled_x[i + 1] = x_values[chosen]
        sampled_y[i + 1] = y_values[chosen]
        previous = chosen
    return sampled_x, sampled_y


def charts(results):
    symbols = list(dict.fromkeys(symbol for symbol, _ in results))
    metrics = [
        ("Price Change %", "pct_prices", 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
                x_values, y_values = downsample(x_values, y_values, CHART_MAX_POINTS)
                fig.add_trace(
                    go.Scatter(
                        x=x_values,
                        y=np.round(y_values, 4),
                        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:
                    gross_x, gross_y = downsample(
                        result["opens"] + offset,
                        result[gross_key],
                        CHART_MAX_POINTS,
                    )
                    fig.add_trace(
                        go.Scatter(
                            x=gross_x,
                            y=np.round(gross_y, 4),
                            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	31.5	-220.6	4.08	45.14	34.5	-0.51
BTCUSDT	1h	1,331.8	35	206.7	286.81	932	294.53	0.49
BTCUSDT	4h	1,318	38.1	330	1,106.96	1,475.87	233.72	0.81
BTCUSDT	1d	1,339.4	39.8	463.9	2,448.63	2,561.86	58.61	1.03
ETHUSDT	30m	444.3	34.2	-3.7	19.21	206.43	50.98	-0.02
ETHUSDT	1h	440.1	36	522.6	3,945.06	12,641.45	3,053.42	1
ETHUSDT	4h	429.1	38	415.9	1,244	1,665.23	194.22	0.77
ETHUSDT	1d	439.5	36.4	456.5	1,176.82	1,233.7	42	0.77
SOLUSDT	30m	1,957.1	33.9	143.2	49.08	244.57	251.34	0.27
SOLUSDT	1h	2,086.3	35.9	439	1,094.9	2,369.64	1,010.28	0.88
SOLUSDT	4h	2,107.4	35.2	360.5	623.51	759.75	107	0.77
SOLUSDT	1d	1,856.3	38.7	861.6	3,401.04	3,504.63	80.5	1.14
BNBUSDT	30m	34,845.9	34.2	107.8	45.74	502.46	153.32	0.19
BNBUSDT	1h	34,877.6	37.2	790.3	34,138.49	108,520.74	22,334.95	1.28
BNBUSDT	4h	34,864.7	37.2	807.5	31,635.32	42,211.94	6,486.77	1.25
BNBUSDT	1d	37,733.2	44.9	1,065.3	19,337.22	20,182.9	402.35	1.16
DOGEUSDT	30m	2,106.6	30.7	-213.8	0.39	2.93	16.76	-0.3
DOGEUSDT	1h	2,041.5	33.1	837.4	2,465.49	6,383.3	1,803.4	0.83
DOGEUSDT	4h	2,148.9	33.8	857.8	4,797.86	6,072.65	777.04	0.91
DOGEUSDT	1d	2,071.8	38.6	768	3,400.81	3,515.63	101.04	0.94
XRPUSDT	30m	23	31	-265.8	1.06	10.33	37.43	-0.43
XRPUSDT	1h	22.4	32.3	344.7	428.43	1,305.9	286.4	0.58
XRPUSDT	4h	23.4	31.2	304.5	196.59	260.65	53.46	0.45
XRPUSDT	1d	27	36.1	781.6	2,044.97	2,125.89	45.5	0.85
ALL	30m	1,305.8	38.2	774.8	74,331.94	342,096.69	19,309.6	2.07
ALL	1h	1,330.2	41.4	910.3	249,879.09	530,092.95	36,866.63	2.26
ALL	4h	1,333.9	37.6	435	1,839.14	2,230.26	257.56	0.88
ALL	1d	1,332.9	41.3	391.2	762.09	785.31	22.46	0.87

