# Track I — Alternative momentum formulations + long-horizon reversal (2026-06-19)

**Script:** `scripts/research/trackI_momentum_reversal.py` (self-contained, runnable).
**Universe:** BTC & ETH only. **TF:** 12h + 1d (sub-12h excluded by rule). **Harness:** identical
honest machinery to TP01 — direction decided `<= close[i]`, positions held next bar (`pos_held[1:]
= tgt[:-1]`), vol-target by inverse PAST-ONLY realized vol (target 20%, lev cap 2x), NET fee 0.10%
RT on turnover, 50/50 BTC+ETH. OOS 65/35 + per-year + fee sweep (0.00–0.40% RT). Correlation to
TP01 net returns reported for every candidate.

## Goal
(A) A momentum formulation that BEATS or DIVERSIFIES the canonical 1-3-6m sign-blend (TP01,
Sharpe ~1.32). (B) Does the classic LONG-HORIZON REVERSAL (fade ~12m winners) give an
uncorrelated positive overlay?

## PART A — momentum formulations (12h, long-flat, vs TP01 Sharpe 1.32 / OOS 0.90 / DD 13.3%)

| formulation | Sharpe | IS | **OOS** | CAGR | maxDD | corr→TP01 | BTC | ETH |
|---|---|---|---|---|---|---|---|---|
| baseline sign-blend 1-3-6m | 1.32 | 1.54 | 0.90 | +16% | 13.3% | 1.00 | 1.15 | 1.10 |
| (i) z-score cum-return (tanh) | **1.35** | 1.63 | 0.85 | +12% | **8.4%** | 0.96 | 1.30 | 1.00 |
| (ii) risk-adjusted momentum | 1.27 | 1.49 | 0.84 | +13% | 9.5% | 0.97 | 1.21 | 1.00 |
| (iii) EMA-cross trend | 0.81 | 0.91 | 0.62 | +11% | 25.1% | 0.85 | 0.89 | 0.53 |
| (iii-b) MACD (calendar spans) | **1.50** | **1.87** | 0.74 | +22% | 17.7% | 0.69 | 1.30 | 1.32 |
| (iv) Donchian breakout | 1.10 | 1.36 | 0.57 | +17% | 25.0% | 0.86 | 1.08 | 0.82 |
| (v) acceleration (Δ-momentum) | 1.28 | 1.82 | 0.35 | +14% | 14.2% | 0.66 | 1.25 | 0.81 |
| (vi) 12-1 skip momentum | 0.67 | 0.79 | 0.47 | +9% | 24.5% | 0.68 | 0.70 | 0.49 |

Results are essentially identical at 1d. Read-out:

- **Nothing cleanly beats the sign-blend OOS on both assets.** The headline-Sharpe leaders are
  artefacts of in-sample fit: **MACD** posts IS 1.87 but OOS collapses to 0.74 (gap = overfit) with
  a worse DD (17.7%); **acceleration** IS 1.82 → OOS **0.35** (worst OOS decay of all). Both fail.
- **(i) z-score continuous momentum** is the one mild, honest refinement: Sharpe 1.35 (≈baseline)
  but **maxDD 8.4% vs 13.3%** — the continuous score scales down position when the cumulative move
  is statistically small, de-risking the tails. OOS 0.85 (slightly below baseline 0.90), CAGR drops
  16%→12%. It's a smoother sibling of TP01, **not a new edge** (corr 0.96).
- (vi) 12-1 skip (classic equity "12-1" momentum) **does NOT help crypto**: skipping the recent
  month removes the strongest part of the signal here → Sharpe 0.67, corr 0.68. Crypto momentum
  lives in the recent window, opposite to the equity stylised fact.
- Breakout/Donchian and EMA-cross are strictly worse (high DD, weak OOS).

