{ "edition": "4.0", "name": "Dual Engine", "period": { "start": "2014-08-01", "end": "2026-10-09", "observations": 3066, "return_intervals": 3065, "warmup": "Earlier available observations are retained for indicator and state warm-up. No warm-up P&L is included.", "history_boundary": "Maximum common history natively exposed by the supplied master: 2014-08-01. No pre-boundary model or invented backward price series." }, "scope": "Native research aggregation of the supplied Tactical and Dynamic engines. Original valuation clocks are preserved. Not a single-clock physical execution backtest, verified live record, or forecast.", "source": { "master_sha256": "0c8bcb1b4381b1c66516ff95f13355c65c791e7d1c9281df4f0e3295d6d36703", "csv_sha256": "dee21d84a636b8b386ada418b02e95a4731cc24c2318969cb84a456218556f7e", "master_version_public": "V5.7 / 03 Oct 2026", "csv_last_date": "2026-10-09", "csv_rows": 24811, "csv_columns": 306, "independent_repeat": "Native ledger reproduced at 3,066 dated observations; absolute tolerance 1e-8 USD and relative tolerance 1e-12." }, "metrics": { "cagr": 0.27848231577813753, "cagr_calendar": 0.2778070180825265, "mdd": -0.11204993691084819, "calmar": 2.485341120715759, "vol": 0.12138569869924933, "sharpe_rf0": 2.0858998895938203, "sortino_mar0": 3.1273508879030674, "return_vol": 2.294193786931341, "ulcer": 0.029676345824706893, "final_multiple": 19.84704088306666, "total_return": 18.84704088306666, "final_usd": 198470.40883066662, "var95": 0.011038863568497991, "es95": 0.017364450032666203, "var99": 0.021815205745783585, "es99": 0.027780318434056726, "best_day": 0.04960403861571616, "worst_day": -0.05882645217155724, "positive_days": 0.5843393148450244, "skew": -0.3521440093177715, "excess_kurtosis": 3.8653493065091045, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 }, "benchmark": { "name": "SPY series as supplied", "metrics": { "cagr": 0.14075117065927945, "cagr_calendar": 0.14042815107731443, "mdd": -0.3371726044127942, "calmar": 0.4174454532105473, "vol": 0.17359510397459524, "sharpe_rf0": 0.8457834449671844, "sortino_mar0": 1.1945707377702346, "return_vol": 0.8108014997927456, "ulcer": 0.06675452581655994, "final_multiple": 4.961305268244205, "total_return": 3.961305268244205, "final_usd": 49613.05268244205, "var95": 0.01630952931092142, "es95": 0.02624329881909966, "var99": 0.030323860967603037, "es99": 0.04531870618320242, "best_day": 0.10501940080127703, "worst_day": -0.10942342516812364, "positive_days": 0.5464926590538336, "skew": -0.30466692132142564, "excess_kurtosis": 14.197823280713369, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 }, "basis": "Identical dated observations; supplied closing-price series rebased to USD 10,000. No transaction costs or subscription fees. Corporate-action/total-return adjustments not independently certified. Native strategy valuation clocks differ." }, "monthly": { "positive_months": 111, "months": 147, "positive_pct": 0.7551020408163265, "best": 0.12645465513222676, "best_month": "2020-11", "worst": -0.08638886778325483, "worst_month": "2026-03", "median": 0.020442272161464103, "profit_factor": 5.035283598618434 }, "annual": [ { "year": 2014, "strategy": 0.08971330697759483, "spy": 0.07865207958951759, "scope": "Partial: Aug-Dec" }, { "year": 2015, "strategy": 0.018926028978175413, "spy": 0.012342760290356969, "scope": "Full calendar year" }, { "year": 2016, "strategy": 0.3424057002473375, "spy": 0.11997864018049165, "scope": "Full calendar year" }, { "year": 2017, "strategy": 0.21240627371868004, "spy": 0.21705439292772932, "scope": "Full calendar year" }, { "year": 2018, "strategy": 0.06682907949529882, "spy": -0.045689950454367634, "scope": "Full calendar year" }, { "year": 2019, "strategy": 0.29064883657306395, "spy": 0.3122388701002574, "scope": "Full calendar year" }, { "year": 2020, "strategy": 0.5736573956154074, "spy": 0.18331604571855453, "scope": "Full calendar year" }, { "year": 2021, "strategy": 0.3348494516996683, "spy": 0.287287711851935, "scope": "Full calendar year" }, { "year": 2022, "strategy": 0.18521917001033716, "spy": -0.18175366421200478, "scope": "Full calendar year" }, { "year": 2023, "strategy": 0.24934078512959879, "spy": 0.26175796510012184, "scope": "Full calendar year" }, { "year": 2024, "strategy": 