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	31.9	1.4	62.99	304.99	118.13	0
BTCUSDT	1h	2,336.9	35.8	204	469.38	1,025.66	181.31	0.85
BTCUSDT	4h	2,348.9	38.2	199.1	470.61	569.32	51.96	0.85
BTCUSDT	1d	2,340.7	47.1	291.4	933.1	959.6	10.69	1.19
ETHUSDT	30m	832	34.7	102.1	120.42	585.43	176.99	0.31
ETHUSDT	1h	825	36.2	267.7	642.11	1,412.68	232.83	0.87
ETHUSDT	4h	833.2	41	341.1	1,212.74	1,456.59	147.14	1.09
ETHUSDT	1d	779.2	36.2	255.2	325.39	335.97	7.09	0.65
SOLUSDT	30m	15,210.4	34.4	415.8	881.67	4,325.88	1,045.63	0.86
SOLUSDT	1h	15,289	34.4	532.9	2,879.23	6,336.97	553.05	1.1
SOLUSDT	4h	15,463.4	37.9	565.4	4,551.26	5,510.32	490.21	1.21
SOLUSDT	1d	15,594.7	47.2	982.6	14,521.66	14,946.01	206.45	1.43
BNBUSDT	30m	5,780.4	34.4	133.4	185.64	924.79	330.07	0.46
BNBUSDT	1h	5,761.4	38.4	503.5	5,991.2	12,925.08	1,839.69	1.57
BNBUSDT	4h	5,540.5	36.6	342.5	1,230.39	1,510.66	172.52	1.09
BNBUSDT	1d	5,641.4	39	536	1,380.82	1,424.01	29.06	1.08
DOGEUSDT	30m	15,851.6	32.3	251	25.72	136.73	157.9	0.28
DOGEUSDT	1h	15,731.9	33.2	1,216.9	22,080.37	48,772.59	9,211.1	1.08
DOGEUSDT	4h	15,847.8	36.4	826.5	10,949.27	13,331	1,495.88	0.99
DOGEUSDT	1d	13,838.4	47.1	704	3,972.62	4,085.44	70.47	0.91
XRPUSDT	30m	633.8	30.9	-134	5.54	29.06	72.89	-0.34
XRPUSDT	1h	632.2	32	399.7	1,037.6	2,345.72	620.42	0.88
XRPUSDT	4h	638	31.3	325.9	254.8	310.97	86.54	0.56
XRPUSDT	1d	616.4	31.9	797	1,790.59	1,840.7	27.95	1.01
ALL	30m	6,774.7	37.9	889.4	141,597.33	661,917.92	40,226.37	1.94
ALL	1h	6,762.7	38.6	846	59,637.8	127,940.59	11,785.63	1.77
ALL	4h	6,778.6	37.8	450.1	2,284.36	2,775.71	263.8	0.91
ALL	1d	6,468.5	41.6	528.2	2,070.34	2,135.1	50.02	0.91

summary_charts(summary=resampled_summary)

Scoring

This section grades the strategy on a 0–100 scale. Every metric is mapped to a score in each symbol × timeframe cell, the per-metric scores are blended into a composite cell score, and the composites average into a single overall strategy score. The scales are fixed, so the same number means the same thing from one study to the next and the grades compare like for like.

• Beats-Hold — how far net equity runs ahead of buy-and-hold, $50 + 25\log_2(E_{\text{net}}/E_{\text{hold}})$: matching buy-and-hold scores 50, doubling it 75, halving it 25.
• Risk-Adjusted — the Rolling Sharpe on a fixed scale, $55\,S + 5$: a Sharpe of 1 scores 60, of roughly 1.7 reaches 100.
• Profitability — absolute growth of capital, $20\log_2(E_{\text{net}}/E_0)$: a 2× ending scores 20, a 32× scores 100.
• Win-Rate — the share of winning trades, $2.5\,(w - 20)$ for a win rate $w$ in percent: 40% scores 50, 60% scores 100.
• Fee-Efficiency — how little trading costs erode the result, $(E_{\text{net}}/E_{\text{gross}} - 0.4)/0.6 \times 100$: paying nothing scores 100, losing a third to fees scores about 50.
• Composite — the weighted blend, $0.35\,\text{Beats-Hold} + 0.30\,\text{Risk-Adjusted} + 0.15\,\text{Profitability} + 0.10\,\text{Win-Rate} + 0.10\,\text{Fee-Efficiency}$.
• Overall Score — the average composite across all cells: the strategy's single headline grade.

SCORE_WEIGHTS = {
    "Beats-Hold": 0.35,
    "Risk-Adjusted": 0.30,
    "Profitability": 0.15,
    "Win-Rate": 0.10,
    "Fee-Efficiency": 0.10,
}


def clamp_score(value):
    return float(max(0.0, min(100.0, value)))


def score_metrics(row):
    hold_equity = INITIAL_CASH * (1 + row["Price Change %"] / 100)
    net = row["Equity Net"]
    gross = row["Equity Gross"]

