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p2-etf-gp-indicator-evolution-results

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GP results 2026-05-08 — fi-commodities

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  1. gp_indicator_2026-05-08_fi-commodities.json +317 -0
gp_indicator_2026-05-08_fi-commodities.json ADDED
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1
+ {
2
+ "run_date": "2026-05-08",
3
+ "universes": {
4
+ "FI_COMMODITIES": {
5
+ "rankings": [
6
+ [
7
+ "SLV",
8
+ 42.69853333333333
9
+ ],
10
+ [
11
+ "VNQ",
12
+ 38.70483333333333
13
+ ],
14
+ [
15
+ "TLT",
16
+ 23.91633333333333
17
+ ],
18
+ [
19
+ "HYG",
20
+ 22.318619999999996
21
+ ],
22
+ [
23
+ "GLD",
24
+ 13.981446666666667
25
+ ],
26
+ [
27
+ "LQD",
28
+ 12.501453333333334
29
+ ]
30
+ ],
31
+ "tickers": {
32
+ "TLT": {
33
+ "mean_sortino": 23.9163,
34
+ "win_rate": 1.0,
35
+ "win_rate_pct": 100.0,
36
+ "positive_windows": 15,
37
+ "total_windows": 15,
38
+ "best_window": "2017-2020",
39
+ "best_sortino": 151.4739,
40
+ "worst_sortino": 0.3965,
41
+ "window_scores": {
42
+ "2008-2011": 39.6449,
43
+ "2009-2012": 32.8194,
44
+ "2010-2013": 8.9547,
45
+ "2011-2014": 8.1022,
46
+ "2012-2015": 26.6848,
47
+ "2013-2016": 14.0552,
48
+ "2014-2017": 1.3839,
49
+ "2015-2018": 2.9684,
50
+ "2016-2019": 2.9388,
51
+ "2017-2020": 151.4739,
52
+ "2018-2021": 50.8784,
53
+ "2019-2022": 16.0156,
54
+ "2020-2023": 0.6997,
55
+ "2021-2024": 1.7286,
56
+ "2022-2025": 0.3965
57
+ },
58
+ "best_formula": "sub(sub(add(-1.0, sub(neg(T10Y2Y), protected_sqrt(T10Y2Y))), add(mul(ret_lag_3, VIX), sig(sub(ret_lag_1, 0.5)))), protected_sqrt(sig(protected_div(ret_lag_1, ret_lag_5))))",
59
+ "all_formulas": {
60
+ "2008-2011": "mul(VIX, sub(sub(1.0, protected_div(ret_lag_2, 0.5)), sub(0.41073834579720936, sub(1.0, T10Y2Y))))",
61
+ "2009-2012": "neg(mul(mul(add(add(ret_lag_2, TBILL_3M), neg(T10Y2Y)), neg(add(add(ret_lag_2, TBILL_3M), TBILL_3M))), mul(protected_sqrt(protected_sqrt(add(ret_lag_2, TBILL_3M))), add(add(VIX, add(VIX, VIX)), 0.5))))",
62
+ "2010-2013": "neg(add(sub(ret_lag_4, protected_sqrt(TBILL_3M)), add(add(sub(mul(ret_lag_4, DXY), sub(-0.9291616383284711, 1.0)), add(protected_sqrt(ret_lag_4), protected_sqrt(ret_lag_4))), protected_sqrt(ret_lag_4))))",
63
+ "2011-2014": "sig(add(protected_div(ret_lag_3, protected_div(ret_lag_4, TBILL_3M)), neg(mul(DXY, sig(neg(ret_lag_3))))))",
64
+ "2012-2015": "protected_div(0.0, protected_div(mul(sig(mul(protected_sqrt(ret_lag_4), protected_div(ret_lag_4, ret_lag_3))), add(ret_lag_5, neg(ret_lag_1))), protected_div(1.0, sig(protected_div(1.0, protected_div(ret_lag_4, ret_lag_3))))))",
65
+ "2013-2016": "sub(neg(add(0.7754278297647668, protected_sqrt(protected_div(0.481229009921297, protected_div(ret_lag_3, ret_lag_4))))), neg(protected_div(sub(sub(0.481229009921297, TBILL_3M), ret_lag_4), protected_div(ret_lag_3, ret_lag_4))))",
66
+ "2014-2017": "add(add(add(add(add(TBILL_3M, sub(TBILL_3M, T10Y2Y)), add(TBILL_3M, sub(TBILL_3M, T10Y2Y))), add(sub(protected_sqrt(ret_lag_4), mul(ret_lag_4, DXY)), sub(TBILL_3M, T10Y2Y))), sub(add(TBILL_3M, sub(TBILL_3M, T10Y2Y)), T10Y2Y)), add(add(add(TBILL_3M, sub(TBILL_3M, T10Y2Y)), add(TBILL_3M, sub(TBILL_3M, T10Y2Y))), add(sub(add(TBILL_3M, sub(TBILL_3M, T10Y2Y)), mul(ret_lag_4, DXY)), sub(TBILL_3M, T10Y2Y))))",