0.2639228610333124, "spy": 0.24886446384167082, "scope": "Full calendar year" }, { "year": 2025, "strategy": 0.6152688764424712, "spy": 0.1771906377670267, "scope": "Full calendar year" }, { "year": 2026, "strategy": 0.25608346168929197, "spy": 0.15124100801841167, "scope": "YTD through 09 Oct" } ], "drawdowns": [ { "peak": "2020-02-21", "trough": "2020-03-19", "recovery": "2020-04-14", "depth": -0.11204993691084819, "underwater_sessions": 36, "underwater_days": 53, "status": "Recovered" }, { "peak": "2026-01-29", "trough": "2026-03-27", "recovery": "2026-05-06", "depth": -0.10794301357992364, "underwater_sessions": 67, "underwater_days": 97, "status": "Recovered" }, { "peak": "2022-04-18", "trough": "2022-07-06", "recovery": "2022-11-25", "depth": -0.091735927896745, "underwater_sessions": 154, "underwater_days": 221, "status": "Recovered" }, { "peak": "2023-09-05", "trough": "2023-10-27", "recovery": "2023-12-14", "depth": -0.0876245217747752, "underwater_sessions": 71, "underwater_days": 100, "status": "Recovered" }, { "peak": "2026-06-03", "trough": "2026-08-03", "recovery": null, "depth": -0.08041374672743196, "underwater_sessions": 89, "underwater_days": 128, "status": "Open at cutoff" }, { "peak": "2025-10-20", "trough": "2025-11-21", "recovery": "2025-12-22", "depth": -0.08034901448583953, "underwater_sessions": 44, "underwater_days": 63, "status": "Recovered" }, { "peak": "2021-02-22", "trough": "2021-03-25", "recovery": "2021-05-06", "depth": -0.07856109611112527, "underwater_sessions": 52, "underwater_days": 73, "status": "Recovered" }, { "peak": "2018-09-14", "trough": "2018-10-29", "recovery": "2019-02-01", "depth": -0.07495748332116225, "underwater_sessions": 95, "underwater_days": 140, "status": "Recovered" }, { "peak": "2015-04-13", "trough": "2015-08-25", "recovery": "2016-03-23", "depth": -0.07319201319946422, "underwater_sessions": 239, "underwater_days": 345, "status": "Recovered" }, { "peak": "2018-01-26", "trough": "2018-02-08", "recovery": "2018-03-12", "depth": -0.07095021531710577, "underwater_sessions": 30, "underwater_days": 45, "status": "Recovered" } ], "underwater": { "max_sessions": 239, "max_calendar_days": 345, "current_drawdown": -0.04138251530148551, "share_days_underwater": 0.8056099151989563, "worst_episode": { "peak": "2020-02-21", "trough": "2020-03-19", "recovery": "2020-04-14", "depth": -0.11204993691084819, "underwater_sessions": 36, "underwater_days": 53, "status": "Recovered" }, "longest_episode": { "peak": "2015-04-13", "trough": "2015-08-25", "recovery": "2016-03-23", "depth": -0.07319201319946422, "underwater_sessions": 239, "underwater_days": 345, "status": "Recovered" } }, "rolling": [ { "sessions": 252, "windows": 2814, "min": -0.01595241167840722, "median": 0.2650069573221171, "max": 0.8585622570706688, "positive_pct": 0.996090973702914, "spy_min": -0.19732692014899578, "spy_median": 0.1584120927656888, "spy_max": 0.7750450253869248 }, { "sessions": 756, "windows": 2310, "min": 0.1429640472493372, "median": 0.27016745670914244, "max": 0.446004123578122, "positive_pct": 1.0, "spy_min": 0.0037179817125214676, "spy_median": 0.13215096961703732, "spy_max": 0.2830578518836482 } ], "rolling_risk": { "vol_252": { "min": 0.07121201301914905, "median": 0.11016543420565854, "max": 0.19058080616314368 }, "sharpe_252": { "min": -0.14844520908594258, "median": 2.135579330670025, "max": 4.397063179633684 }, "mdd_252": { "min": -0.11204993691084819, "median": -0.07319201319946422, "max": -0.03634932215639275 } }, "periods": [ { "label": "Early history", "start": "2014-08-01", "end": "2019-12-31", "strategy": { "cagr": 0.18365931274229585, "cagr_calendar": 0.18341099578847864, "mdd": -0.07495748332116225, "calmar": 2.4501798166754156, "vol": 0.09107639030492867, "sharpe_rf0": 1.8974644737309532, "sortino_mar0": 2.8280721270658784, "return_vol": 2.0165414124055046, "ulcer": 0.027257033097277027, "final_multiple": 2.489221626496656, "total_return": 1.489221626496656, "final_usd": 24892.21626496656, "var95": 0.008490903595995103, "es95": 0.012739940728932427, "var99": 0.016766961371000262, "es99": 0.019323417242449546, "best_day": 0.02474103695973473, "worst_day": -0.025110617299224924, "positive_days": 0.5693323550990462, "skew": -0.32936892419963393, "excess_kurtosis": 1.3741922549967454, "sessions": 