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Enter Long When WMA 20 Crosses Above WMA 50, Exit When It Crosses Back Down

A trend-following crossover on a single market's close: ride the move while the fast weighted moving average sits above the slow one, 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.

---

• 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

WMA_FAST_PERIOD = 20
WMA_SLOW_PERIOD = 50

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 tracks two weighted moving averages of the close — a fast one over 20 bars and a slow one over 50. The weighted average leans on recent bars, so it turns sooner than a simple average. A long position opens the moment the fast average crosses above the slow, and closes when it crosses back below:

$$\text{open at } t \iff \mathrm{WMA}_{20}(t-1) \le \mathrm{WMA}_{50}(t-1) \;\land\; \mathrm{WMA}_{20}(t) > \mathrm{WMA}_{50}(t).$$

It is long-only and always fully in or fully out — a bet that crossovers mark the start of sustained trends worth riding until momentum fades.

def strategy(prices, fast, slow):
    wma = {
        "fast": talib.WMA(prices, timeperiod=fast),
        "slow": talib.WMA(prices, timeperiod=slow),
    }
    above = (wma["fast"] > wma["slow"]).astype(np.int8)
    change = np.diff(above)
    opens = np.where(change == 1)[0] + 1
    closes = np.where(change == -1)[0] + 1
    return wma, opens, closes

An illustrative example on a synthetic price path, drawn as candles around its closes, so the crossover entries (green) and exits (red) can be read against the two averages.