    if net > 0 and hold_equity > 0:
        beats_hold = clamp_score(50 + 25 * np.log2(net / hold_equity))
    else:
        beats_hold = 0.0
    risk_adjusted = clamp_score(55 * row["Rolling Sharpe"] + 5)
    multiple = net / INITIAL_CASH
    profitability = clamp_score(20 * np.log2(multiple)) if multiple > 0 else 0.0
    win_rate = clamp_score(2.5 * (row["Cumulative Win Rate %"] - 20))
    fee_efficiency = clamp_score((net / gross - 0.4) / 0.6 * 100) if gross > 0 else 0.0

    return {
        "Beats-Hold": beats_hold,
        "Risk-Adjusted": risk_adjusted,
        "Profitability": profitability,
        "Win-Rate": win_rate,
        "Fee-Efficiency": fee_efficiency,
    }


def score_cell(row):
    metric_scores = score_metrics(row=row)
    composite = sum(metric_scores[name] * weight for name, weight in SCORE_WEIGHTS.items())
    return composite, metric_scores


def strategy_score(summary):
    rows = []
    for _, row in summary.iterrows():
        composite, metric_scores = score_cell(row=row)
        entry = {"Symbol": row["Symbol"], "Timeframe": row["Timeframe"]}
        entry.update({name: round(value, 1) for name, value in metric_scores.items()})
        entry["Composite"] = round(composite, 1)
        rows.append(entry)
    score_table = pd.DataFrame(rows)
    overall = int(round(score_table["Composite"].mean()))
    return overall, score_table


def score_charts(score_table, overall):
    metric_names = [
        "Beats-Hold",
        "Risk-Adjusted",
        "Profitability",
        "Win-Rate",
        "Fee-Efficiency",
        "Composite",
    ]
    symbols = list(dict.fromkeys(score_table["Symbol"]))
    n_cols = 3
    n_rows = 2

    col_width = 600
    row_height = 300
    gap_px = 70
    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
    v_spacing = gap_px / total_h

    colorscale = [[0.0, "#eef0f2"], [0.5, "#bfe3d3"], [1.0, "#1d9e75"]]

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

    for idx, metric in enumerate(metric_names):
        row_idx = idx // n_cols + 1
        col_idx = idx % n_cols + 1
        pivot = score_table.pivot(index="Symbol", columns="Timeframe", values=metric)
        pivot = pivot.reindex(index=symbols, columns=TIMEFRAMES)
        values = pivot.to_numpy()
        fig.add_trace(
            go.Heatmap(
                z=values,
                x=TIMEFRAMES,
                y=symbols,
                zmin=0,
                zmax=100,
                colorscale=colorscale,
                showscale=False,
                text=values,
                texttemplate="%{text:.0f}",
                textfont=dict(size=11),
                hovertemplate="%{y} · %{x}: %{z:.0f}<extra></extra>",
                xgap=2,
                ygap=2,
            ),
            row=row_idx,
            col=col_idx,
        )

    fig.update_layout(
        template="plotly_white",
        height=total_h,
        width=total_w,
        font=dict(size=11),
        title=dict(text=f"Overall strategy score: {overall} / 100", x=0.5, font=dict(size=17)),
        margin=dict(l=90, r=20, t=100, b=40),
    )
    fig.update_annotations(font=dict(size=13))
    fig.update_yaxes(autorange="reversed")
    fig.show()

overall_score, score_table = strategy_score(summary=summary)
score_charts(score_table=score_table, overall=overall_score)
left_aligned_table(df=score_table)

Symbol	Timeframe	Beats-Hold	Risk-Adjusted	Profitability	Win-Rate	Fee-Efficiency	Composite
BTCUSDT	30m	0	0	0	28.8	0	2.9
BTCUSDT	1h	0	31.9	30.4	37.5	0	17.9
BTCUSDT	4h	41.1	49.6	69.4	45.2	58.3	50
BTCUSDT	1d	69.2	61.6	92.3	49.5	92.6	70.8
ETHUSDT	30m	0	3.9	0	35.5	0	4.7
ETHUSDT	1h	100	60	100	40	0	72
ETHUSDT	4h	80.8	47.4	72.7	45	57.8	63.7
ETHUSDT	1d	78.1	47.4	71.1	41	92.3	65.6
SOLUSDT	30m	0	19.9	0	34.8	0	9.4
SOLUSDT	1h	25.1	53.4	69.1	39.8	10.3	40.2
SOLUSDT	4h	4.4	47.4	52.8	38	70.1	34.5
SOLUSDT	1d	69.9	67.7	100	46.8	95.1	74
BNBUSDT	30m	0	15.4	0	35.5	0	8.2
BNBUSDT	1h	49.1	75.4	100	43	0	59.1
BNBUSDT	4h	46.4	73.8	100	43	58.2	63.5
BNBUSDT	1d	25.8	68.8	100	62.2	93	60.2
DOGEUSDT	30m	0	0	0	26.8	0	2.7
DOGEUSDT	1h	55.1	50.6	92.5	32.8	0	51.6
DOGEUSDT	4h	77.3	55.1	100	34.5	65	68.5
DOGEUSDT	1d	66.2	56.7	100	46.5	94.6	69.3
XRPUSDT	30m	0	0	0	27.5	0	2.8
XRPUSDT	1h	95.2	36.9	42	30.7	0	53.8
XRPUSDT	4h	66.8	29.8	19.5	28	59	43.9
XRPUSDT	1d	100	51.8	87.1	40.2	93.7	77
ALL	30m	100	100	100	45.5	0	84.5
ALL	1h	100	100	100	53.5	11.9	86.5
ALL	4h	59	53.4	84	44	70.8	60.7
ALL	1d	27.2	52.9	58.6	53.2	95.1	49