1364, "intervals": 1363, "years": 5.408730158730159 }, "benchmark": { "cagr": 0.12201586637100337, "cagr_calendar": 0.12185514085529348, "mdd": -0.19348913905110066, "calmar": 0.6306083481966338, "vol": 0.1333247608438826, "sharpe_rf0": 0.930465900571555, "sortino_mar0": 1.3020125112250878, "return_vol": 0.915177837925234, "ulcer": 0.03878347176633459, "final_multiple": 1.863936401934858, "total_return": 0.8639364019348581, "final_usd": 18639.36401934858, "var95": 0.014058468468703655, "es95": 0.02120565563841811, "var99": 0.02510985521083853, "es99": 0.03203888288733549, "best_day": 0.05052507687166252, "worst_day": -0.04210718340526698, "positive_days": 0.5451210564930301, "skew": -0.4445729778225116, "excess_kurtosis": 3.8349296866550526, "sessions": 1364, "intervals": 1363, "years": 5.408730158730159 }, "treatment": "Observed path rebased at first sample; first sample return excluded; not a fresh run or out-of-sample test." }, { "label": "Middle history", "start": "2020-01-02", "end": "2023-12-29", "strategy": { "cagr": 0.32526463035884956, "cagr_calendar": 0.32517543825056316, "mdd": -0.11204993691084819, "calmar": 2.9028542034579123, "vol": 0.13731537379552575, "sharpe_rf0": 2.120557729332491, "sortino_mar0": 3.2280961466666125, "return_vol": 2.3687415426854987, "ulcer": 0.030506720526950998, "final_multiple": 3.074358053478691, "total_return": 2.074358053478691, "final_usd": 30743.58053478691, "var95": 0.012895579684533453, "es95": 0.018776879598166776, "var99": 0.023592120015987254, "es99": 0.028440065290933025, "best_day": 0.04960403861571616, "worst_day": -0.04122129935969154, "positive_days": 0.5880597014925373, "skew": -0.1166259591188699, "excess_kurtosis": 2.6387333921124845, "sessions": 1006, "intervals": 1005, "years": 3.988095238095238 }, "benchmark": { "cagr": 0.11761500575146355, "cagr_calendar": 0.11758530507210319, "mdd": -0.3371726044127942, "calmar": 0.348827289679412, "vol": 0.2262703383313983, "sharpe_rf0": 0.6051997314698793, "sortino_mar0": 0.8436626281482322, "return_vol": 0.5197986029401838, "ulcer": 0.10383328409307732, "final_multiple": 1.5580951995253425, "total_return": 0.5580951995253425, "final_usd": 15580.951995253425, "var95": 0.020376671004494695, "es95": 0.034356901313329385, "var99": 0.04021793700992119, "es99": 0.05972999828468555, "best_day": 0.09060294657745693, "worst_day": -0.10942342516812376, "positive_days": 0.5373134328358209, "skew": -0.5092222205328747, "excess_kurtosis": 10.350625932060863, "sessions": 1006, "intervals": 1005, "years": 3.988095238095238 }, "treatment": "Observed path rebased at first sample; first sample return excluded; not a fresh run or out-of-sample test." }, { "label": "Recent history", "start": "2024-01-02", "end": "2026-10-09", "strategy": { "cagr": 0.41473772532580044, "cagr_calendar": 0.4129601412388326, "mdd": -0.10794301357992353, "calmar": 3.842191463542186, "vol": 0.14580230834339752, "sharpe_rf0": 2.454220483814356, "sortino_mar0": 3.626303248605998, "return_vol": 2.844520982130125, "ulcer": 0.03271272762259787, "final_multiple": 2.6034824879632033, "total_return": 1.6034824879632033, "final_usd": 26034.824879632033, "var95": 0.013814884838583785, "es95": 0.021773018102255664, "var99": 0.024860546394399503, "es99": 0.034494816518652556, "best_day": 0.03190961189039121, "worst_day": -0.05882645217155724, "positive_days": 0.6086330935251798, "skew": -0.7143085118409419, "excess_kurtosis": 3.9737747338686042, "sessions": 696, "intervals": 695, "years": 2.757936507936508 }, "benchmark": { "cagr": 0.21267889373234805, "cagr_calendar": 0.21183178232571565, "mdd": -0.1875522908467666, "calmar": 1.1339711862336583, "vol": 0.15502943865160806, "sharpe_rf0": 1.3212581242590058, "sortino_mar0": 1.9793377030467791, "return_vol": 1.371861341833879, "ulcer": 0.033132999487802954, "final_multiple": 1.702023888610945, "total_return": 0.7020238886109449, "final_usd": 17020.238886109448, "var95": 0.014720887392104275, "es95": 0.021944630686240706, "var99": 0.025858938679586142, "es99": 0.03774761373146834, "best_day": 0.10501940080127725, "worst_day": -0.05854298617947307, "positive_days": 0.5625899280575539, "skew": 0.9615151501658931, "excess_kurtosis": 21.70959613811829, "sessions": 696, "intervals": 695, "years": 2.757936507936508 }, "treatment": "Observed path rebased at first sample; first sample return excluded; not a fresh run or out-of-sample test." }, { "label": "Latest 1-year window", "start": "2025-10-08", "end": "2026-10-09", "strategy": { "cagr": 0.27903087823614525, "cagr_calendar": 0.27838601440528943, "mdd": -0.10794301357992364, "calmar": 2.5849832145879823, "vol": 0.1824201605958271, "sharpe_rf0": 1.4411526980594265, "sortino_mar0": 1.9999896291138188, "return_vol": 1.5296054850777723, "ulcer": 0.049240249331007596, "final_multiple": 1.2790308782361453, "total_return": 0.27903087823614525, "final_usd": 12790.308782361453, "var95": 0.02025513772421139, "es95": 0.029387348638614526, "var99": 0.02976916466261579, "es99": 0.043158598920685964, "best_day": 0.03190961189039143, "worst_day": -0.05882645217155735, "positive_days": 0.5753968253968254, "skew": -0.879265687841996, "excess_kurtosis": 3.54209481966433, "sessions": 253, "intervals": 252, "years": 1.0 }, "benchmark": { "cagr": 0.16975536647002487, "cagr_calendar": 0.16937958387197782, "mdd": -0.08884964925337813, "calmar": 1.9105912954807827, "vol": 0.13014764898214956, "sharpe_rf0": 1.2699484457394221, "sortino_mar0": 1.8714433682609126, "return_vol": 1.3043291046564178, "ulcer": 0.02147025762538358, "final_multiple": 1.1697553664700249, "total_return": 0.16975536647002487, "final_usd": 11697.553664700248, "var95": 0.014125645584814212, "es95": 0.01773734028052832, "var99": 0.019082793643285995, "es99": 0.024398026538608637, "best_day": 0.02906782833016619, "worst_day": -0.02702787419005026, "positive_days": 0.5277777777777778, "skew": -0.13867164708024715, "excess_kurtosis": 0.9940410812143323, "sessions": 253, "intervals": 252, "years": 1.0 }, "treatment": "Observed path rebased at first sample; first sample return excluded; not a fresh run or out-of-sample test." }, { "label": "Latest 3-year window", "start": "2023-10-04", "end": "2026-10-09", "strategy": { "cagr": 0.3996205332346743, "cagr_calendar": 0.3973785445498539, "mdd": -0.10794301357992364, "calmar": 3.7021435661399753, "vol": 0.14274920290685483, "sharpe_rf0": 2.4282608186847803, "sortino_mar0": 3.5868059392931833, "return_vol": 2.799458946859622, "ulcer": 0.03213307179602612, "final_multiple": 2.7417693401443533, "total_return": 1.7417693401443533, "final_usd": 27417.693401443532, "var95": 0.01354474825386276, "es95": 0.02125805576226904, "var99": 0.024628746632471228, "es99": 0.03327446848875876, "best_day": 0.03190961189039121, "worst_day": -0.05882645217155724, "positive_days": 0.6084656084656085, "skew": -0.706071909635903, "excess_kurtosis": 4.025185051505938, "sessions": 757, "intervals": 756, "years": 3.0 }, "benchmark": { "cagr": 0.23900690209745323, "cagr_calendar": 0.23774138909822096, "mdd": -0.1875522908467666, "calmar": 1.2743480819049333, "vol": 0.15245383977892676, "sharpe_rf0": 1.4820276429632042, "sortino_mar0": 2.232590250583529, "return_vol": 1.5677329114441265, "ulcer": 0.03216128614793022, "final_multiple": 1.902046705841308, "total_return": 0.902046705841308, "final_usd": 19020.46705841308, "var95": 0.014204784893704081, "es95": 0.02134926280656061, "var99": 0.02470570210799831, "es99": 0.03625533321656532, "best_day": 0.10501940080127703, "worst_day": -0.05854298617947307, "positive_days": 0.5674603174603174, "skew": 0.9166660438181434, "excess_kurtosis": 21.332422419191396, "sessions": 757, "intervals": 756, "years": 3.0 }, "treatment": "Observed path rebased at first sample; first sample return excluded; not a fresh run or out-of-sample test." }, { "label": "All replacement ETFs available", "start": "2023-09-14", "end": "2026-10-09", "strategy": { "cagr": 0.3769326326243163, "cagr_calendar": 0.3749859585749049, "mdd": -0.10794301357992364, "calmar": 3.4919595082939408, "vol": 0.14200049050971184, "sharpe_rf0": 2.325069505213524, "sortino_mar0": 3.4290877889411284, "return_vol": 2.6544459900899904, "ulcer": 0.032493992347477206, "final_multiple": 2.6573909379744167, "total_return": 1.6573909379744167, "final_usd": 26573.909379744167, "var95": 0.01333498038885354, "es95": 0.02105823679875014, "var99": 0.02460245574049968, "es99": 0.03327446848875876, "best_day": 0.03190961189039143, "worst_day": -0.05882645217155735, "positive_days": 0.6038961038961039, "skew": -0.6891091207822774, "excess_kurtosis": 