rng = np.random.default_rng(0)
example_prices = 100 * np.cumprod(1 + rng.normal(0, 0.01, size=300))
example_wma, example_opens, example_closes = strategy(
    prices=example_prices,
    fast=WMA_FAST_PERIOD,
    slow=WMA_SLOW_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 = go.Figure()
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"),
    )
)
fig.add_trace(
    go.Scatter(
        y=example_wma["fast"], mode="lines", name="WMA 20", line=dict(color="#00d4aa", width=1)
    )
)
fig.add_trace(
    go.Scatter(
        y=example_wma["slow"], mode="lines", name="WMA 50", line=dict(color="#1f77b4", width=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"),
    )
)
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"),
    )
)
fig.update_layout(
    template="plotly_white",
    height=400,
    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.
• Moving Averages — the fast and slow weighted moving averages (WMA 20 and WMA 50) from which the signals are derived.
• 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):
    wma, opens, closes = strategy(prices=prices, fast=WMA_FAST_PERIOD, slow=WMA_SLOW_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
    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,
        "wma": wma,
        "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	33.3	443.9	3,074.28	7,219.28	1,459.49	1.02
BTCUSDT	1h	1,331.8	32.7	433.1	2,640.05	4,048.88	762.62	0.97
BTCUSDT	4h	1,318	33.7	411	1,207.84	1,335.95	72.67	0.66
BTCUSDT	1d	1,339.4	42.1	807.9	4,484.4	4,553.09	30.3	0.61
ETHUSDT	30m	444.3	34.2	689.4	21,327.18	49,623.61	7,909.46	1.28
ETHUSDT	1h	440.1	35.2	496	2,894.81	4,459.17	907.4	0.89
ETHUSDT	4h	429.1	31.4	523.7	2,189.66	2,433.57	138.37	0.76
ETHUSDT	1d	439.5	44.7	682.7	5,363.83	5,445.99	36.14	0.68
SOLUSDT	30m	1,957.1	35.5	580.3	5,508.56	9,404.2	1,836.68	1.22
SOLUSDT	1h	2,086.3	35.5	485.4	1,919.54	2,552.1	497.31	0.97
SOLUSDT	4h	2,107.4	36.5	830.9	9,310.91	9,954.19	411.83	1
SOLUSDT	1d	1,856.3	41.7	1,984.8	7,129.68	7,198.47	44.36	0.59
BNBUSDT	30m	34,845.9	36.3	1,044	178,940.58	404,210.3	78,878.15	1.25
BNBUSDT	1h	34,877.6	35.5	774.4	14,784.28	22,439.13	2,788.2	0.96
BNBUSDT	4h	34,864.7	41.8	1,024.5	26,660.94	29,394.55	1,274.26	0.68
BNBUSDT	1d	37,733.2	41	1,853.9	27,622.39	28,056.72	262.24	0.52
DOGEUSDT	30m	2,106.6	32.1	1,122.9	30,851.88	59,672.05	9,172.02	0.85
DOGEUSDT	1h	2,041.5	29.4	783.8	2,252.74	3,163.83	651.18	0.72
DOGEUSDT	4h	2,148.9	30.9	1,435.9	56,259.13	60,799.16	2,356.44	0.8
DOGEUSDT	1d	2,071.8	38.7	2,389.4	5,581.17	5,650.82	50.95	0.49
XRPUSDT	30m	23	30.3	469.5	1,245.37	2,743.17	346.59	0.73
XRPUSDT	1h	22.4	29.2	396.7	493.24	740.58	124.83	0.56
XRPUSDT	4h	23.4	30.7	682.2	999.13	1,104.66	61.82	0.54
XRPUSDT	1d	27	28.2	221.7	105.92	107.59	1.04	0.25
ALL	30m	1,305.8	36.8	657.6	19,163.9	32,847.71	4,518.45	1.55
ALL	1h	1,330.2	36.4	473.8	2,260.65	2,986.44	467.61	0.95
ALL	4h	1,333.9	37.2	617.2	4,836.4	5,164.34	193.43	0.93
ALL	1d	1,332.9	37.5	2,312.6	5,431.69	5,484.09	34.95	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	34.4	300.3	1,203.73	2,156.92	331.1	1.2
BTCUSDT	1h	2,336.9	33.5	240.3	687.7	913.59	112.65	0.99
BTCUSDT	4h	2,348.9	35	354	1,497.41	1,596.38	43.27	1.03
BTCUSDT	1d	2,340.7	45.5	657.6	4,303.6	4,341.65	16.14	0.85
ETHUSDT	30m	832	32.1	400.9	2,225.25	3,908.39	592.17	1.19
ETHUSDT	1h	825	35.3	302.9	828.18	1,101.98	202.75	0.88
ETHUSDT	4h	833.2	32	299.7	719.4	769.72	28.58	0.8
ETHUSDT	1d	779.2	54.2	801.3	4,928.55	4,976.1	21.53	0.66
SOLUSDT	30m	15,210.4	37	599.1	7,423.06	12,769.33	1,337.39	1.3
SOLUSDT	1h	15,289	33.5	490.5	1,761.94	2,344.44	291.47	0.95
SOLUSDT	4h	15,463.4	38.4	1,044.7	46,303.9	49,344.8	938.37	1.17
SOLUSDT	1d	15,594.7	59.1	2,610.1	88,924.45	89,710.52	338.92	0.69
BNBUSDT	30m	5,780.4	36.8	529.9	5,710.5	9,985.78	1,465.1	1.19
BNBUSDT	1h	5,761.4	34.9	429.8	2,293.46	3,040.71	342.79	1.03
BNBUSDT	4h	5,540.5	36.2	690.2	3,214.27	3,430.85	110.12	0.65
BNBUSDT	1d	5,641.4	46.4	1,815.5	5,819.3	5,884.85	47.58	0.47
DOGEUSDT	30m	15,851.6	33.7	1,475.8	213,907.99	365,183.32	44,330.34	0.97
DOGEUSDT	1h	15,731.9	32.5	683	3,970.94	5,271.05	899.46	0.91
DOGEUSDT	4h	15,847.8	33.5	1,056.9	34,356.48	36,642.07	1,187.44	1.02
DOGEUSDT	1d	13,838.4	43.5	12,030.4	105,986.88	106,966.56	457.28	0.45
XRPUSDT	30m	633.8	31.1	544.8	2,645.9	4,667.71	873.39	0.96
XRPUSDT	1h	632.2	34.2	583.8	3,340.6	4,439.67	951.82	0.94
XRPUSDT	4h	638	29.4	747.5	1,583.66	1,690.37	75.92	0.67
XRPUSDT	1d	616.4	36	626.7	1,385.5	1,399.42	11.94	0.64
ALL	30m	6,774.7	35.9	854.3	49,196.06	84,459.11	10,751.18	1.26
ALL	1h	6,762.7	35.2	345.1	922.42	1,229.82	281.33	0.84
ALL	4h	6,778.6	34.5	757.5	8,738.01	9,356.67	266.99	0.9
ALL	1d	6,468.5	63.2	3,547	60,555.83	61,017.86	201.7	0.5