67
+ "2015-2018": "mul(protected_div(VIX, sub(sub(protected_sqrt(mul(ret_lag_3, VIX)), T10Y2Y), T10Y2Y)), protected_sqrt(ret_lag_4))",
68
+ "2016-2019": "sub(sub(sub(TBILL_3M, mul(sub(mul(-1.0, -1.0), mul(VIX, ret_lag_2)), sig(sig(1.730420827483166)))), ret_lag_5), sig(sig(mul(VIX, mul(VIX, ret_lag_2)))))",
69
+ "2017-2020": "sub(sub(add(-1.0, sub(neg(T10Y2Y), protected_sqrt(T10Y2Y))), add(mul(ret_lag_3, VIX), sig(sub(ret_lag_1, 0.5)))), protected_sqrt(sig(protected_div(ret_lag_1, ret_lag_5))))",
70
+ "2018-2021": "protected_div(neg(add(add(sub(T10Y2Y, TBILL_3M), protected_div(-1.0, 1.8562371092981276)), add(protected_div(neg(ret_lag_1), neg(VIX)), protected_div(mul(T10Y2Y, ret_lag_4), sig(1.0))))), add(sub(T10Y2Y, add(ret_lag_1, TBILL_3M)), protected_div(-1.0, 1.8562371092981276)))",
71
+ "2019-2022": "protected_div(add(protected_sqrt(ret_lag_4), sub(0.5, TBILL_3M)), mul(sub(sig(T10Y2Y), TBILL_3M), neg(sig(add(protected_div(ret_lag_5, ret_lag_2), protected_div(ret_lag_5, ret_lag_2))))))",
72
+ "2020-2023": "sub(protected_sqrt(add(protected_div(ret_lag_5, ret_lag_4), protected_sqrt(VIX))), neg(add(protected_div(ret_lag_5, ret_lag_4), add(protected_div(ret_lag_5, ret_lag_3), protected_sqrt(DXY)))))",
73
+ "2021-2024": "mul(sub(sub(ret_lag_2, ret_lag_1), neg(add(sub(sub(T10Y2Y, ret_lag_1), ret_lag_1), ret_lag_2))), neg(DXY))",
74
+ "2022-2025": "protected_div(TBILL_3M, add(add(sub(TBILL_3M, sig(T10Y2Y)), ret_lag_4), sub(sub(ret_lag_4, T10Y2Y), protected_sqrt(VIX))))"
75
+ },
76
+ "rank": 3,
77
+ "signal_strength": "STRONG"
78
+ },
79
+ "GLD": {
80
+ "mean_sortino": 13.9814,
81
+ "win_rate": 1.0,
82
+ "win_rate_pct": 100.0,
83
+ "positive_windows": 15,
84
+ "total_windows": 15,
85
+ "best_window": "2017-2020",
86
+ "best_sortino": 34.4581,
87
+ "worst_sortino": 1.5041,
88
+ "window_scores": {
89
+ "2008-2011": 16.3143,
90
+ "2009-2012": 14.0858,
91
+ "2010-2013": 29.3083,
92
+ "2011-2014": 17.7749,
93
+ "2012-2015": 19.35,
94
+ "2013-2016": 21.9086,
95
+ "2014-2017": 11.9931,
96
+ "2015-2018": 2.1236,
97
+ "2016-2019": 4.2973,
98
+ "2017-2020": 34.4581,
99
+ "2018-2021": 16.9437,
100
+ "2019-2022": 1.5041,
101
+ "2020-2023": 6.4668,
102
+ "2021-2024": 2.2505,
103
+ "2022-2025": 10.9426
104
+ },
105
+ "best_formula": "protected_div(sig(sub(sub(protected_div(0.0, T10Y2Y), mul(TBILL_3M, VIX)), mul(add(sub(T10Y2Y, ret_lag_5), mul(TBILL_3M, VIX)), mul(TBILL_3M, VIX)))), protected_div(sub(sub(T10Y2Y, sub(ret_lag_1, mul(TBILL_3M, VIX))), sig(sub(VIX, protected_sqrt(ret_lag_1)))), add(protected_sqrt(ret_lag_1), add(sub(T10Y2Y, 0.0), protected_div(VIX, VIX)))))",
106
+ "all_formulas": {
107
+ "2008-2011": "neg(add(T10Y2Y, add(mul(add(TBILL_3M, TBILL_3M), protected_div(ret_lag_1, ret_lag_3)), sub(mul(mul(ret_lag_1, T10Y2Y), protected_sqrt(VIX)), 1.0))))",
108
+ "2009-2012": "neg(add(sub(mul(T10Y2Y, protected_sqrt(ret_lag_1)), neg(protected_sqrt(ret_lag_1))), add(sub(mul(T10Y2Y, protected_sqrt(ret_lag_1)), neg(protected_sqrt(ret_lag_1))), neg(protected_div(-1.0, TBILL_3M)))))",
109