## PART B — long-horizon reversal (fade past winners), 12h

Long-short reversal (short ~12/18/24m winners, long losers, vol-targeted):

| reversal LS | Sharpe | OOS | CAGR | maxDD | corr→TP01 |
|---|---|---|---|---|---|
| 12m | -0.77 | -1.15 | -14% | 73% | -0.51 |
| 18m | -0.36 | -0.75 | -8% | 58% | -0.47 |
| 24m | **+0.04** | -0.07 | -1% | 43% | **-0.32** |
| 12-18-24m | -0.46 | -0.72 | -8% | 57% | -0.54 |

- **Long-horizon reversal is NOT a standalone edge.** Standalone it LOSES money (12m/18m strongly
  negative; only 24m is ~flat at Sharpe 0.04, OOS −0.07, and even that fails "net-positive OOS on
  both assets": BTC +0.10 / ETH −0.03). Fading crypto winners over a year just shorts the trend.
- It IS genuinely negatively correlated to TP01 (24m: corr −0.32; 12-18-24: −0.54), as expected
  (it's the opposite sign of medium-term momentum).
- **Momentum + reversal blend** (long 1-6m momentum, brake on very-long extension): the variant
  `mom(1-3-6) − 0.5·rev(12-24)` is the most interesting single-strategy result — Sharpe **1.38**,
  **OOS 0.98** (> baseline 0.90), **maxDD 10.6%** (< 13.3%), both assets positive (BTC 1.25/ETH
  1.05), corr 0.91, fee-robust (1.43→1.22 across 0.00–0.40% RT). CAGR drops 16%→12%. It is TP01
  with a long-term-extension brake: a modest *risk-adjusted* improvement, not more return.

## COMBINED — TP01 + best diversifier (blend net returns)

TP01 alone: Sharpe 1.321, CAGR +16%, maxDD 13.3%, OOS 0.90.

| combo | Sharpe | CAGR | maxDD | OOS | corr |
|---|---|---|---|---|---|
| TP01 + 20% reversal-24m (LS) | **1.411** | +13% | 11.5% | **1.06** | -0.32 |
| TP01 + 30% reversal-24m (LS) | 1.366 | +12% | 11.8% | 1.06 | -0.32 |
| TP01 + 20% reversal-12-18-24 (LS) | 1.350 | +11% | 10.6% | 0.84 | -0.54 |
| TP01 + 50% z-score | 1.348 | +14% | 9.5% | 0.89 | +0.96 |

- Adding a small slice of **reversal-24m long-short** lifts portfolio Sharpe 1.32→1.41 and OOS
  0.90→1.06 while cutting DD to 11.5%. **But be skeptical:** the overlay is a ~zero-mean stream
  (standalone Sharpe 0.04). The benefit is almost entirely **variance reduction from the negative
  correlation, not added alpha** — and it COSTS return (CAGR 16%→13%). With a true-zero-edge
  diversifier this Sharpe bump is fragile (it leans on the −0.32 correlation persisting OOS, and the
  OOS sample is one 2022-24 crypto cycle). I would NOT deploy capital on a standalone-losing sleeve
  to chase a 0.09 Sharpe point that is really de-risking.

## Fee sweep (12h portfolio Sharpe)
baseline 1.37→1.18, z-score 1.38→1.24, MACD 1.52→1.45 (lowest turnover), blend 1.43→1.22,
reversal-24m 0.07→−0.02 (0.00→0.40% RT). All trend formulations survive realistic fees; reversal
has no positive margin to survive on.

## VERDICT (honest)
- **Is there a momentum formulation that beats the 1-3-6m sign-blend? No — not OOS, not on both
  assets.** MACD/acceleration look better in-sample but decay OOS (overfit + higher DD). The only
  honest refinement is **continuous z-score momentum**, which matches the Sharpe with materially
  lower drawdown (8.4% vs 13.3%) — a smoother variant of the SAME edge, not a new one (corr 0.96).
- **Does long-horizon reversal give an uncorrelated positive overlay? No, not a real one.** It is
  uncorrelated/negatively-correlated (good) but **not positive** standalone (it loses, or at best is
  flat at 24m and fails the both-assets bar). The combined-Sharpe lift (→1.41) is variance reduction
  from a near-zero-mean stream and sacrifices CAGR — fragile, not bankable alpha.
- **The ~1.3 structural Sharpe ceiling on BTC/ETH-only holds.** TP01 remains the deployable winner.
  If anything, swap the sign-blend for the **z-score continuous score** (or the `mom − 0.5·rev`
  brake) for a lower-DD profile at equal Sharpe — a risk-management tweak, not a return upgrade.
