Study 70 Digital-Gold: bitcoin is a high-beta risk asset, not digital gold (None/Fragile)

Author: Guillain-RDCDE

README.md

@@ -122,6 +122,7 @@ teaching are in **[What 60 teardowns taught us](docs/bench.md)**.
 | **[67](studies/67-fed-drift/)** | **Fed-Drift** | Do stocks drift up before FOMC meetings (Lucca-Moench)? They *did*, hugely: 3% of sessions (the pre-FOMC days) earned 11.5% of SPY's whole cumulative return since 1993 — 19.8% pre-2011. Then publication killed it: the pre-FOMC day decayed from +0.24%/day (t 1.7) to +0.09% (t 0.4) after 2011. A real giant, arbitraged away in plain sight. | ![Real](https://img.shields.io/badge/Real-2ea44f?style=flat-square) | ![Fragile](https://img.shields.io/badge/Fragile-dab617?style=flat-square) |
 | **[68](studies/68-all-weather/)** | **All-Weather** | Does Dalio's risk-parity portfolio beat everything? It *diversifies* for real — unlevered on SPY/IEF/GLD/DBC it earned the best Sharpe (0.92 vs 0.81 for 60/40, 0.65 for SPY) and a drawdown a third of equities' (−17% vs −55%). But it returned only +6.7%/yr, ~half of SPY: the edge is risk-adjusted, and closing the gap needs leverage + the bond bull that 2022 ended. | ![Real](https://img.shields.io/badge/Real-2ea44f?style=flat-square) | ![Investable](https://img.shields.io/badge/Investable-2ea44f?style=flat-square) |
 | **[69](studies/69-safe-haven/)** | **Safe-Haven** | Does gold hedge inflation and crashes? As an inflation hedge: no — YoY gold vs YoY CPI correlate just +0.09, and gold earned the same in high-inflation months (+10.6%) as low (+10.2%). As a crisis hedge: only half-true — flat in equity crashes (−0.2% vs SPY −10%) and uncorrelated, but up in just 50% of them. A real diversifier, oversold as inflation insurance. | ![None](https://img.shields.io/badge/None-c0392b?style=flat-square) | ![Fragile](https://img.shields.io/badge/Fragile-dab617?style=flat-square) |
+| **[70](studies/70-digital-gold/)** | **Digital-Gold** | Is bitcoin "digital gold"? No: it's ~uncorrelated with gold (+0.09), its correlation with stocks has *risen* (+0.13→+0.36), and in equity crashes it fell harder than stocks (−18% vs −10%), up in 0% of them — the opposite of a haven. It was a phenomenal risk asset (+64%/yr, −83% drawdown), so a small sleeve lifted Sharpe — but as a leveraged growth bet, not a store of value. | ![None](https://img.shields.io/badge/None-c0392b?style=flat-square) | ![Fragile](https://img.shields.io/badge/Fragile-dab617?style=flat-square) |
 
 > **Click any study** for the full teardown — two narrative notebooks (one for the curious,
 > one for the quant), reproducible code, and every number behind the two stamps.

