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p2-etf-gp-indicator-evolution-results

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P2SAMAPA commited on May 13

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GP results 2026-05-13 — fi-commodities

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+{
+  "run_date": "2026-05-13",
+  "universes": {
+    "FI_COMMODITIES": {
+      "rankings": [
+        [
+          "VNQ",
+          58.11146666666666
+        ],
+        [
+          "SLV",
+          47.128546666666665
+        ],
+        [
+          "TLT",
+          25.9936
+        ],
+        [
+          "GLD",
+          21.286353333333338
+        ],
+        [
+          "LQD",
+          14.431173333333335
+        ],
+        [
+          "HYG",
+          13.626906666666665
+        ]
+      ],
+      "tickers": {
+        "TLT": {
+          "mean_sortino": 25.9936,
+          "win_rate": 1.0,
+          "win_rate_pct": 100.0,
+          "positive_windows": 15,
+          "total_windows": 15,
+          "best_window": "2017-2020",
+          "best_sortino": 191.7419,
+          "worst_sortino": 0.5647,
+          "window_scores": {
+            "2008-2011": 27.0868,
+            "2009-2012": 28.7224,
+            "2010-2013": 18.1384,
+            "2011-2014": 11.0201,
+            "2012-2015": 20.8956,
+            "2013-2016": 18.1916,
+            "2014-2017": 11.3879,
+            "2015-2018": 3.6806,
+            "2016-2019": 3.2573,
+            "2017-2020": 191.7419,
+            "2018-2021": 21.7497,
+            "2019-2022": 21.0465,
+            "2020-2023": 9.6096,
+            "2021-2024": 2.8109,
+            "2022-2025": 0.5647
+          },
+          "best_formula": "sub(add(ret_lag_4, protected_div(neg(add(T10Y2Y, 1.7810935586464685)), neg(add(TBILL_3M, ret_lag_5)))), mul(protected_div(sub(sub(ret_lag_4, -0.2712914917363416), ret_lag_5), sig(protected_sqrt(T10Y2Y))), neg(add(neg(add(1.7810935586464685, 1.7810935586464685)), neg(DXY)))))",
+          "all_formulas": {
+            "2008-2011": "sub(sub(ret_lag_1, sub(ret_lag_5, protected_div(TBILL_3M, sub(ret_lag_5, -1.0)))), sub(ret_lag_5, protected_div(TBILL_3M, sub(protected_sqrt(ret_lag_2), sig(-1.0)))))",
+            "2009-2012": "mul(mul(VIX, neg(ret_lag_3)), protected_div(protected_sqrt(mul(ret_lag_2, mul(sub(ret_lag_3, ret_lag_1), ret_lag_3))), protected_sqrt(sub(protected_sqrt(mul(ret_lag_2, TBILL_3M)), ret_lag_2))))",
+            "2010-2013": "add(sub(sub(protected_div(protected_sqrt(mul(TBILL_3M, 0.0)), sig(protected_div(TBILL_3M, ret_lag_4))), sub(sig(sig(ret_lag_5)), mul(neg(TBILL_3M), protected_div(ret_lag_4, ret_lag_1)))), sub(sig(protected_div(TBILL_3M, ret_lag_4)), mul(neg(TBILL_3M), protected_div(ret_lag_4, ret_lag_1)))), neg(1.0))",
+            "2011-2014": "mul(mul(ret_lag_5, ret_lag_3), protected_sqrt(protected_div(protected_div(0.5, mul(ret_lag_3, ret_lag_4)), mul(mul(ret_lag_4, ret_lag_3), mul(ret_lag_4, 0.5)))))",
+            "2012-2015": "protected_div(sub(ret_lag_5, mul(sig(ret_lag_4), add(ret_lag_1, ret_lag_5))), protected_div(protected_div(sub(ret_lag_5, ret_lag_1), sub(neg(ret_lag_4), protected_sqrt(TBILL_3M))), DXY))",
+            "2013-2016": "sub(add(protected_sqrt(sub(protected_sqrt(sub(0.5, TBILL_3M)), TBILL_3M)), sig(sub(ret_lag_5, sig(ret_lag_1)))), add(ret_lag_5, add(mul(mul(mul(1.0, ret_lag_5), sig(1.0)), VIX), T10Y2Y)))",
+            "2014-2017": "mul(add(add(neg(-1.3718204980158055), mul(-1.0, TBILL_3M)), protected_div(protected_div(neg(DXY), protected_div(neg(ret_lag_2), mul(ret_lag_4, -0.5751226908255522))), add(sig(protected_sqrt(TBILL_3M)), protected_div(neg(DXY), protected_div(ret_lag_3, DXY))))), neg(DXY))",