4.0298403732460875, "sessions": 771, "intervals": 770, "years": 3.0555555555555554 }, "benchmark": { "cagr": 0.21207771017992227, "cagr_calendar": 0.21104700030229484, "mdd": -0.1875522908467666, "calmar": 1.1307657678955962, "vol": 0.15227144496737094, "sharpe_rf0": 1.3392077075577002, "sortino_mar0": 2.0040321155961203, "return_vol": 1.3927608700723024, "ulcer": 0.03330046366697107, "final_multiple": 1.7998320269744006, "total_return": 0.7998320269744006, "final_usd": 17998.320269744007, "var95": 0.014344767846769708, "es95": 0.02123476334605626, "var99": 0.024424768561462966, "es99": 0.03625533321656532, "best_day": 0.10501940080127703, "worst_day": -0.05854298617947307, "positive_days": 0.5636363636363636, "skew": 0.9086030404358272, "excess_kurtosis": 21.06968174035262, "sessions": 771, "intervals": 770, "years": 3.0555555555555554 }, "treatment": "Observed path rebased at first sample; first sample return excluded; not a fresh run or out-of-sample test." } ], "rebased_starts": [ { "start": "2015-01-02", "cagr": 0.2802560809755912, "cagr_calendar": 0.2795783778477545, "mdd": -0.11204993691084808, "calmar": 2.501171251872952, "vol": 0.12264862000589077, "sharpe_rf0": 2.0767260964938377, "sortino_mar0": 3.1111891837552332, "return_vol": 2.2850324851770085, "ulcer": 0.03002994566347863, "final_multiple": 18.192249091808055, "total_return": 17.192249091808055, "final_usd": 181922.49091808056, "var95": 0.011225135215012306, "es95": 0.0175731127375816, "var99": 0.022123392442861715, "es99": 0.027971102325266763, "best_day": 0.049604038615716384, "worst_day": -0.05882645217155724, "positive_days": 0.582967218654951, "skew": -0.3544411128971471, "excess_kurtosis": 3.795166810755169, "sessions": 2960, "intervals": 2959, "years": 11.742063492063492 }, { "start": "2017-01-03", "cagr": 0.30521775841251486, "cagr_calendar": 0.30446615311729075, "mdd": -0.11204993691084819, "calmar": 2.7239440451926304, "vol": 0.1276969109021719, "sharpe_rf0": 2.150954952363264, "sortino_mar0": 3.214737651505201, "return_vol": 2.39017338991341, "ulcer": 0.02978154714609468, "final_multiple": 13.39648549065291, "total_return": 12.39648549065291, "final_usd": 133964.8549065291, "var95": 0.011890619217843401, "es95": 0.018397013762140185, "var99": 0.023488854548036453, "es99": 0.029000352136184678, "best_day": 0.04960403861571616, "worst_day": -0.05882645217155724, "positive_days": 0.589816700610998, "skew": -0.38719678233345456, "excess_kurtosis": 3.7278775966585704, "sessions": 2456, "intervals": 2455, "years": 9.742063492063492 }, { "start": "2020-01-02", "cagr": 0.3578447707426293, "cagr_calendar": 0.3567425405622817, "mdd": -0.11204993691084819, "calmar": 3.1936186722474122, "vol": 0.14091756309104927, "sharpe_rf0": 2.242586224897455, "sortino_mar0": 3.3651190136463156, "return_vol": 2.5393908530153877, "ulcer": 0.031481272616627747, "final_multiple": 7.88384972673785, "total_return": 6.88384972673785, "final_usd": 78838.4972673785, "var95": 0.01317592552685698, "es95": 0.020036801876497822, "var99": 0.02432423953418883, "es99": 0.030903566034777747, "best_day": 0.04960403861571616, "worst_day": -0.05882645217155724, "positive_days": 0.5961199294532628, "skew": -0.3839102588507072, "excess_kurtosis": 3.2333932265715695, "sessions": 1702, "intervals": 1701, "years": 6.75 }, { "start": "2022-01-03", "cagr": 0.3222966699294565, "cagr_calendar": 0.32091488438562665, "mdd": -0.10794301357992364, "calmar": 2.9858038907800197, "vol": 0.13206644015354277, "sharpe_rf0": 2.182670268992197, "sortino_mar0": 3.247462189681954, "return_vol": 2.440413094763126, "ulcer": 0.033546152757790215, "final_multiple": 3.7655709171086906, "total_return": 2.7655709171086906, "final_usd": 37655.709171086906, "var95": 0.012073898536545752, "es95": 0.0188615566923971, "var99": 0.02362215973406414, "es99": 0.03029695152797468, "best_day": 0.03190961189039121, "worst_day": -0.05882645217155713, "positive_days": 0.5844481605351171, "skew": -0.5620814557881448, "excess_kurtosis": 3.6090757376577787, "sessions": 1197, "intervals": 1196, "years": 4.746031746031746 }, { "start": "2024-01-02", "cagr": 0.41473772532580044, "cagr_calendar": 0.4129601412388326, "mdd": -0.10794301357992353, "calmar": 3.842191463542186, "vol": 0.14580230834339752, "sharpe_rf0": 