+ "2010-2013": "mul(protected_div(sig(protected_div(protected_div(ret_lag_3, TBILL_3M), TBILL_3M)), 0.5), protected_div(protected_div(protected_div(ret_lag_3, TBILL_3M), TBILL_3M), protected_div(protected_div(protected_div(0.5, protected_div(ret_lag_3, 0.5)), ret_lag_5), protected_div(protected_div(ret_lag_3, 0.5), TBILL_3M))))",
110
+ "2011-2014": "add(add(mul(protected_div(ret_lag_2, mul(TBILL_3M, TBILL_3M)), protected_div(0.5, VIX)), -1.8128109863738904), mul(protected_div(ret_lag_2, ret_lag_4), protected_div(0.5, VIX)))",
111
+ "2012-2015": "sub(protected_div(-0.1678475887387454, protected_sqrt(TBILL_3M)), add(sig(sub(protected_div(-1.5727506388144272, mul(-0.1678475887387454, TBILL_3M)), add(sig(ret_lag_3), protected_div(TBILL_3M, ret_lag_3)))), sub(protected_div(-1.5727506388144272, mul(protected_div(ret_lag_1, ret_lag_4), VIX)), -0.1678475887387454)))",
112
+ "2013-2016": "mul(add(sub(mul(mul(mul(-1.0, ret_lag_5), add(-1.0, DXY)), 0.5), sub(1.0, neg(ret_lag_3))), add(neg(1.0), mul(ret_lag_4, DXY))), protected_sqrt(sub(sub(1.7021388814332123, ret_lag_3), mul(mul(mul(-1.0, ret_lag_5), add(DXY, DXY)), -1.0))))",
113
+ "2014-2017": "add(protected_div(ret_lag_3, protected_sqrt(ret_lag_4)), protected_div(neg(protected_sqrt(ret_lag_1)), mul(protected_sqrt(add(-1.0, T10Y2Y)), sub(mul(protected_sqrt(ret_lag_1), 0.5), ret_lag_3))))",
114
+ "2015-2018": "sub(neg(sub(protected_div(sub(sub(ret_lag_2, T10Y2Y), add(T10Y2Y, T10Y2Y)), sub(T10Y2Y, protected_sqrt(T10Y2Y))), TBILL_3M)), sub(protected_div(sub(ret_lag_3, add(T10Y2Y, T10Y2Y)), sub(add(T10Y2Y, ret_lag_1), protected_sqrt(T10Y2Y))), TBILL_3M))",
115
+ "2016-2019": "add(sub(add(protected_sqrt(neg(VIX)), sub(0.0, ret_lag_5)), add(add(ret_lag_2, 1.0), add(T10Y2Y, TBILL_3M))), -1.0)",
116
+ "2017-2020": "protected_div(sig(sub(sub(protected_div(0.0, T10Y2Y), mul(TBILL_3M, VIX)), mul(add(sub(T10Y2Y, ret_lag_5), mul(TBILL_3M, VIX)), mul(TBILL_3M, VIX)))), protected_div(sub(sub(T10Y2Y, sub(ret_lag_1, mul(TBILL_3M, VIX))), sig(sub(VIX, protected_sqrt(ret_lag_1)))), add(protected_sqrt(ret_lag_1), add(sub(T10Y2Y, 0.0), protected_div(VIX, VIX)))))",
117
+ "2018-2021": "protected_div(protected_div(neg(sub(protected_sqrt(DXY), protected_div(ret_lag_3, ret_lag_2))), protected_div(-1.0, ret_lag_5)), mul(TBILL_3M, protected_div(-1.0, ret_lag_5)))",
118
+ "2019-2022": "add(neg(1.0), protected_sqrt(mul(mul(mul(TBILL_3M, T10Y2Y), sub(T10Y2Y, mul(TBILL_3M, T10Y2Y))), sub(T10Y2Y, mul(TBILL_3M, T10Y2Y)))))",
119
+ "2020-2023": "add(sub(protected_div(VIX, add(sub(ret_lag_1, T10Y2Y), sub(ret_lag_1, T10Y2Y))), mul(TBILL_3M, protected_sqrt(VIX))), sig(sub(TBILL_3M, mul(sub(ret_lag_1, T10Y2Y), protected_sqrt(VIX)))))",
120
+ "2021-2024": "protected_sqrt(mul(add(protected_div(mul(1.8916555551919125, T10Y2Y), mul(VIX, ret_lag_4)), protected_div(sub(protected_sqrt(0.0), protected_sqrt(ret_lag_2)), protected_sqrt(ret_lag_4))), mul(protected_div(mul(1.8916555551919125, T10Y2Y), mul(VIX, ret_lag_4)), protected_sqrt(protected_sqrt(ret_lag_2)))))",
121
+ "2022-2025": "sub(mul(sub(sub(T10Y2Y, mul(add(0.5, VIX), ret_lag_5)), ret_lag_2), mul(0.5, protected_div(sig(ret_lag_2), protected_sqrt(ret_lag_3)))), protected_sqrt(protected_div(add(protected_div(sig(T10Y2Y), protected_sqrt(ret_lag_3)), DXY), protected_div(sig(-1.0), neg(ret_lag_2)))))"