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, going long when the MACD line crosses above its signal and flat when it crosses back is profitable after fees in 22 of 28 symbol × timeframe cells. The five losses are all single markets on the 30-minute timeframe — BTC ends at 4 on 100, DOGE at essentially zero, ETH at 19, SOL at 49, BNB at 46 — where the crossover fires ~6,000 times and fees plus whipsaw eat the result. Every cell at 1h and slower is profitable.

Risk-adjusted, the edge builds with the timeframe. Rolling Sharpe climbs across each symbol's row — BTC −0.51 / 0.49 / 0.81 / 1.03 from 30m to 1d — and the slow single-market cells settle at a steady 0.8–1.2. The fastest cells either lose outright or earn thin returns through heavy turnover.

The basket is the strongest market. ALL compounds 100 into 234,036 at 1h (Rolling Sharpe 2.26) and 104,755 at 30m (2.07), far ahead of any single market at those speeds. Averaging the five symbols cancels their idiosyncratic noise, so a crossover on the smoothed basket marks a shared shift in trend rather than one market's flutter — and the rule feeds on exactly that. The two fast basket cells do lean on all-in compounding, so read their six-figure totals as the least literal numbers in the table.

Versus buy-and-hold it wins 14 of 28 cells, and the wins have structure — the entire ETH row beyond 30m, the entire DOGE row beyond 30m, three of four basket cells, plus SOL and BTC at the daily. It loses where one market's own drift was unbeatable: BNB rose ~348× and the rule trails holding in all four BNB cells despite compounding 100 into 34,138 at 1h.

On resampled history the edge repeats — 25 of 28 cells profitable. Replayed in a new order, the market's own behavior carries the rule: the Rolling Sharpe ladder returns (negative-to-flat at 30m, 0.9–1.6 by 1h–4h), the basket at 30m again reaches six figures (141,397 at Sharpe 1.94), and it still beats buy-and-hold in 5 cells. Performance this durable on a history the rule has never seen means it rides momentum structure, not one memorized chronology.

Fees are the binding cost at speed. The gross-to-net gap is wide intraday — BNB at 1h pays 22,335 in Cumulative Fees against a 108,521 gross result (about a fifth), ETH at 1h pays 3,053 against 12,641 — and nearly vanishes by the daily (BTC 1d pays 59 over 113 trades). Cumulative Win Rate % sits at 30–45% throughout, the trend-following shape where a few large winners carry many small losers; the signal smoothing keeps the loser count far below a raw price-versus-average cross, which is why 19 cells survive rather than collapsing at 30m.

Caveats. Results come from one historical window with the standard (12, 26, 9) parameters; the basket is five liquid survivors (and ALL inherits that survivorship); the strategy is long-only over a window in which every symbol rose; the resampled run is a single draw — one alternative history — not a distribution; the large terminal figures come from compounding all-in over roughly a decade; and prices are spot klines while the fee rate models the futures taker rate.

Call: pursue. The signal-line crossover is broadly profitable after fees, strengthens under risk adjustment as the timeframe slows, beats buy-and-hold across a structured set of cells, and repeats on a resampled history that stands in for the future — the signature of a real trend edge. Its smoothing keeps the whipsaw count low enough to survive where a bare price-versus-average cross would not. The credible engine is the 1h through 1d cells and the basket; the 30-minute single-market cells are fee-and-whipsaw losses to exclude. Worth carrying forward with explicit position sizing and a parameter-robustness sweep before any further claim.

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