2.454220483814356, "sortino_mar0": 3.626303248605998, "return_vol": 2.844520982130125, "ulcer": 0.03271272762259787, "final_multiple": 2.6034824879632033, "total_return": 1.6034824879632033, "final_usd": 26034.824879632033, "var95": 0.013814884838583785, "es95": 0.021773018102255664, "var99": 0.024860546394399503, "es99": 0.034494816518652556, "best_day": 0.03190961189039121, "worst_day": -0.05882645217155724, "positive_days": 0.6086330935251798, "skew": -0.7143085118409419, "excess_kurtosis": 3.9737747338686042, "sessions": 696, "intervals": 695, "years": 2.757936507936508 } ], "relative": { "correlation": 0.503182245136608, "beta": 0.3518482203732124, "tracking_error": 0.1538300122942978, "information_ratio": 0.6915071308871389, "alpha_rf0_arithmetic": 0.20153869988216405, "up_capture": 0.5607500758215376, "down_capture": 0.3545094702055931, "vol_match_factor": 0.6992460957713041, "vol_matched_spy": { "cagr": 0.09995704940965178, "cagr_calendar": 0.0997317037512293, "mdd": -0.24512256093488982, "calmar": 0.4077839633708896, "vol": 0.1213856986992493, "sharpe_rf0": 0.8457834449671805, "sortino_mar0": 1.1945707377702293, "return_vol": 0.8234664419348929, "ulcer": 0.0460013645877997, "final_multiple": 3.1859612815575264, "total_return": 2.1859612815575264, "final_usd": 31859.612815575263, "var95": 0.011404374694529328, "es95": 0.01835052423941511, "var99": 0.021203841390308276, "es99": 0.031688928364011125, "best_day": 0.07343440599053475, "worst_day": -0.07651390283473392, "positive_days": 0.5464926590538336, "skew": -0.3046669213214238, "excess_kurtosis": 14.197823280713362, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 } }, "annual_drag": [ { "annual_drag": 0, "cagr": 0.27848231577813753, "cagr_calendar": 0.2778070180825265, "mdd": -0.11204993691084819, "calmar": 2.485341120715759, "vol": 0.12138569869924933, "sharpe_rf0": 2.0858998895938203, "sortino_mar0": 3.1273508879030674, "return_vol": 2.294193786931341, "ulcer": 0.029676345824706893, "final_multiple": 19.84704088306666, "total_return": 18.84704088306666, "final_usd": 198470.40883066662, "var95": 0.011038863568497991, "es95": 0.017364450032666203, "var99": 0.021815205745783585, "es99": 0.027780318434056726, "best_day": 0.04960403861571616, "worst_day": -0.05882645217155724, "positive_days": 0.5843393148450244, "skew": -0.3521440093177715, "excess_kurtosis": 3.8653493065091045, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 }, { "annual_drag": 0.005, "cagr": 0.27208990419924683, "cagr_calendar": 0.271431688821705, "mdd": -0.11238545624255358, "calmar": 2.4210419505884677, "vol": 0.12138328423559773, "sharpe_rf0": 2.044605142931561, "sortino_mar0": 3.0600313734848847, "return_vol": 2.241576390956242, "ulcer": 0.030276665898566875, "final_multiple": 18.67319153744816, "total_return": 17.67319153744816, "final_usd": 186731.9153744816, "var95": 0.011058534837373134, "es95": 0.01738399548030574, "var99": 0.02183466266414829, "es99": 0.027799656701312386, "best_day": 0.04958316110850647, "worst_day": -0.05884517290509794, "positive_days": 0.5827079934747145, "skew": -0.35214400931777057, "excess_kurtosis": 3.865349306509084, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 }, { "annual_drag": 0.01, "cagr": 0.26569749262035613, "cagr_calendar": 0.2650562906622913, "mdd": -0.11272253811676847, "calmar": 2.3570928854096773, "vol": 0.12138085765673928, "sharpe_rf0": 2.003101533782178, "sortino_mar0": 2.992600576929295, "return_vol": 2.188957120172434, "ulcer": 0.030897617200584003, "final_multiple": 17.563374126577695, "total_return": 16.563374126577695, "final_usd": 175633.74126577695, "var95": 0.01107830481201788, "es95": 0.017403639002373735, "var99": 0.02185421721272229, "es99": 0.027819092003414373, "best_day": 0.04956217884290881, "worst_day": -0.058863987574847565, "positive_days": 0.5820554649265905, "skew": -0.35214400931777073, "excess_kurtosis": 3.865349306509117, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 }, { "annual_drag": 0.02, "cagr": 0.25291266946257474, "cagr_calendar": 0.2523052862492403, "mdd": -0.11340145061487461, "calmar": 2.2302419245190923, "vol": 0.1213759676617676, "sharpe_rf0": 1.919459218445056, "sortino_mar0": 2.857403026017637, "return_vol": 2.0837128991412364, "ulcer": 0.0322173649422524, "final_multiple": 