studies/70-digital-gold/README.md

@@ -0,0 +1,32 @@
+# Study 70 — Digital-Gold ₿
+
+[![tests](https://github.com/Guillain-RDCDE/Open-Alpha-Lab/actions/workflows/tests.yml/badge.svg)](https://github.com/Guillain-RDCDE/Open-Alpha-Lab/actions/workflows/tests.yml)
+
+> *Part of [Open-Alpha-Lab](../../README.md) — see the [desk](../../README.md) and its [house style](../../METHODOLOGY.md).*
+
+## Verdict
+
+| Axis | Stamp | Why |
+|---|---|---|
+| **Signal** — is bitcoin a gold-like store of value / haven? | ![None](https://img.shields.io/badge/None-c0392b?style=flat-square) | No: ~uncorrelated with gold (**+0.09**), correlation with stocks **rising +0.13→+0.36**, and in equity crashes it fell **harder than stocks (−18% vs −10%)**, up in **0%** of them. |
+| **Tradability** — did a small sleeve help a portfolio? | ![Fragile](https://img.shields.io/badge/Fragile-dab617?style=flat-square) | Yes historically (5% BTC: Sharpe 0.82→0.95) — but purely on a **+64%/yr, −83%-drawdown** trend. A leveraged return bet, not a hedge. |
+| **"Bitcoin is digital gold"?** | ![Not supported](https://img.shields.io/badge/Not_supported-8b949e?style=flat-square) | It's a high-beta risk asset, the opposite of a haven when it matters. |
+
+> **In one sentence:** bitcoin isn't digital gold — it's near-uncorrelated with gold, increasingly correlated with stocks, and in crashes it falls *harder* than equities and never rallies; it's been a spectacular high-beta *return* asset (so a small sleeve flattered Sharpe), but that's a drawdown-heavy growth bet, not the safe-haven store of value it's sold as.
+
+## What we tested
+
+The **"digital gold" thesis**: that bitcoin is a gold-like store of value and crisis hedge. We test it on daily **BTC-USD / SPY / GLD**, 2014–2026 — BTC's correlation with gold and with stocks (and how that correlation has *drifted*), its return in equity-crash months (does it hold/rise like a haven, or fall like a risk asset?), and the effect of adding a small BTC sleeve to a stock portfolio. The offline control is a synthetic world where the bitcoin-like asset either loads on the stock factor (a risk asset) or stays uncorrelated (a true digital gold).
+
+## The full teardown lives in the notebooks
+
+| | For whom | Inside |
+|---|---|---|
+| **[01_for_the_curious](notebooks/01_for_the_curious.ipynb)** | the curious | why a thing that crashes with stocks isn't gold — and what the sleeve really is |
+| **[02_for_the_quants](notebooks/02_for_the_quants.ipynb)** | quants | the correlations & their drift, the crash-month behaviour, the sleeve overlay |
+
+The fingerprinted real-data run (BTC/SPY/GLD, 2014–2026, fp `6e2e2a7c7c98`) is in [docs/results.md](docs/results.md). Reproduce via [examples/verify.py](examples/verify.py) (reads the BTC/SPY/GLD pull); the offline machinery proof runs on the synthetic world in [digital_gold/data.py](digital_gold/data.py).
+
+---
+
+*Sources & literature map: [docs/references.md](docs/references.md). Engine: [`quantlab/`](../../quantlab/). **Not investment advice** — research & education. See [LICENSE](../../LICENSE).*

studies/70-digital-gold/digital_gold/__init__.py

@@ -0,0 +1,9 @@
+"""Study 70 — Digital-Gold: is bitcoin a gold-like store of value, or a high-beta risk asset?
+
+The "digital gold" thesis fails the data (2014–2026). BTC is ~uncorrelated with gold (0.09), but its
+correlation with stocks has *risen* (0.13 → 0.36) and in equity-crash months it fell harder than stocks
+(−18% vs SPY −10%), rising in 0% of them — the opposite of a safe haven. It *was* a phenomenal return
+asset (+64%/yr, but −83% drawdown), so a small sleeve historically lifted a portfolio's Sharpe — but as
+a leveraged bet, not as digital gold.
+"""
+from . import data, strategy  # noqa: F401

studies/70-digital-gold/digital_gold/data.py

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+"""Data for the bitcoin "digital gold" study — an offline synthetic world, and the cached BTC / SPY /
+GLD daily panel."""
+from __future__ import annotations
+import os
+from dataclasses import dataclass
+import numpy as np, pandas as pd
+
+_HERE = os.path.dirname(os.path.abspath(__file__))
+REPO_ROOT = os.path.abspath(os.path.join(_HERE, "..", "..", ".."))
+DEFAULT_CACHE = os.path.join(REPO_ROOT, "_cache")
+ASSETS = ["BTC-USD", "SPY", "GLD"]
+
+
+@dataclass(frozen=True)
+class WorldTruth:
+    btc_stock_beta: float
+
+    @property
+    def is_risk_asset(self) -> bool:
+        return self.btc_stock_beta > 0.0
+
+
+def synthetic_world(n_days=3000, btc_stock_beta=1.5, seed=70):
+    """A daily world with stocks, gold and a bitcoin-like asset. Gold is ~uncorrelated with stocks; BTC
+    loads on the stock factor with ``btc_stock_beta`` (and its own high vol). ``btc_stock_beta>0`` ⇒ BTC
+    behaves like a (high-beta) risk asset that falls *with* stocks; ``=0`` ⇒ a true uncorrelated haven."""
+    rng = np.random.default_rng(seed)
+    idx = pd.bdate_range("2014-09-18", periods=n_days, name="date")
+    eq_shock = rng.standard_normal(n_days)
+    spy = 0.0005 + 0.011 * eq_shock
+    gld = 0.0003 + 0.010 * rng.standard_normal(n_days)                      # ~independent of stocks
+    btc = 0.001 + btc_stock_beta * 0.011 * eq_shock + 0.012 * rng.standard_normal(n_days)
+    df = pd.DataFrame({"BTC-USD": btc, "SPY": spy, "GLD": gld}, index=idx)
+    return df, WorldTruth(btc_stock_beta)
+
+
+def fetch_panel(cache_dir=DEFAULT_CACHE, fetch=False):
+    """Daily returns for BTC-USD / SPY / GLD, cache-first (from the ``digital_gold_panel`` pull)."""
+    cache = os.path.join(cache_dir, "digital_gold_panel.parquet")
+    if os.path.exists(cache):
+        px = pd.read_parquet(cache)[ASSETS].dropna()
+        px.index = pd.DatetimeIndex(px.index).tz_localize(None)
+        ret = px.pct_change().dropna(); ret.index.name = "date"
+        return ret
+    if not fetch:
+        return pd.DataFrame()
+    import yfinance as yf
+    px = yf.download(ASSETS, period="max", auto_adjust=True, progress=False)["Close"][ASSETS].dropna()
+    px.index = pd.DatetimeIndex(px.index).tz_localize(None)
+    os.makedirs(cache_dir, exist_ok=True)
+    px.to_parquet(cache)
+    ret = px.pct_change().dropna(); ret.index.name = "date"
+    return ret