122
+ },
123
+ "rank": 5,
124
+ "signal_strength": "STRONG"
125
+ },
126
+ "SLV": {
127
+ "mean_sortino": 42.6985,
128
+ "win_rate": 1.0,
129
+ "win_rate_pct": 100.0,
130
+ "positive_windows": 15,
131
+ "total_windows": 15,
132
+ "best_window": "2017-2020",
133
+ "best_sortino": 260.1534,
134
+ "worst_sortino": 2.254,
135
+ "window_scores": {
136
+ "2008-2011": 70.7939,
137
+ "2009-2012": 45.8546,
138
+ "2010-2013": 33.1947,
139
+ "2011-2014": 23.8503,
140
+ "2012-2015": 54.2438,
141
+ "2013-2016": 7.7993,
142
+ "2014-2017": 3.8018,
143
+ "2015-2018": 11.2786,
144
+ "2016-2019": 52.4143,
145
+ "2017-2020": 260.1534,
146
+ "2018-2021": 25.6261,
147
+ "2019-2022": 33.7202,
148
+ "2020-2023": 2.254,
149
+ "2021-2024": 3.6381,
150
+ "2022-2025": 11.8549
151
+ },
152
+ "best_formula": "protected_div(add(protected_sqrt(mul(add(TBILL_3M, ret_lag_1), protected_sqrt(mul(ret_lag_2, ret_lag_1)))), TBILL_3M), neg(sub(TBILL_3M, ret_lag_1)))",
153
+ "all_formulas": {
154
+ "2008-2011": "sub(protected_div(sub(0.0, ret_lag_2), sub(TBILL_3M, ret_lag_3)), protected_sqrt(protected_sqrt(mul(VIX, protected_sqrt(DXY)))))",
155
+ "2009-2012": "sub(add(add(protected_div(TBILL_3M, mul(add(TBILL_3M, TBILL_3M), add(-1.0, 0.5))), add(neg(ret_lag_1), neg(ret_lag_1))), add(protected_div(neg(ret_lag_1), 0.5), neg(ret_lag_1))), mul(VIX, ret_lag_1))",
156
+ "2010-2013": "sub(sig(sub(protected_div(ret_lag_1, protected_div(ret_lag_5, sub(ret_lag_5, VIX))), neg(T10Y2Y))), sub(add(protected_sqrt(protected_sqrt(0.5)), protected_sqrt(0.5)), mul(neg(ret_lag_1), add(T10Y2Y, add(T10Y2Y, VIX)))))",
157
+ "2011-2014": "sub(sig(protected_div(protected_div(0.0, ret_lag_3), sub(add(T10Y2Y, add(ret_lag_1, ret_lag_1)), 1.0))), sig(add(add(add(T10Y2Y, add(ret_lag_1, ret_lag_1)), add(ret_lag_1, ret_lag_1)), protected_div(1.0, -1.6901836756703483))))",
158
+ "2012-2015": "add(sub(neg(add(VIX, protected_div(ret_lag_4, ret_lag_5))), 1.0), -1.0)",
159
+ "2013-2016": "protected_div(T10Y2Y, protected_div(protected_div(sub(mul(protected_div(ret_lag_5, ret_lag_3), ret_lag_4), sig(ret_lag_3)), sig(protected_div(ret_lag_5, ret_lag_3))), sig(T10Y2Y)))",
160
+ "2014-2017": "add(protected_div(mul(TBILL_3M, sub(protected_sqrt(TBILL_3M), sig(1.0))), neg(neg(add(ret_lag_2, ret_lag_3)))), protected_div(mul(1.0, sub(protected_sqrt(TBILL_3M), sig(T10Y2Y))), neg(neg(add(add(ret_lag_2, ret_lag_3), ret_lag_3)))))",
161
+ "2015-2018": "add(protected_div(protected_div(0.0, ret_lag_2), protected_div(add(T10Y2Y, mul(TBILL_3M, mul(TBILL_3M, ret_lag_3))), 0.5)), protected_div(add(add(T10Y2Y, mul(TBILL_3M, mul(TBILL_3M, ret_lag_3))), mul(protected_div(protected_div(ret_lag_3, ret_lag_2), protected_sqrt(T10Y2Y)), mul(protected_div(T10Y2Y, 0.5), ret_lag_3))), neg(T10Y2Y)))",
162
+ "2016-2019": "protected_div(mul(sig(protected_div(ret_lag_5, mul(T10Y2Y, T10Y2Y))), mul(sig(protected_div(ret_lag_5, mul(T10Y2Y, T10Y2Y))), mul(-1.0, T10Y2Y))), protected_sqrt(mul(T10Y2Y, T10Y2Y)))",
163
+ "2017-2020": "protected_div(add(protected_sqrt(mul(add(TBILL_3M, ret_lag_1), protected_sqrt(mul(ret_lag_2, ret_lag_1)))), TBILL_3M), neg(sub(TBILL_3M, ret_lag_1)))",