15.523197001351027, "total_return": 14.523197001351027, "final_usd": 155231.97001351026, "var95": 0.011118144884087133, "es95": 0.017443224249646037, "var99": 0.021893623162323697, "es99": 0.027858257649822235, "best_day": 0.04951989578546412, "worst_day": -0.05890190253489358, "positive_days": 0.5784665579119086, "skew": -0.3521440093177704, "excess_kurtosis": 3.865349306509115, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 }, { "annual_drag": 0.03, "cagr": 0.24012784630479334, "cagr_calendar": 0.23955400201070853, "mdd": -0.11408679894228935, "calmar": 2.10478204780083, "vol": 0.12137102771216784, "sharpe_rf0": 1.8349555964395907, "sortino_mar0": 2.721753841512539, "return_vol": 1.9784610119167652, "ulcer": 0.03363521611704296, "final_multiple": 13.702643461201456, "total_return": 12.702643461201456, "final_usd": 137026.43461201456, "var95": 0.011158391949618407, "es95": 0.017483213887171847, "var99": 0.021933431670530763, "es99": 0.02789782339997503, "best_day": 0.049477180777797836, "worst_day": -0.05894020482207207, "positive_days": 0.5765089722675367, "skew": -0.3521440093177711, "excess_kurtosis": 3.8653493065091027, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 } ], "stress_windows": [ { "label": "2015-16 equity drawdown", "start": "2015-08-03", "end": "2016-02-11", "return": 0.012691476730191109, "mdd": -0.048891515133607455, "spy_return": -0.11862041052347483, "spy_mdd": -0.12820721759932663 }, { "label": "Q4 2018", "start": "2018-10-01", "end": "2018-12-31", "return": -0.04766220092179707, "mdd": -0.0716750763505466, "spy_return": -0.1383146734608791, "spy_mdd": -0.1920321605708043 }, { "label": "COVID-19 selloff", "start": "2020-02-19", "end": "2020-03-23", "return": -0.09868398326503935, "mdd": -0.11204993691084819, "spy_return": -0.3371726044127942, "spy_mdd": -0.3371726044127942 }, { "label": "2022 calendar year", "start": "2022-01-03", "end": "2022-12-30", "return": 0.17534677915899133, "mdd": -0.0917359278967449, "spy_return": -0.18646383551205037, "spy_mdd": -0.24496378575805022 }, { "label": "2025 Q1", "start": "2025-01-02", "end": "2025-03-31", "return": 0.11590947587136413, "mdd": -0.02438244648240684, "spy_return": -0.040310775130325216, "spy_mdd": -0.10035395318801565 } ], "bootstrap": { "paths": 5000, "horizon_sessions": 756, "block_sessions": 21, "seed": 314159, "method": "Circular fixed-length block bootstrap of native aggregate daily returns; no refit, no independent out-of-sample interpretation.", "terminal_percentiles": { "p05": 1.5068662207543548, "p25": 1.8221435745107981, "p50": 2.0868205790533167, "p75": 2.402383758098269, "p95": 2.9241521666978016 }, "cagr_percentiles": { "p05": 0.14645821658579147, "p50": 0.27789459990945076, "p95": 0.4299910570040059 }, "mdd_percentiles": { "p05": -0.16110848079099876, "p50": -0.10298655106273769, "p95": -0.06590295655665881 }, "finish_below_start": 0.0002, "ever_below_half_initial": 0.0, "drawdown_beyond_30": 0.0002, "drawdown_beyond_50": 0.0 }, "components": { "Tactical": { "cagr": 0.2397443698241566, "cagr_calendar": 0.23917152716611922, "mdd": -0.10141658015321897, "calmar": 2.3639563615924892, "vol": 0.13152607133238473, "sharpe_rf0": 1.7004840090810482, "sortino_mar0": 2.4917746461300463, "return_vol": 1.8227897130622044, "ulcer": 0.030118755337196608, "final_multiple": 13.651196803440966, "total_return": 12.651196803440966, "final_usd": 136511.96803440966, "var95": 0.012355833719721376, "es95": 0.019292331901141463, "var99": 0.02328278360742515, "es99": 0.030531285176243612, "best_day": 0.037871855056883064, "worst_day": -0.0560252260306372, "positive_days": 0.567373572593801, "skew": -0.42916474432743723, "excess_kurtosis": 2.8474899055165963, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 }, "Dynamic": { "cagr": 0.33075554105792837, "cagr_calendar": 0.3299380124894784, "mdd": -0.1440114421560037, "calmar": 2.2967309826647653, "vol": 0.18305806500827346, "sharpe_rf0": 1.6538430224705096, "sortino_mar0": 2.4899702547113005, "return_vol": 1.806834028552523, "ulcer": 0.05144520971249769, "final_multiple": 32.31245769851044, "total_return": 31.312457698510443, "final_usd": 323124.5769851044, "var95": 0.017513408479995208, "es95": 0.026183377860165457, "var99": 0.03188673783275333, "es99": 0.041889115439592804, "best_day": 