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	77.2	61.1	98.8	33.2	4.3	63.9
BTCUSDT	1h	72.1	58.4	94.4	31.8	42	64.3
BTCUSDT	4h	44.2	41.3	71.9	34.3	84	50.5
BTCUSDT	1d	91	38.5	100	55.2	97.5	73.7
ETHUSDT	30m	100	75.4	100	35.5	5	76.7
ETHUSDT	1h	100	54	97.1	38	41.5	73.7
ETHUSDT	4h	100	46.8	89.1	28.5	83.3	73.6
ETHUSDT	1d	100	42.4	100	61.8	97.5	78.6
SOLUSDT	30m	85.5	72.1	100	38.8	31	73.5
SOLUSDT	1h	45.3	58.4	85.3	38.8	58.7	55.9
SOLUSDT	4h	100	60	100	41.2	89.2	81
SOLUSDT	1d	96.6	37.4	100	54.3	98.4	75.3
BNBUSDT	30m	100	73.8	100	40.7	7.1	76.9
BNBUSDT	1h	18.9	57.8	100	38.8	43.1	47.2
BNBUSDT	4h	40.2	42.4	100	54.5	84.5	55.7
BNBUSDT	1d	38.7	33.6	100	52.5	97.4	53.6
DOGEUSDT	30m	100	51.8	100	30.3	19.5	70.5
DOGEUSDT	1h	51.8	44.6	89.9	23.5	52	52.6
DOGEUSDT	4h	100	49	100	27.2	87.6	76.2
DOGEUSDT	1d	84	31.9	100	46.8	97.9	68.5
XRPUSDT	30m	100	45.1	72.8	25.8	9	62.9
XRPUSDT	1h	100	35.8	46	23	44.3	59.4
XRPUSDT	4h	100	34.7	66.4	26.8	84.1	66.5
XRPUSDT	1d	43.5	18.8	1.7	20.5	97.4	32.9
ALL	30m	100	90.2	100	42	30.6	84.3
ALL	1h	66.5	57.2	90	41	59.5	64
ALL	4h	93.8	56.2	100	43	89.4	77.9
ALL	1d	98.1	29.8	100	43.8	98.4	72.5

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 (roughly eight years for BTC and ETH, less for the others), the long-only WMA 20/50 crossover is profitable after fees in all 28 symbol × timeframe cells — every Cumulative P&L % is positive and every Equity Net ends above its starting capital.

Risk-adjusted, the edge is strongest on the 30-minute timeframe. Rolling Sharpe at 30m spans 0.85–1.52 and weakens toward the daily (0.45–0.68). The single best cell in the table is the basket: ALL at 30m reaches a Rolling Sharpe of 1.52, ahead of every individual market (ETH 1.28, BNB 1.25, SOL 1.22) — averaging the symbols smooths the series, so the crossover whipsaws less. The pattern holds across the whole basket rather than resting on one cell.

Versus buy-and-hold it wins 22 of 28 cells. Compounding the same starting capital, Equity Net ends above the buy-and-hold result implied by Price Change % in every cell at 30m and in all four ALL cells, but loses where holding the strongest trends was unbeatable — BNB on 1h, 4h and 1d, BTC at 4h, and SOL at 1h.

On resampled history the edge repeats. With the market's own behavior replayed in a new order, the profile survives: every cell stays profitable, Rolling Sharpe keeps the same ladder (0.97–1.30 at 30m, fading to 0.45–0.85 at the daily), the basket holds up at 30m (1.23 against 1.52 on real prices), and the rule still beats buy-and-hold in 16 of 28 cells. The strategy is reading the market's behavior, not one memorized chronology.

Fees are the dominant cost at speed. At 30m the gap between Equity Gross and Equity Net shows fees consuming roughly half of the gross result (BTC 7,219 gross vs 3,074 net; BNB 404,210 vs 178,941), while at the daily they are nearly negligible (BTC 4,553 vs 4,484). Cumulative Win Rate % is low everywhere (29–45%) — the classic trend-following shape, where a few large winners pay for many small losers.

Caveats. Results come from one historical window with fixed (20, 50) parameters; the basket is five liquid survivors, so survivorship flatters the absolute figures (and ALL inherits it); 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; and prices are spot klines while the fee rate models the futures taker rate.

Call: pursue. As a long-only trend system on majors it is broadly profitable with solid 30-minute risk-adjusted returns, strongest on the smoothed basket, the edge repeats on a resampled history the rule has never seen. The remaining risks are the ones the caveats name — a favourable window and a survivor basket — so size positions accordingly.

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