164
+ "2018-2021": "neg(sub(sub(neg(protected_div(protected_sqrt(0.5), -1.9269178393266917)), ret_lag_4), mul(neg(DXY), mul(ret_lag_4, mul(neg(ret_lag_4), 1.0)))))",
165
+ "2019-2022": "sub(protected_div(sig(protected_div(neg(add(-1.0, T10Y2Y)), ret_lag_1)), add(add(protected_div(neg(-1.8259993065051385), add(ret_lag_2, ret_lag_4)), add(add(ret_lag_2, ret_lag_4), add(ret_lag_2, ret_lag_4))), protected_div(-1.0, ret_lag_5))), sig(neg(add(sub(protected_sqrt(-1.0), protected_div(ret_lag_1, ret_lag_4)), protected_div(protected_sqrt(T10Y2Y), T10Y2Y)))))",
166
+ "2020-2023": "protected_div(ret_lag_5, mul(protected_div(neg(ret_lag_5), protected_div(VIX, ret_lag_1)), mul(neg(VIX), neg(ret_lag_2))))",
167
+ "2021-2024": "add(mul(neg(mul(protected_sqrt(VIX), add(mul(-1.2215944037116095, DXY), VIX))), -1.4990338443544982), protected_div(-1.808318282420211, ret_lag_1))",
168
+ "2022-2025": "protected_div(protected_div(0.0, ret_lag_5), mul(sub(add(T10Y2Y, ret_lag_4), sub(ret_lag_2, neg(sig(ret_lag_2)))), ret_lag_1))"
169
+ },
170
+ "rank": 1,
171
+ "signal_strength": "STRONG"
172
+ },
173
+ "LQD": {
174
+ "mean_sortino": 12.5015,
175
+ "win_rate": 0.9333,
176
+ "win_rate_pct": 93.3,
177
+ "positive_windows": 14,
178
+ "total_windows": 15,
179
+ "best_window": "2017-2020",
180
+ "best_sortino": 132.0607,
181
+ "worst_sortino": -0.6221,
182
+ "window_scores": {
183
+ "2008-2011": 22.2488,
184
+ "2009-2012": 3.8443,
185
+ "2010-2013": 0.3161,
186
+ "2011-2014": 2.2702,
187
+ "2012-2015": 3.3042,
188
+ "2013-2016": 2.5037,
189
+ "2014-2017": 2.0154,
190
+ "2015-2018": -0.6221,
191
+ "2016-2019": 4.0271,
192
+ "2017-2020": 132.0607,
193
+ "2018-2021": 9.5854,
194
+ "2019-2022": 1.5208,
195
+ "2020-2023": 1.5343,
196
+ "2021-2024": 2.4367,
197
+ "2022-2025": 0.4762
198
+ },
199
+ "best_formula": "add(protected_div(sub(protected_div(ret_lag_1, sub(protected_div(ret_lag_1, TBILL_3M), 0.5)), TBILL_3M), TBILL_3M), protected_div(ret_lag_1, sub(protected_div(ret_lag_1, TBILL_3M), 0.5)))",
200
+ "all_formulas": {
201
+ "2008-2011": "protected_div(protected_div(sub(add(protected_sqrt(mul(VIX, ret_lag_2)), protected_sqrt(mul(VIX, ret_lag_2))), neg(neg(-1.0))), sub(protected_div(protected_sqrt(T10Y2Y), protected_div(-1.0, T10Y2Y)), add(protected_div(mul(VIX, ret_lag_2), protected_sqrt(TBILL_3M)), T10Y2Y))), sub(VIX, add(add(protected_sqrt(mul(VIX, ret_lag_2)), protected_div(T10Y2Y, protected_div(-1.0, T10Y2Y))), add(sub(mul(ret_lag_5, 1.953634293283962), protected_div(0.5, ret_lag_5)), protected_sqrt(ret_lag_4)))))",
202
+ "2009-2012": "protected_sqrt(protected_div(0.0, TBILL_3M))",
203
+ "2010-2013": "sub(protected_sqrt(protected_sqrt(-1.5441584924414724)), mul(VIX, sub(T10Y2Y, protected_div(sig(T10Y2Y), sub(T10Y2Y, protected_div(VIX, VIX))))))",
204
+ "2011-2014": "T10Y2Y",
205
+ "2012-2015": "protected_div(neg(mul(ret_lag_5, ret_lag_5)), TBILL_3M)",
206
+ "2013-2016": "add(sub(T10Y2Y, add(-1.0, mul(T10Y2Y, mul(mul(T10Y2Y, T10Y2Y), mul(T10Y2Y, T10Y2Y))))), sub(protected_div(protected_sqrt(T10Y2Y), T10Y2Y), add(-1.0, mul(mul(mul(T10Y2Y, T10Y2Y), T10Y2Y), mul(T10Y2Y, T10Y2Y)))))",