studies/70-digital-gold/digital_gold/strategy.py

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+"""Is bitcoin "digital gold"? Test the thesis that BTC is a gold-like store of value / safe haven: its
+correlation with gold and with stocks (and how that correlation has drifted), its behaviour in equity
+crashes, and whether a small BTC sleeve helped a portfolio. The alternative hypothesis: BTC is just a
+high-beta risk asset that falls harder than stocks when it matters.
+"""
+from __future__ import annotations
+import numpy as np, pandas as pd
+
+TRADING_DAYS = 252
+
+
+def annualized(ret: pd.Series) -> dict:
+    r = pd.Series(ret).astype(float).dropna()
+    if len(r) < 2:
+        return {k: np.nan for k in ("ann", "vol", "sharpe", "max_drawdown", "n")}
+    ann, vol = r.mean() * TRADING_DAYS, r.std(ddof=1) * np.sqrt(TRADING_DAYS)
+    eq = (1.0 + r).cumprod(); dd = (eq / eq.cummax() - 1.0).min()
+    return {"ann": float(ann), "vol": float(vol), "sharpe": float(ann / vol) if vol > 0 else np.nan,
+            "max_drawdown": float(dd), "n": int(len(r))}
+
+
+def correlations(ret: pd.DataFrame, btc="BTC-USD", eq="SPY", gold="GLD") -> dict:
+    """BTC's correlation with stocks and gold, plus first-half vs second-half BTC–stock correlation to
+    show whether it's drifting toward (or away from) being a risk asset."""
+    half = len(ret) // 2
+    return {"btc_stock": float(ret[btc].corr(ret[eq])), "btc_gold": float(ret[btc].corr(ret[gold])),
+            "stock_gold": float(ret[eq].corr(ret[gold])),
+            "btc_stock_first": float(ret[btc].iloc[:half].corr(ret[eq].iloc[:half])),
+            "btc_stock_second": float(ret[btc].iloc[half:].corr(ret[eq].iloc[half:]))}
+
+
+def crisis_behavior(monthly: pd.DataFrame, crash: float = -0.08, btc="BTC-USD", eq="SPY", gold="GLD") -> dict:
+    """In equity-crash months (stock monthly return < ``crash``): mean BTC / gold / stock return and the
+    share of crashes where BTC rose. A 'digital gold' would hold or rise; a risk asset falls harder."""
+    cr = monthly[monthly[eq] < crash]
+    return {"btc_in_crash": float(cr[btc].mean()), "gold_in_crash": float(cr[gold].mean()),
+            "eq_in_crash": float(cr[eq].mean()),
+            "btc_up_share": float((cr[btc] > 0).mean()) if len(cr) else np.nan,
+            "gold_up_share": float((cr[gold] > 0).mean()) if len(cr) else np.nan, "n_crash": int(len(cr))}
+
+
+def sleeve_effect(eq_ret: pd.Series, btc_ret: pd.Series, weights=(0.0, 0.05, 0.10)) -> pd.DataFrame:
+    """Stats for a stock portfolio with a small BTC sleeve rebalanced daily — does a little BTC help, and
+    at what drawdown cost?"""
+    df = pd.concat([eq_ret.rename("eq"), btc_ret.rename("btc")], axis=1).dropna()
+    rows = {}
+    for w in weights:
+        port = (1.0 - w) * df["eq"] + w * df["btc"]
+        rows[f"{int(w*100)}% BTC"] = annualized(port)
+    return pd.DataFrame(rows).T