+            "2015-2018": "protected_div(VIX, add(sig(sub(neg(T10Y2Y), 0.5)), mul(-1.937071610930412, T10Y2Y)))",
+            "2016-2019": "mul(neg(sub(add(add(add(1.663230466702478, ret_lag_5), ret_lag_5), neg(protected_div(ret_lag_2, 0.153595845373506))), TBILL_3M)), add(add(TBILL_3M, neg(sub(add(1.663230466702478, 0.153595845373506), TBILL_3M))), neg(sub(add(add(1.663230466702478, ret_lag_5), ret_lag_5), TBILL_3M))))",
+            "2017-2020": "sub(add(ret_lag_4, protected_div(neg(add(T10Y2Y, 1.7810935586464685)), neg(add(TBILL_3M, ret_lag_5)))), mul(protected_div(sub(sub(ret_lag_4, -0.2712914917363416), ret_lag_5), sig(protected_sqrt(T10Y2Y))), neg(add(neg(add(1.7810935586464685, 1.7810935586464685)), neg(DXY)))))",
+            "2018-2021": "sub(add(add(protected_sqrt(mul(VIX, ret_lag_5)), mul(VIX, ret_lag_5)), mul(ret_lag_5, VIX)), protected_sqrt(sub(T10Y2Y, protected_div(mul(VIX, TBILL_3M), protected_sqrt(ret_lag_1)))))",
+            "2019-2022": "sub(protected_div(protected_div(1.0, sub(protected_sqrt(protected_div(T10Y2Y, ret_lag_5)), add(mul(ret_lag_4, DXY), protected_sqrt(T10Y2Y)))), sub(protected_sqrt(protected_div(1.148425598250416, ret_lag_5)), add(mul(ret_lag_4, DXY), protected_sqrt(T10Y2Y)))), 1.0)",
+            "2020-2023": "sub(protected_div(protected_div(protected_sqrt(mul(protected_div(ret_lag_4, ret_lag_1), neg(ret_lag_3))), neg(DXY)), sig(mul(add(ret_lag_1, add(ret_lag_1, T10Y2Y)), sub(sub(VIX, TBILL_3M), 1.0)))), add(ret_lag_1, ret_lag_2))",
+            "2021-2024": "mul(neg(T10Y2Y), mul(protected_sqrt(ret_lag_5), protected_sqrt(protected_div(mul(DXY, mul(DXY, ret_lag_5)), protected_div(ret_lag_1, mul(DXY, ret_lag_5))))))",
+            "2022-2025": "sub(neg(sub(protected_sqrt(protected_div(protected_div(ret_lag_4, ret_lag_1), protected_div(ret_lag_2, ret_lag_1))), add(protected_div(add(TBILL_3M, -1.0), protected_sqrt(TBILL_3M)), add(protected_div(-0.3691814402756144, ret_lag_5), add(T10Y2Y, ret_lag_4))))), neg(sub(protected_div(neg(sub(T10Y2Y, 0.24132113503465868)), mul(sub(ret_lag_5, 0.0), protected_div(ret_lag_4, VIX))), sub(sig(sig(T10Y2Y)), protected_div(protected_div(ret_lag_2, ret_lag_1), sub(T10Y2Y, TBILL_3M))))))"
+          },
+          "rank": 3,
+          "signal_strength": "STRONG"
+        },
+        "GLD": {
+          "mean_sortino": 21.2864,
+          "win_rate": 1.0,
+          "win_rate_pct": 100.0,
+          "positive_windows": 15,
+          "total_windows": 15,
+          "best_window": "2008-2011",
+          "best_sortino": 154.5943,
+          "worst_sortino": 1.9965,
+          "window_scores": {
+            "2008-2011": 154.5943,
+            "2009-2012": 16.0538,
+            "2010-2013": 23.8168,
+            "2011-2014": 28.5591,
+            "2012-2015": 16.7161,
+            "2013-2016": 20.95,
+            "2014-2017": 4.8091,
+            "2015-2018": 2.9993,
+            "2016-2019": 2.4633,
+            "2017-2020": 16.9454,
+            "2018-2021": 16.3752,
+            "2019-2022": 2.3293,
+            "2020-2023": 5.9168,
+            "2021-2024": 1.9965,
+            "2022-2025": 4.7703
+          },
+          "best_formula": "sub(protected_div(ret_lag_2, add(protected_div(add(protected_div(TBILL_3M, T10Y2Y), neg(ret_lag_1)), add(TBILL_3M, add(ret_lag_2, ret_lag_3))), sub(protected_sqrt(T10Y2Y), protected_sqrt(TBILL_3M)))), protected_sqrt(TBILL_3M))",
+          "all_formulas": {
+            "2008-2011": "sub(protected_div(ret_lag_2, add(protected_div(add(protected_div(TBILL_3M, T10Y2Y), neg(ret_lag_1)), add(TBILL_3M, add(ret_lag_2, ret_lag_3))), sub(protected_sqrt(T10Y2Y), protected_sqrt(TBILL_3M)))), protected_sqrt(TBILL_3M))",