207
+ "2014-2017": "add(sub(mul(protected_div(protected_div(TBILL_3M, T10Y2Y), 0.5), protected_div(protected_div(protected_div(TBILL_3M, T10Y2Y), T10Y2Y), T10Y2Y)), T10Y2Y), mul(protected_div(mul(protected_div(TBILL_3M, 0.5), protected_div(protected_div(TBILL_3M, T10Y2Y), T10Y2Y)), protected_sqrt(sub(TBILL_3M, T10Y2Y))), protected_div(protected_div(TBILL_3M, protected_sqrt(sub(TBILL_3M, T10Y2Y))), T10Y2Y)))",
208
+ "2015-2018": "sub(protected_div(protected_sqrt(protected_div(ret_lag_2, mul(add(T10Y2Y, T10Y2Y), ret_lag_2))), T10Y2Y), add(add(T10Y2Y, protected_sqrt(ret_lag_2)), add(add(add(T10Y2Y, T10Y2Y), add(add(T10Y2Y, T10Y2Y), T10Y2Y)), add(T10Y2Y, protected_sqrt(ret_lag_2)))))",
209
+ "2016-2019": "sig(protected_sqrt(sub(mul(mul(mul(VIX, TBILL_3M), 0.5), TBILL_3M), add(protected_sqrt(DXY), mul(mul(VIX, TBILL_3M), 0.5)))))",
210
+ "2017-2020": "add(protected_div(sub(protected_div(ret_lag_1, sub(protected_div(ret_lag_1, TBILL_3M), 0.5)), TBILL_3M), TBILL_3M), protected_div(ret_lag_1, sub(protected_div(ret_lag_1, TBILL_3M), 0.5)))",
211
+ "2018-2021": "protected_div(protected_div(sig(sub(sub(neg(T10Y2Y), T10Y2Y), add(add(T10Y2Y, T10Y2Y), T10Y2Y))), mul(mul(mul(mul(T10Y2Y, T10Y2Y), add(T10Y2Y, T10Y2Y)), mul(mul(T10Y2Y, T10Y2Y), add(T10Y2Y, T10Y2Y))), mul(mul(mul(T10Y2Y, T10Y2Y), add(T10Y2Y, T10Y2Y)), T10Y2Y))), mul(mul(mul(T10Y2Y, T10Y2Y), add(T10Y2Y, T10Y2Y)), protected_div(add(add(protected_div(0.0, 0.5), sig(-1.0)), neg(protected_div(0.0, 0.5))), add(protected_sqrt(mul(0.0, T10Y2Y)), mul(sub(ret_lag_1, 0.0), mul(T10Y2Y, ret_lag_1))))))",
212
+ "2019-2022": "protected_div(protected_sqrt(protected_sqrt(mul(protected_div(neg(VIX), protected_sqrt(ret_lag_5)), mul(mul(ret_lag_1, ret_lag_3), add(-0.31258695516408297, DXY))))), sub(mul(-1.522961519067147, T10Y2Y), sig(mul(-1.522961519067147, T10Y2Y))))",
213
+ "2020-2023": "add(protected_sqrt(add(-1.082186441323611, protected_sqrt(add(ret_lag_5, add(ret_lag_5, T10Y2Y))))), protected_div(sub(ret_lag_5, -1.082186441323611), add(-1.082186441323611, add(-1.082186441323611, TBILL_3M))))",
214
+ "2021-2024": "sub(protected_sqrt(protected_div(DXY, ret_lag_2)), sub(mul(DXY, sub(mul(DXY, T10Y2Y), protected_sqrt(DXY))), TBILL_3M))",
215
+ "2022-2025": "protected_sqrt(protected_div(mul(mul(TBILL_3M, protected_div(mul(TBILL_3M, -1.3266431369064042), protected_sqrt(VIX))), protected_div(mul(TBILL_3M, -1.3266431369064042), protected_sqrt(VIX))), protected_sqrt(VIX)))"
216
+ },
217
+ "rank": 6,
218
+ "signal_strength": "STRONG"
219
+ },
220
+ "HYG": {
221
+ "mean_sortino": 22.3186,
222
+ "win_rate": 1.0,
223
+ "win_rate_pct": 100.0,
224
+ "positive_windows": 15,
225
+ "total_windows": 15,
226
+ "best_window": "2008-2011",
227
+ "best_sortino": 114.5237,
228
+ "worst_sortino": 0.8601,
229
+ "window_scores": {
230
+ "2008-2011": 114.5237,
231
+ "2009-2012": 18.097,
232
+ "2010-2013": 1.7142,
233
+ "2011-2014": 10.5366,
234
+ "2012-2015": 80.3358,
235
+ "2013-2016": 4.3247,
236
+ "2014-2017": 2.1302,
237
+ "2015-2018": 0.8601,
238
+ "2016-2019": 2.7756,
239
+ "2017-2020": 80.9236,
240
+ "2018-2021": 3.0775,
241
+ "2019-2022": 8.448,
242
+ "2020-2023": 1.9446,
243
+ "2021-2024": 3.2263,