studies/70-digital-gold/docs/references.md

@@ -0,0 +1,28 @@
+# References & literature map — Study 70 (Digital-Gold)
+
+## The thesis and the evidence
+
+- **Baur, D., Hong, K., & Lee, A. (2018).** *Bitcoin: Medium of Exchange or Speculative Assets?* Journal
+  of International Financial Markets — bitcoin behaves as a speculative asset, not a currency or gold
+  substitute.
+- **Smales, L. (2019).** *Bitcoin as a Safe Haven: Is It Even Worth Considering?* Finance Research
+  Letters — bitcoin is too volatile and illiquid to function as a safe haven.
+- **Conlon, T., & McGee, R. (2020).** *Safe Haven or Risky Hazard? Bitcoin During the COVID-19 Crash.*
+  Finance Research Letters — BTC fell *with* equities in March 2020; no haven property.
+- **Bouri, Molnár, et al. (2017).** on bitcoin's hedge/diversifier properties — a weak diversifier at
+  best, not a hedge.
+
+## Context
+
+- **Open-Alpha-Lab** kin: [69 Safe-Haven](../../69-safe-haven/) (gold — the asset BTC is pitched to
+  replace) and [68 All-Weather](../../68-all-weather/) (diversification via uncorrelated sleeves).
+
+## Data
+
+- **Yahoo! Finance** — BTC-USD, SPY, GLD daily total returns, 2014–2026. Tests: BTC–gold and BTC–stock
+  correlations (and first/second-half drift), equity-crash-month behaviour, and a small-sleeve overlay.
+  The offline synthetic world drives BTC off the stock factor with a tunable beta (a risk asset) versus a
+  zero-beta counterfactual (a true uncorrelated "digital gold").
+
+*A diversifier/safe-haven companion to [69 Safe-Haven](../../69-safe-haven/) (gold) and [68
+All-Weather](../../68-all-weather/) (risk parity).*

studies/70-digital-gold/docs/results.md

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+# Results — Study 70 (Digital-Gold): is bitcoin a store of value or a risk asset? 2014–2026
+
+*Generated by [`examples/verify.py`](../examples/verify.py). Daily total returns for **BTC-USD**, **SPY**
+and **GLD**, 2014–2026 (Yahoo). We test the "digital gold" thesis: BTC's correlation with gold and with
+stocks (and its drift), its behaviour in equity-crash months, and the effect of a small BTC sleeve.
+Inputs fingerprint `6e2e2a7c7c98`.*
+
+## The verdict, earned — Signal `NONE` · Tradability `FRAGILE` · "Bitcoin is digital gold"? `NOT SUPPORTED`
+
+The "digital gold" thesis is `NOT SUPPORTED`. Bitcoin behaves nothing like gold: it's **near-uncorrelated
+with gold (+0.09)** but its **correlation with stocks has risen from +0.13 to +0.36**, and in equity-crash
+months it fell **harder than stocks (−17.7% vs SPY −10.1%)**, rising in **0% of them** (gold rose in
+20%). That's the opposite of a safe haven — BTC is a **high-beta risk asset**, not a store of value. What
+it *was* is a phenomenal **return** engine: **+64%/yr** over the window (at **66% vol and an −83%
+drawdown**), so a small sleeve historically lifted a stock portfolio's Sharpe (5% BTC: 0.82 → 0.95). But
+that's a leveraged growth bet, `FRAGILE` to extreme drawdown and regime risk — not the inflation-proof
+digital gold of the pitch. As "digital gold" the Signal is `NONE`.
+
+## Data stamp
+
+- **Assets**: BTC-USD / SPY / GLD daily total returns, 2014–2026 (2,950 days; 5 equity-crash months),
+  fingerprint `6e2e2a7c7c98`.
+
+## Risk & return — a leveraged risk asset, not gold
+
+| asset | ann return | vol | Sharpe | max drawdown |
+|---|---|---|---|---|
+| **BTC** | **+64%** | **66%** | 0.97 | **−83%** |
+| SPY | +14% | 18% | 0.82 | −34% |
+| GLD | +11% | 16% | 0.71 | −24% |
+
+BTC's volatility (66%) and drawdown (−83%) are an order of magnitude beyond gold's. Its high Sharpe is a
+function of an extraordinary trend, not of haven-like stability.
+
+## It doesn't behave like gold — and is drifting toward stocks
+
+| correlation | value |
+|---|---|
+| BTC – stocks | **+0.23** |
+| BTC – gold | **+0.09** |
+| stocks – gold | +0.06 |
+| BTC – stocks, **first half** | +0.13 |
+| BTC – stocks, **second half** | **+0.36** |
+
+If BTC were "digital gold" it would track gold (it doesn't, +0.09) and stay aloof from equities. Instead
+its equity correlation has nearly *tripled* as institutional ownership grew — it increasingly trades as a
+levered risk-on asset.
+
+## In a crisis it's the opposite of a haven
+
+| equity-crash months (SPY < −8%) | mean return | rose in… |
+|---|---|---|
+| **BTC** | **−17.7%** | **0%** of crashes |
+| gold | −0.4% | 20% |
+| stocks | −10.1% | — |
+
+When you'd want a haven most, BTC fell *nearly twice as hard as stocks* and never rose. Gold at least
+held flat. This is the single cleanest refutation of the "safe haven" claim.
+
+## So why did a small sleeve help?
+
+| stock book + BTC sleeve | ann | Sharpe | max drawdown |
+|---|---|---|---|
+| 0% BTC | +14.4% | 0.82 | −34% |
+| 5% BTC | +16.9% | 0.95 | −33% |
+| 10% BTC | +19.4% | 1.05 | −33% |
+
+A small BTC sleeve *did* raise Sharpe — but purely because BTC returned +64%/yr, not because it hedged
+anything. That's a **return bet**, and it rests entirely on a past trend continuing; the −83% drawdown is
+the risk it conceals. Sizing it as "insurance" would be a category error.
+
+## The honest takeaway
+
+Bitcoin is `NOT` digital gold: it's near-uncorrelated with gold, increasingly correlated with stocks, and
+in crashes it falls *harder* than equities and never rallies — a `NONE` on the store-of-value / safe-haven
+claim. It has been a spectacular **risk asset**, so a small sleeve flattered a portfolio's Sharpe — but
+that's a `FRAGILE`, drawdown-heavy growth bet on a trend, not the haven its marketing sells.