+            "2009-2012": "protected_div(mul(mul(mul(ret_lag_4, DXY), mul(mul(mul(ret_lag_4, DXY), DXY), mul(ret_lag_4, DXY))), mul(mul(ret_lag_4, mul(mul(ret_lag_4, DXY), mul(ret_lag_4, DXY))), mul(sub(ret_lag_2, ret_lag_5), mul(ret_lag_4, DXY)))), protected_div(-1.0, TBILL_3M))",
+            "2010-2013": "neg(mul(sub(VIX, protected_div(ret_lag_3, neg(ret_lag_5))), sub(protected_sqrt(ret_lag_5), ret_lag_3)))",
+            "2011-2014": "sub(neg(mul(DXY, ret_lag_1)), sub(sub(protected_div(add(protected_sqrt(1.0), 1.0), protected_sqrt(sig(-0.22375249431447175))), protected_div(protected_div(protected_sqrt(ret_lag_4), 0.5), 0.5)), add(-0.22375249431447175, add(protected_div(ret_lag_2, protected_sqrt(1.0)), 0.5))))",
+            "2012-2015": "sub(protected_div(mul(T10Y2Y, mul(T10Y2Y, ret_lag_5)), protected_div(protected_div(TBILL_3M, TBILL_3M), add(VIX, 1.0))), neg(protected_div(neg(TBILL_3M), TBILL_3M)))",
+            "2013-2016": "protected_div(protected_div(mul(sub(protected_sqrt(ret_lag_3), ret_lag_2), protected_sqrt(neg(-1.1427085114522613))), protected_sqrt(protected_sqrt(protected_sqrt(ret_lag_3)))), add(protected_div(protected_div(add(add(ret_lag_5, ret_lag_2), add(ret_lag_5, ret_lag_2)), ret_lag_2), ret_lag_2), add(ret_lag_5, -1.0)))",
+            "2014-2017": "protected_div(mul(sig(ret_lag_5), protected_div(protected_div(sub(sig(-0.41570452067588803), TBILL_3M), protected_sqrt(ret_lag_2)), protected_sqrt(ret_lag_2))), mul(sub(protected_sqrt(ret_lag_1), mul(ret_lag_5, T10Y2Y)), add(protected_div(VIX, 1.0), sub(protected_sqrt(ret_lag_1), mul(sub(TBILL_3M, 1.0), T10Y2Y)))))",
+            "2015-2018": "protected_div(sub(T10Y2Y, protected_sqrt(add(sub(1.9328950625254513, TBILL_3M), T10Y2Y))), add(neg(sub(TBILL_3M, 1.9328950625254513)), neg(add(neg(T10Y2Y), neg(T10Y2Y)))))",
+            "2016-2019": "protected_div(add(protected_sqrt(T10Y2Y), TBILL_3M), protected_div(sig(protected_div(sig(ret_lag_2), protected_sqrt(T10Y2Y))), protected_sqrt(T10Y2Y)))",
+            "2017-2020": "mul(neg(add(ret_lag_4, protected_sqrt(ret_lag_5))), mul(add(ret_lag_4, DXY), add(ret_lag_2, protected_sqrt(mul(-1.0, ret_lag_3)))))",
+            "2018-2021": "add(mul(mul(T10Y2Y, protected_div(protected_div(VIX, ret_lag_3), add(add(-1.0, -1.0), sub(TBILL_3M, T10Y2Y)))), protected_div(protected_div(mul(ret_lag_3, protected_sqrt(-1.0)), protected_sqrt(mul(ret_lag_3, TBILL_3M))), sig(protected_sqrt(T10Y2Y)))), protected_div(add(sub(sub(ret_lag_2, TBILL_3M), sub(TBILL_3M, T10Y2Y)), -1.0), sub(TBILL_3M, sub(sub(ret_lag_2, TBILL_3M), sub(TBILL_3M, T10Y2Y)))))",
+            "2019-2022": "sub(sub(add(sub(TBILL_3M, sub(ret_lag_1, T10Y2Y)), mul(sub(protected_sqrt(VIX), add(1.0, 1.0)), protected_div(sig(ret_lag_5), protected_div(-0.5811017899094337, 0.5)))), ret_lag_1), add(sub(ret_lag_1, T10Y2Y), 1.0))",
+            "2020-2023": "protected_div(sub(sig(T10Y2Y), protected_div(add(protected_sqrt(-1.1049229891635615), add(TBILL_3M, 0.5)), VIX)), protected_div(protected_div(protected_sqrt(protected_div(protected_sqrt(VIX), neg(ret_lag_5))), sub(mul(neg(0.33026242276966356), protected_div(ret_lag_2, ret_lag_3)), protected_div(protected_sqrt(0.5), mul(1.0, -0.8207104496694577)))), VIX))",
+            "2021-2024": "protected_sqrt(mul(sub(mul(sig(T10Y2Y), TBILL_3M), add(1.0, sig(protected_sqrt(ret_lag_1)))), mul(sub(mul(0.5, TBILL_3M), add(1.0, sig(1.0))), sub(mul(0.5, TBILL_3M), 1.0))))",