244
+ "2022-2025": 1.8614
245
+ },
246
+ "best_formula": "protected_div(protected_div(ret_lag_5, add(sig(neg(sig(ret_lag_3))), neg(sig(ret_lag_3)))), mul(sig(mul(DXY, ret_lag_3)), protected_sqrt(protected_div(protected_div(protected_div(DXY, TBILL_3M), ret_lag_3), neg(ret_lag_2)))))",
247
+ "all_formulas": {
248
+ "2008-2011": "protected_div(protected_div(ret_lag_5, add(sig(neg(sig(ret_lag_3))), neg(sig(ret_lag_3)))), mul(sig(mul(DXY, ret_lag_3)), protected_sqrt(protected_div(protected_div(protected_div(DXY, TBILL_3M), ret_lag_3), neg(ret_lag_2)))))",
249
+ "2009-2012": "protected_div(add(mul(T10Y2Y, -1.0), protected_div(add(mul(-1.0, -1.0), protected_div(ret_lag_2, TBILL_3M)), TBILL_3M)), add(mul(add(mul(-1.0, T10Y2Y), protected_div(ret_lag_2, TBILL_3M)), T10Y2Y), protected_div(TBILL_3M, sig(DXY))))",
250
+ "2010-2013": "sub(mul(protected_div(neg(sig(1.0)), protected_sqrt(add(0.9523700306366996, 0.9523700306366996))), T10Y2Y), -1.0)",
251
+ "2011-2014": "add(add(protected_sqrt(mul(ret_lag_5, DXY)), protected_div(sub(-1.0, DXY), sub(sub(sub(DXY, ret_lag_3), ret_lag_3), ret_lag_3))), mul(neg(sig(protected_sqrt(mul(ret_lag_5, DXY)))), mul(sig(protected_div(DXY, ret_lag_5)), protected_div(TBILL_3M, ret_lag_5))))",
252
+ "2012-2015": "sub(mul(sub(0.0, ret_lag_2), add(DXY, protected_div(add(mul(T10Y2Y, ret_lag_1), TBILL_3M), protected_div(ret_lag_2, TBILL_3M)))), protected_sqrt(mul(add(protected_sqrt(add(-1.0, 0.0)), add(mul(T10Y2Y, ret_lag_1), TBILL_3M)), mul(mul(protected_div(ret_lag_2, ret_lag_1), add(ret_lag_1, 0.5)), add(1.0, protected_sqrt(1.0))))))",
253
+ "2013-2016": "neg(protected_div(neg(sig(mul(ret_lag_1, VIX))), sub(mul(protected_sqrt(0.5), mul(protected_sqrt(0.5), VIX)), mul(sig(mul(ret_lag_5, VIX)), add(protected_sqrt(DXY), sub(ret_lag_4, ret_lag_5))))))",
254
+ "2014-2017": "protected_sqrt(sub(add(0.5, protected_div(TBILL_3M, sig(neg(VIX)))), add(TBILL_3M, 1.0)))",
255
+ "2015-2018": "sub(protected_div(VIX, sig(sub(-0.08713841079258033, VIX))), mul(protected_sqrt(ret_lag_4), DXY))",
256
+ "2016-2019": "add(sig(mul(protected_div(T10Y2Y, neg(protected_div(TBILL_3M, T10Y2Y))), mul(add(protected_div(VIX, ret_lag_1), protected_div(VIX, T10Y2Y)), add(neg(T10Y2Y), neg(T10Y2Y))))), sig(neg(add(protected_div(VIX, T10Y2Y), neg(DXY)))))",
257
+ "2017-2020": "add(sub(sub(ret_lag_3, ret_lag_4), mul(sub(ret_lag_3, ret_lag_4), neg(DXY))), sub(neg(protected_div(1.0, TBILL_3M)), add(TBILL_3M, neg(sig(-1.0)))))",
258
+ "2018-2021": "protected_div(sub(sub(sub(sub(DXY, VIX), VIX), neg(sub(sub(DXY, VIX), VIX))), neg(sub(sub(DXY, VIX), VIX))), mul(mul(add(ret_lag_3, T10Y2Y), mul(add(add(ret_lag_3, T10Y2Y), VIX), sig(ret_lag_4))), VIX))",
259
+ "2019-2022": "protected_div(add(protected_sqrt(protected_sqrt(ret_lag_2)), mul(sig(VIX), T10Y2Y)), add(sub(sub(mul(protected_sqrt(T10Y2Y), protected_sqrt(ret_lag_5)), protected_div(T10Y2Y, 0.5)), sig(sig(ret_lag_5))), add(protected_sqrt(protected_sqrt(ret_lag_2)), neg(neg(protected_sqrt(ret_lag_5))))))",
260
+ "2020-2023": "mul(protected_sqrt(add(protected_div(sig(T10Y2Y), ret_lag_2), T10Y2Y)), protected_sqrt(protected_sqrt(ret_lag_1)))",
261