0.07807266384443823, "worst_day": -0.08825649811624015, "positive_days": 0.5569331158238173, "skew": -0.15865608520119692, "excess_kurtosis": 4.718359139423001, "sessions": 3066, "intervals": 3065, "years": 12.162698412698413 } }, "component_dependence": { "correlation": 0.25805208178147476, "both_negative_days": 0.22805872756933115, "rolling_252_correlation_min": -0.007974845541420214, "rolling_252_correlation_max": 0.511334347882911 }, "proxies": [ { "instrument": "GLDM", "prehistory": "GLD", "real_from": "2018-06-26", "method": "Scaled historical gold proxy; original real ETF data used from splice date." }, { "instrument": "DBMF", "prehistory": "ASFYX", "real_from": "2019-05-08", "method": "Managed-futures mutual-fund proxy before ETF launch; not an identical investment." }, { "instrument": "SGOV", "prehistory": "BIL", "real_from": "2020-06-01", "method": "Scaled short-Treasury proxy, with original Open/Close splice semantics." }, { "instrument": "KMLM", "prehistory": "PQTIX", "real_from": "2020-12-02", "method": "Managed-futures mutual-fund proxy before ETF launch; not an identical investment.", "proxy_first_available": "2014-01-06" }, { "instrument": "SHLD", "prehistory": "PPA", "real_from": "2023-09-14", "method": "Native hybrid defense-fund transition; proxy before availability, real instrument thereafter under the unchanged engine." } ], "quality": { "unique_sorted_dates": true, "required_recent_series": 49, "status_ok": 49, "recent_window": 260, "min_recent_close_coverage": 1.0, "real_etf_not_replaced_after_splice": true, "external_price_downloads": false, "native_input_repairs": [ { "instrument": "BTAL", "date": "2015-04-29", "fields": [ "Open", "Close" ], "treatment": "Existing conditional source-engine repair retained, not a newly fitted price adjustment." } ] }, "definitions": { "annualization": "Native CAGR: final_multiple ** (252 / (n - 1)) - 1. Annual volatility: sample standard deviation of dated percentage changes excluding initial entry-only return, times sqrt(252).", "sharpe": "Annualized arithmetic mean daily return / annualized volatility; risk-free = 0. Not excess over Treasury returns.", "sortino": "Annualized arithmetic mean / root mean square of negative daily returns annualized; target = 0; denominator uses all observations.", "mdd": "Minimum equity / running peak - 1, including starting capital 1.0 before first entry cost.", "calmar": "Native annualized CAGR / absolute full-period maximum drawdown.", "tail": "Historical empirical daily VaR and mean loss beyond empirical quantile; positive numbers denote loss.", "monthly": "Compounded daily native returns, including initial entry-only cost in Aug 2014. 2014 and 2026 are partial years.", "cost_scope": "Original Tactical commissions and slippage, Dynamic turnover costs and master aggregation rebalance costs are retained. Additional annual drags are hypothetical, not subscription prices. Taxes, signal fees, actual follower slippage and cash flows are not included.", "adjustments": "Supplied OHLC are processed by native proxy splices and the existing conditional BTAL Open/Close repair on 2015-04-29. No external price series or separately added dividends. Corporate-action/total-return adjustments are not independently certified.", "slices": "Rebased windows and date splits reuse the full-history path and prior strategy state; not restarted accounts or untouched holdouts." }, "implementation_reruns": { "higher_friction": { "label": "Higher modeled friction", "metrics": { "CAGR": 0.2679584241260944, "MDD": -0.11201283504028947, "Calmar": 2.3922117856378997, "Ann_Volatility": 0.12126471666465685, "Worst_1Y": -0.01419736311821096, "Final_Multiple": 17.94879028109795 }, "aggregate_series": "dual-engine-higher-friction.csv", "cost_and_delay_assumptions": { "slip": 15.0, "delay": 0, "d_fee": 0.002, "master_fee": 0.003 } }, "one_session_late": { "label": "One additional session delay", "metrics": { "CAGR": 0.26975749244977365, "MDD": -0.10954020005865328, "Calmar": 2.4626346519846782, "Ann_Volatility": 0.12185873190384178, "Worst_1Y": -0.003562344413918783, "Final_Multiple": 18.26100253267643 }, "aggregate_series": "dual-engine-one-session-late.csv", "cost_and_delay_assumptions": { "slip": 5.0, "delay": 1, "d_fee": 0.001, "master_fee": 0.0015 } } } }