+            "2022-2025": "neg(mul(mul(protected_div(-1.0, add(neg(ret_lag_5), protected_div(T10Y2Y, DXY))), protected_sqrt(protected_sqrt(protected_div(ret_lag_3, 0.5)))), protected_sqrt(sub(protected_div(0.5, DXY), ret_lag_1))))"
+          },
+          "rank": 4,
+          "signal_strength": "STRONG"
+        },
+        "SLV": {
+          "mean_sortino": 47.1285,
+          "win_rate": 1.0,
+          "win_rate_pct": 100.0,
+          "positive_windows": 15,
+          "total_windows": 15,
+          "best_window": "2017-2020",
+          "best_sortino": 189.1788,
+          "worst_sortino": 4.465,
+          "window_scores": {
+            "2008-2011": 74.7451,
+            "2009-2012": 60.5001,
+            "2010-2013": 55.3995,
+            "2011-2014": 55.3604,
+            "2012-2015": 55.1714,
+            "2013-2016": 8.9206,
+            "2014-2017": 15.3536,
+            "2015-2018": 4.465,
+            "2016-2019": 30.752,
+            "2017-2020": 189.1788,
+            "2018-2021": 50.3998,
+            "2019-2022": 17.7678,
+            "2020-2023": 37.8616,
+            "2021-2024": 16.624,
+            "2022-2025": 34.4285
+          },
+          "best_formula": "neg(protected_div(protected_div(protected_div(protected_div(1.8268317671211896, add(ret_lag_5, TBILL_3M)), DXY), add(add(protected_div(ret_lag_3, 1.0), add(ret_lag_5, ret_lag_3)), sig(0.634976493828812))), 1.8268317671211896))",
+          "all_formulas": {
+            "2008-2011": "mul(add(mul(protected_sqrt(TBILL_3M), sub(VIX, DXY)), mul(add(add(VIX, T10Y2Y), T10Y2Y), protected_sqrt(TBILL_3M))), T10Y2Y)",
+            "2009-2012": "add(protected_div(-1.619199701232533, TBILL_3M), neg(mul(protected_div(1.0, sub(add(1.0, ret_lag_4), sig(1.0))), mul(add(add(ret_lag_4, ret_lag_2), add(ret_lag_4, ret_lag_4)), -1.619199701232533))))",
+            "2010-2013": "sub(sub(ret_lag_4, VIX), add(add(protected_div(ret_lag_4, ret_lag_1), VIX), add(VIX, VIX)))",
+            "2011-2014": "add(protected_div(mul(ret_lag_4, protected_div(ret_lag_1, ret_lag_5)), 0.46924684801291416), -1.0045308254055931)",
+            "2012-2015": "protected_div(protected_div(mul(neg(DXY), add(TBILL_3M, add(neg(ret_lag_1), TBILL_3M))), DXY), TBILL_3M)",
+            "2013-2016": "add(neg(mul(neg(protected_div(ret_lag_2, protected_sqrt(TBILL_3M))), sub(VIX, ret_lag_2))), protected_div(sub(ret_lag_1, TBILL_3M), TBILL_3M))",
+            "2014-2017": "sub(mul(add(ret_lag_5, mul(T10Y2Y, VIX)), mul(mul(DXY, ret_lag_5), sub(mul(mul(DXY, ret_lag_5), sub(ret_lag_4, ret_lag_2)), 0.0))), add(sub(protected_sqrt(add(0.17527927034521573, T10Y2Y)), add(mul(DXY, ret_lag_5), mul(T10Y2Y, -1.0))), protected_div(protected_sqrt(-1.0), protected_sqrt(protected_sqrt(0.5)))))",
+            "2015-2018": "protected_div(ret_lag_1, neg(protected_sqrt(protected_sqrt(sub(protected_div(DXY, ret_lag_2), sig(DXY))))))",
+            "2016-2019": "protected_div(mul(-1.0, mul(mul(T10Y2Y, 0.7792976193609249), sub(mul(mul(T10Y2Y, 0.7792976193609249), 0.7792976193609249), ret_lag_1))), T10Y2Y)",
+            "2017-2020": "neg(protected_div(protected_div(protected_div(protected_div(1.8268317671211896, add(ret_lag_5, TBILL_3M)), DXY), add(add(protected_div(ret_lag_3, 1.0), add(ret_lag_5, ret_lag_3)), sig(0.634976493828812))), 1.8268317671211896))",
+            "2018-2021": "add(add(neg(DXY), protected_div(add(add(neg(DXY), neg(DXY)), add(neg(DXY), neg(DXY))), VIX)), protected_div(protected_div(add(protected_div(ret_lag_4, add(ret_lag_1, 0.5)), TBILL_3M), ret_lag_2), sub(T10Y2Y, ret_lag_4)))",
+            "2019-2022": "sub(sub(add(add(add(add(TBILL_3M, -1.0), ret_lag_2), ret_lag_2), ret_lag_2), protected_div(add(sig(ret_lag_3), add(ret_lag_1, ret_lag_3)), protected_sqrt(ret_lag_3))), protected_sqrt(protected_sqrt(add(mul(sig(ret_lag_1), sub(ret_lag_4, 0.5)), sig(ret_lag_3)))))",