studies/70-digital-gold/examples/verify.py

@@ -0,0 +1,39 @@
+"""Reproduce the real run (docs/results.md) — bitcoin as "digital gold".
+    python examples/verify.py   # cache-only (reads the BTC/SPY/GLD pull)
+"""
+from __future__ import annotations
+import os, sys
+try: sys.stdout.reconfigure(encoding="utf-8", errors="replace")
+except Exception: pass
+sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), "..")))
+sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), "..", "..", "..")))
+from digital_gold import data, strategy as st
+
+
+def main(fetch):
+    ret = data.fetch_panel(fetch=fetch)
+    if ret.empty:
+        print("No cached BTC/SPY/GLD data."); return
+    print(f"\nBitcoin as 'digital gold' — BTC/SPY/GLD, {ret.index.min().date()}–{ret.index.max().date()} ({len(ret)} days)\n")
+    for nm in ["BTC-USD", "SPY", "GLD"]:
+        s = st.annualized(ret[nm])
+        print(f"  {nm:8s} ann {s['ann']:+.0%}  vol {s['vol']:.0%}  Sharpe {s['sharpe']:.2f}  maxDD {s['max_drawdown']:.0%}")
+    c = st.correlations(ret)
+    print(f"\n  corr(BTC, stocks) {c['btc_stock']:+.2f}  |  corr(BTC, gold) {c['btc_gold']:+.2f}  |  corr(stocks, gold) {c['stock_gold']:+.2f}")
+    print(f"  BTC–stock corr drifting: {c['btc_stock_first']:+.2f} (first half) → {c['btc_stock_second']:+.2f} (second half)")
+    m = (1 + ret).resample("ME").prod() - 1
+    cb = st.crisis_behavior(m)
+    print(f"\n  in {cb['n_crash']} equity-crash months (SPY<-8%): BTC {cb['btc_in_crash']:+.1%}  gold {cb['gold_in_crash']:+.1%}  stocks {cb['eq_in_crash']:+.1%}")
+    print(f"  BTC rose in {cb['btc_up_share']:.0%} of crashes (gold {cb['gold_up_share']:.0%}) → not a safe haven")
+    print("\n  a small BTC sleeve added to an all-stock book:")
+    sl = st.sleeve_effect(ret["SPY"], ret["BTC-USD"])
+    for name, row in sl.iterrows():
+        print(f"    {name:8s} ann {row['ann']:+.1%}  Sharpe {row['sharpe']:.2f}  maxDD {row['max_drawdown']:.0%}")
+    try:
+        from quantlab import repro
+        print(f"\ninputs fingerprint {repro.fingerprint(ret)}")
+    except Exception: pass
+
+
+if __name__ == "__main__":
+    main("--fetch" in sys.argv)