+            "2020-2023": "sub(protected_div(mul(ret_lag_4, VIX), add(protected_div(protected_div(T10Y2Y, mul(ret_lag_4, VIX)), -1.0), ret_lag_4)), sub(add(add(add(protected_div(T10Y2Y, -1.0), neg(ret_lag_3)), neg(ret_lag_3)), neg(ret_lag_3)), sub(0.09629400646554487, add(add(protected_div(T10Y2Y, -1.0), neg(ret_lag_3)), add(protected_div(T10Y2Y, -1.0), neg(ret_lag_3))))))",
+            "2021-2024": "neg(sub(protected_div(mul(VIX, ret_lag_1), ret_lag_1), add(protected_sqrt(mul(add(VIX, VIX), ret_lag_4)), protected_div(ret_lag_4, ret_lag_5))))",
+            "2022-2025": "protected_div(VIX, neg(protected_div(protected_div(ret_lag_1, neg(VIX)), neg(sig(neg(VIX))))))"
+          },
+          "rank": 2,
+          "signal_strength": "STRONG"
+        },
+        "LQD": {
+          "mean_sortino": 14.4312,
+          "win_rate": 0.9333,
+          "win_rate_pct": 93.3,
+          "positive_windows": 14,
+          "total_windows": 15,
+          "best_window": "2017-2020",
+          "best_sortino": 163.582,
+          "worst_sortino": -0.4778,
+          "window_scores": {
+            "2008-2011": 9.3368,
+            "2009-2012": 3.8437,
+            "2010-2013": 8.801,
+            "2011-2014": 2.3407,
+            "2012-2015": 5.1449,
+            "2013-2016": 2.5445,
+            "2014-2017": 1.7673,
+            "2015-2018": -0.4778,
+            "2016-2019": 4.6726,
+            "2017-2020": 163.582,
+            "2018-2021": 7.0743,
+            "2019-2022": 1.5549,
+            "2020-2023": 1.9208,
+            "2021-2024": 2.8085,
+            "2022-2025": 1.5534
+          },
+          "best_formula": "mul(protected_div(protected_div(protected_sqrt(protected_div(ret_lag_4, protected_sqrt(DXY))), TBILL_3M), add(add(add(protected_div(TBILL_3M, ret_lag_1), TBILL_3M), TBILL_3M), TBILL_3M)), sig(add(protected_sqrt(ret_lag_2), sub(sub(neg(0.5), TBILL_3M), ret_lag_4))))",
+          "all_formulas": {
+            "2008-2011": "protected_div(protected_div(sub(protected_sqrt(ret_lag_4), -0.1398539839115691), DXY), add(sig(protected_div(sig(sig(-0.1398539839115691)), protected_sqrt(ret_lag_4))), add(neg(add(TBILL_3M, ret_lag_4)), add(neg(1.0), neg(ret_lag_5)))))",
+            "2009-2012": "sub(protected_div(0.0, TBILL_3M), TBILL_3M)",
+            "2010-2013": "protected_div(add(protected_sqrt(VIX), sub(sig(protected_sqrt(VIX)), protected_div(protected_sqrt(ret_lag_4), add(neg(ret_lag_5), add(ret_lag_4, TBILL_3M))))), neg(protected_sqrt(protected_sqrt(add(sub(-1.0, ret_lag_3), add(ret_lag_4, TBILL_3M))))))",
+            "2011-2014": "add(T10Y2Y, protected_div(T10Y2Y, neg(protected_div(1.0, add(ret_lag_5, ret_lag_2)))))",
+            "2012-2015": "add(protected_div(T10Y2Y, protected_div(sub(0.0, VIX), TBILL_3M)), mul(protected_div(T10Y2Y, protected_div(sub(sub(0.0, VIX), VIX), sub(ret_lag_5, ret_lag_2))), T10Y2Y))",
+            "2013-2016": "protected_div(protected_div(-1.0, TBILL_3M), add(protected_div(-1.0, T10Y2Y), sig(protected_sqrt(protected_sqrt(VIX)))))",
+            "2014-2017": "sub(sub(mul(sub(mul(TBILL_3M, TBILL_3M), neg(mul(TBILL_3M, TBILL_3M))), sub(mul(TBILL_3M, TBILL_3M), neg(mul(TBILL_3M, TBILL_3M)))), neg(mul(TBILL_3M, TBILL_3M))), sig(DXY))",
+            "2015-2018": "add(sub(sub(neg(sig(TBILL_3M)), TBILL_3M), TBILL_3M), protected_div(1.0, mul(T10Y2Y, sig(T10Y2Y))))",
+            "2016-2019": "protected_sqrt(mul(sub(sub(T10Y2Y, 1.0), add(1.0, add(mul(ret_lag_3, DXY), 1.0))), add(mul(sub(T10Y2Y, 1.0), add(1.0, 1.0)), add(sub(ret_lag_3, ret_lag_5), TBILL_3M))))",
+            "2017-2020": "mul(protected_div(protected_div(protected_sqrt(protected_div(ret_lag_4, protected_sqrt(DXY))), TBILL_3M), add(add(add(protected_div(TBILL_3M, ret_lag_1), TBILL_3M), TBILL_3M), TBILL_3M)), sig(add(protected_sqrt(ret_lag_2), sub(sub(neg(0.5), TBILL_3M), ret_lag_4))))",
+            "2018-2021": "mul(sig(mul(add(protected_div(1.2949641209115375, DXY), sig(protected_sqrt(-1.0))), sub(neg(sig(0.5)), protected_div(neg(-1.0), protected_div(ret_lag_3, TBILL_3M))))), add(sub(0.5, T10Y2Y), protected_div(add(mul(sig(1.2949641209115375), 0.5), protected_div(add(ret_lag_3, ret_lag_3), -0.6183002747860411)), add(add(sub(ret_lag_3, 0.5), T10Y2Y), 1.2949641209115375))))",
+            "2019-2022": "add(add(protected_div(T10Y2Y, mul(mul(0.26695995644121684, protected_sqrt(-1.0)), protected_sqrt(T10Y2Y))), mul(DXY, sub(add(mul(-1.0, ret_lag_2), -1.0), protected_div(mul(T10Y2Y, 1.0), sig(ret_lag_4))))), T10Y2Y)",
+            "2020-2023": "protected_sqrt(mul(mul(mul(add(add(ret_lag_5, ret_lag_2), ret_lag_2), protected_div(TBILL_3M, ret_lag_1)), mul(mul(add(ret_lag_5, ret_lag_2), protected_div(TBILL_3M, ret_lag_1)), protected_sqrt(0.33602184069562124))), mul(mul(mul(add(ret_lag_5, ret_lag_2), protected_div(TBILL_3M, ret_lag_1)), mul(add(ret_lag_5, ret_lag_2), protected_div(TBILL_3M, ret_lag_1))), mul(add(ret_lag_5, ret_lag_2), protected_div(TBILL_3M, ret_lag_1)))))",
+            "2021-2024": "protected_div(protected_sqrt(protected_sqrt(ret_lag_1)), mul(add(protected_div(0.6911279983017753, add(0.6911279983017753, protected_div(0.6911279983017753, T10Y2Y))), neg(add(protected_sqrt(0.0), mul(VIX, ret_lag_2)))), neg(sig(sub(neg(TBILL_3M), protected_div(0.6911279983017753, T10Y2Y))))))",
+            "2022-2025": "sub(protected_sqrt(DXY), mul(add(sig(sig(1.0)), -1.0), add(sub(protected_div(protected_sqrt(ret_lag_1), protected_sqrt(ret_lag_3)), sig(neg(1.0))), neg(VIX))))"
+          },
+          "rank": 5,
+          "signal_strength": "STRONG"
+        },
+        "HYG": {
+          "mean_sortino": 13.6269,
+          "win_rate": 0.9333,
+          "win_rate_pct": 93.3,
+          "positive_windows": 14,
+          "total_windows": 15,
+          "best_window": "2017-2020",
+          "best_sortino": 115.0907,
+          "worst_sortino": -0.3433,
+          "window_scores": {
+            "2008-2011": 27.734,
+            "2009-2012": 7.0348,
+            "2010-2013": 3.5646,
+            "2011-2014": 5.2204,
+            "2012-2015": 18.7837,
+            "2013-2016": 4.2884,
+            "2014-2017": 2.8256,
+            "2015-2018": -0.3433,
+            "2016-2019": 4.5879,
+            "2017-2020": 115.0907,
+            "2018-2021": 6.0013,
+            "2019-2022": 2.9739,
+            "2020-2023": 2.4242,
+            "2021-2024": 3.3091,
+            "2022-2025": 0.9083
+          },
+          "best_formula": "sig(mul(add(add(DXY, add(DXY, protected_div(ret_lag_2, ret_lag_5))), add(DXY, DXY)), sub(ret_lag_2, TBILL_3M)))",
+          "all_formulas": {
+            "2008-2011": "add(neg(add(add(T10Y2Y, add(ret_lag_5, ret_lag_5)), add(add(add(ret_lag_5, ret_lag_5), add(ret_lag_5, ret_lag_5)), add(add(ret_lag_5, ret_lag_5), -0.6896677711457735)))), mul(DXY, ret_lag_2))",
+            "2009-2012": "add(sub(sub(sub(ret_lag_2, protected_sqrt(ret_lag_4)), protected_sqrt(ret_lag_4)), ret_lag_5), sub(sub(mul(T10Y2Y, ret_lag_1), ret_lag_5), ret_lag_5))",
+            "2010-2013": "mul(protected_div(protected_div(sub(protected_sqrt(protected_sqrt(DXY)), mul(neg(T10Y2Y), sub(0.5, T10Y2Y))), sub(VIX, protected_sqrt(DXY))), T10Y2Y), protected_div(DXY, mul(mul(neg(T10Y2Y), sub(0.5, T10Y2Y)), mul(T10Y2Y, mul(T10Y2Y, VIX)))))",
+            "2011-2014": "sub(protected_div(T10Y2Y, VIX), sub(sub(mul(mul(VIX, ret_lag_5), protected_div(VIX, 0.5)), add(sub(ret_lag_3, 0.0), neg(ret_lag_4))), protected_div(protected_sqrt(sig(neg(-1.0))), sub(sig(-1.0), sig(TBILL_3M)))))",
+            "2012-2015": "protected_div(neg(protected_div(protected_div(TBILL_3M, sub(neg(-1.0), mul(DXY, ret_lag_1))), sub(sub(1.1101453482311507, -0.04487151428673908), neg(mul(DXY, ret_lag_5))))), sig(neg(mul(DXY, ret_lag_5))))",
+            "2013-2016": "protected_sqrt(protected_div(protected_div(protected_sqrt(sig(mul(-0.4673296897676451, VIX))), add(add(add(T10Y2Y, ret_lag_2), ret_lag_2), sub(add(T10Y2Y, ret_lag_2), protected_sqrt(T10Y2Y)))), sub(add(T10Y2Y, ret_lag_2), protected_sqrt(T10Y2Y))))",
+            "2014-2017": "protected_sqrt(sub(protected_div(0.5, sig(sub(ret_lag_2, VIX))), sig(add(sub(VIX, DXY), protected_div(DXY, ret_lag_4)))))",
+            "2015-2018": "add(add(sub(add(add(add(1.0, 0.8882544791328688), sig(ret_lag_2)), sub(0.8882544791328688, sub(TBILL_3M, ret_lag_4))), protected_sqrt(TBILL_3M)), add(add(0.8882544791328688, sig(ret_lag_4)), sub(add(0.0, 0.8882544791328688), TBILL_3M))), add(add(add(add(add(1.0, 0.8882544791328688), 0.8882544791328688), sub(add(0.0, 0.8882544791328688), sub(TBILL_3M, ret_lag_2))), sig(ret_lag_2)), sub(add(add(1.0, 0.8882544791328688), sub(add(0.0, 0.8882544791328688), TBILL_3M)), sub(TBILL_3M, ret_lag_4))))",
+            "2016-2019": "add(add(protected_div(neg(VIX), protected_div(DXY, VIX)), neg(T10Y2Y)), protected_sqrt(add(protected_sqrt(DXY), neg(T10Y2Y))))",
+            "2017-2020": "sig(mul(add(add(DXY, add(DXY, protected_div(ret_lag_2, ret_lag_5))), add(DXY, DXY)), sub(ret_lag_2, TBILL_3M)))",
+            "2018-2021": "protected_div(TBILL_3M, add(sub(protected_sqrt(protected_sqrt(protected_sqrt(ret_lag_5))), T10Y2Y), TBILL_3M))",
+            "2019-2022": "sub(add(sub(sub(neg(1.0), protected_sqrt(protected_sqrt(ret_lag_3))), protected_sqrt(ret_lag_1)), TBILL_3M), mul(T10Y2Y, mul(add(protected_sqrt(ret_lag_1), T10Y2Y), VIX)))",
+            "2020-2023": "protected_sqrt(mul(mul(protected_div(protected_div(ret_lag_2, 0.9270471590243221), ret_lag_5), protected_div(protected_div(protected_div(ret_lag_1, ret_lag_3), T10Y2Y), add(1.0, protected_div(ret_lag_1, ret_lag_4)))), protected_div(protected_div(ret_lag_1, ret_lag_4), ret_lag_3)))",
+            "2021-2024": "sub(protected_div(DXY, VIX), protected_sqrt(VIX))",
+            "2022-2025": "sig(sub(DXY, neg(mul(mul(0.5, VIX), add(protected_div(ret_lag_2, ret_lag_5), 1.0)))))"
+          },
+          "rank": 6,
+          "signal_strength": "STRONG"
+        },
+        "VNQ": {
+          "mean_sortino": 58.1115,
+          "win_rate": 1.0,
+          "win_rate_pct": 100.0,
+          "positive_windows": 15,
+          "total_windows": 15,
+          "best_window": "2017-2020",
+          "best_sortino": 215.9663,
+          "worst_sortino": 1.3417,
+          "window_scores": {
+            "2008-2011": 95.9807,
+            "2009-2012": 110.5593,
+            "2010-2013": 93.4762,
+            "2011-2014": 5.821,
+            "2012-2015": 172.7266,
+            "2013-2016": 19.4018,
+            "2014-2017": 15.438,
+            "2015-2018": 19.4904,
+            "2016-2019": 13.7856,
+            "2017-2020": 215.9663,
+            "2018-2021": 25.8126,
+            "2019-2022": 54.0931,
+            "2020-2023": 24.2243,
+            "2021-2024": 3.5544,
+            "2022-2025": 1.3417
+          },
+          "best_formula": "mul(protected_div(add(protected_div(neg(ret_lag_1), 0.09810245925519867), -1.0), TBILL_3M), sub(protected_sqrt(add(protected_div(ret_lag_2, 0.09810245925519867), -1.0)), add(protected_div(ret_lag_2, -1.0), add(protected_div(ret_lag_2, TBILL_3M), ret_lag_2))))",
+          "all_formulas": {
+            "2008-2011": "add(sub(sub(add(sig(-0.43549883006811596), neg(0.5)), ret_lag_5), ret_lag_5), mul(protected_sqrt(sub(mul(ret_lag_3, DXY), add(protected_div(ret_lag_2, ret_lag_2), protected_sqrt(ret_lag_1)))), neg(ret_lag_1)))",
+            "2009-2012": "sub(add(protected_div(protected_sqrt(add(ret_lag_4, neg(0.5))), neg(sub(sub(ret_lag_4, 0.14556144613790734), sub(1.0, T10Y2Y)))), protected_div(sub(ret_lag_2, sig(ret_lag_4)), mul(protected_div(T10Y2Y, -1.0), 0.5))), neg(protected_div(-0.3663205778247405, TBILL_3M)))",
+            "2010-2013": "protected_div(sub(neg(mul(VIX, ret_lag_5)), sig(sub(sig(TBILL_3M), neg(mul(VIX, ret_lag_4))))), sig(sub(mul(VIX, ret_lag_4), neg(mul(VIX, ret_lag_4)))))",
+            "2011-2014": "protected_div(protected_div(protected_div(neg(sig(1.9031930024115158)), add(neg(T10Y2Y), 1.9031930024115158)), neg(add(protected_div(TBILL_3M, ret_lag_3), sub(DXY, ret_lag_5)))), protected_sqrt(add(add(neg(T10Y2Y), 1.9031930024115158), add(sig(T10Y2Y), VIX))))",
+            "2012-2015": "sub(mul(mul(add(DXY, sub(-1.0, protected_sqrt(ret_lag_2))), sig(T10Y2Y)), mul(protected_sqrt(ret_lag_2), sub(mul(sig(ret_lag_3), sub(ret_lag_5, ret_lag_3)), ret_lag_2))), sig(sig(T10Y2Y)))",
+            "2013-2016": "protected_div(add(sub(0.7328957359439889, protected_div(ret_lag_3, ret_lag_4)), neg(VIX)), protected_sqrt(sub(ret_lag_2, ret_lag_5)))",
+            "2014-2017": "protected_div(VIX, sub(mul(protected_sqrt(ret_lag_4), mul(neg(VIX), ret_lag_4)), add(add(ret_lag_5, add(ret_lag_5, protected_sqrt(ret_lag_1))), ret_lag_2)))",
+            "2015-2018": "sub(sub(protected_div(-1.0, protected_sqrt(ret_lag_1)), sub(sig(ret_lag_1), sub(-1.0, 1.0))), mul(mul(neg(ret_lag_2), add(-1.0, ret_lag_2)), sub(protected_div(DXY, TBILL_3M), mul(-1.0, DXY))))",
+            "2016-2019": "protected_div(protected_div(sub(add(protected_div(0.0, ret_lag_2), add(protected_div(0.0, ret_lag_3), 1.0)), protected_sqrt(mul(sub(T10Y2Y, 0.5), neg(VIX)))), T10Y2Y), protected_sqrt(ret_lag_4))",
+            "2017-2020": "mul(protected_div(add(protected_div(neg(ret_lag_1), 0.09810245925519867), -1.0), TBILL_3M), sub(protected_sqrt(add(protected_div(ret_lag_2, 0.09810245925519867), -1.0)), add(protected_div(ret_lag_2, -1.0), add(protected_div(ret_lag_2, TBILL_3M), ret_lag_2))))",
+            "2018-2021": "mul(add(ret_lag_2, protected_sqrt(ret_lag_5)), mul(neg(sig(DXY)), add(DXY, 0.5)))",
+            "2019-2022": "protected_div(add(TBILL_3M, sub(TBILL_3M, 1.0)), protected_div(protected_div(protected_div(protected_div(1.0, mul(ret_lag_4, ret_lag_4)), sub(TBILL_3M, -1.0)), TBILL_3M), ret_lag_3))",
+            "2020-2023": "protected_div(add(neg(TBILL_3M), protected_sqrt(VIX)), sub(protected_div(VIX, ret_lag_3), protected_div(add(add(0.0, sig(1.0)), sub(ret_lag_5, protected_div(TBILL_3M, ret_lag_3))), neg(add(neg(TBILL_3M), protected_sqrt(VIX))))))",
+            "2021-2024": "protected_div(add(T10Y2Y, mul(neg(TBILL_3M), ret_lag_5)), sub(neg(add(add(T10Y2Y, mul(ret_lag_2, 0.3869348174585925)), ret_lag_1)), 0.3869348174585925))",
+            "2022-2025": "sub(neg(sub(sig(VIX), -1.0)), sub(mul(add(DXY, sub(sub(TBILL_3M, ret_lag_3), -1.0)), neg(ret_lag_2)), mul(add(add(DXY, VIX), protected_div(DXY, VIX)), ret_lag_3)))"
+          },
+          "rank": 1,
+          "signal_strength": "STRONG"
+        }
+      }
+    }
+  }
+}