+ "2021-2024": "protected_sqrt(sub(protected_sqrt(sub(protected_sqrt(add(DXY, -1.0)), protected_div(mul(DXY, VIX), DXY))), TBILL_3M))",
262
+ "2022-2025": "sub(sub(ret_lag_1, neg(protected_div(protected_div(add(-1.0, -1.440269472439161), sub(1.0, VIX)), protected_sqrt(protected_div(ret_lag_1, 1.0))))), protected_sqrt(protected_div(ret_lag_1, protected_div(add(-1.0, -1.440269472439161), sub(ret_lag_1, VIX)))))"
263
+ },
264
+ "rank": 4,
265
+ "signal_strength": "STRONG"
266
+ },
267
+ "VNQ": {
268
+ "mean_sortino": 38.7048,
269
+ "win_rate": 1.0,
270
+ "win_rate_pct": 100.0,
271
+ "positive_windows": 15,
272
+ "total_windows": 15,
273
+ "best_window": "2017-2020",
274
+ "best_sortino": 170.91,
275
+ "worst_sortino": 0.1822,
276
+ "window_scores": {
277
+ "2008-2011": 50.0703,
278
+ "2009-2012": 155.1268,
279
+ "2010-2013": 14.8441,
280
+ "2011-2014": 13.0994,
281
+ "2012-2015": 61.2132,
282
+ "2013-2016": 17.2964,
283
+ "2014-2017": 3.435,
284
+ "2015-2018": 0.1822,
285
+ "2016-2019": 9.022,
286
+ "2017-2020": 170.91,
287
+ "2018-2021": 27.6371,
288
+ "2019-2022": 45.8496,
289
+ "2020-2023": 4.8309,
290
+ "2021-2024": 3.4072,
291
+ "2022-2025": 3.6483
292
+ },
293
+ "best_formula": "sub(neg(mul(sig(add(ret_lag_5, sig(ret_lag_5))), -1.7308324173127763)), sub(mul(VIX, TBILL_3M), add(ret_lag_5, sig(ret_lag_5))))",
294
+ "all_formulas": {
295
+ "2008-2011": "add(add(neg(sig(neg(sig(-1.0)))), -1.0), mul(ret_lag_2, add(protected_sqrt(ret_lag_4), add(protected_sqrt(mul(ret_lag_5, -1.0)), VIX))))",
296
+ "2009-2012": "sub(add(protected_div(sub(TBILL_3M, VIX), TBILL_3M), mul(sub(TBILL_3M, sub(1.4816166956583183, ret_lag_5)), ret_lag_5)), mul(neg(protected_div(ret_lag_1, ret_lag_3)), mul(sig(ret_lag_1), protected_sqrt(T10Y2Y))))",
297
+ "2010-2013": "protected_div(protected_sqrt(protected_sqrt(mul(ret_lag_2, sig(0.5)))), protected_div(add(protected_sqrt(ret_lag_2), neg(ret_lag_4)), sub(mul(-1.0, TBILL_3M), TBILL_3M)))",
298
+ "2011-2014": "add(add(neg(T10Y2Y), neg(T10Y2Y)), add(protected_sqrt(mul(DXY, ret_lag_3)), protected_sqrt(mul(DXY, add(ret_lag_5, TBILL_3M)))))",
299
+ "2012-2015": "protected_div(protected_div(sub(sub(neg(T10Y2Y), ret_lag_3), sig(VIX)), protected_sqrt(add(sig(ret_lag_3), sub(sub(ret_lag_5, DXY), sig(ret_lag_2))))), add(sub(sig(VIX), mul(protected_div(VIX, 0.5), sig(neg(ret_lag_2)))), mul(protected_div(mul(protected_div(VIX, 0.5), sig(ret_lag_3)), 0.5), sig(ret_lag_3))))",
300
+ "2013-2016": "protected_div(protected_div(protected_div(0.0, add(ret_lag_2, ret_lag_3)), add(add(ret_lag_2, mul(ret_lag_3, ret_lag_3)), ret_lag_5)), TBILL_3M)",
301
+ "2014-2017": "add(sub(-1.0, add(sig(add(T10Y2Y, -0.8162875598763732)), add(mul(VIX, 1.0), sub(sub(ret_lag_1, VIX), ret_lag_3)))), protected_div(1.0, sig(mul(TBILL_3M, protected_div(1.0, ret_lag_2)))))",
302
+ "2015-2018": "add(protected_div(-1.0, sub(protected_sqrt(sig(1.0)), T10Y2Y)), add(TBILL_3M, TBILL_3M))",
303
+ "2016-2019": "sub(protected_div(protected_div(VIX, protected_div(add(VIX, ret_lag_3), neg(ret_lag_4))), protected_sqrt(ret_lag_3)), protected_sqrt(sub(protected_sqrt(ret_lag_3), protected_sqrt(add(mul(VIX, ret_lag_1), protected_sqrt(ret_lag_1))))))",
304
+ "2017-2020": "sub(neg(mul(sig(add(ret_lag_5, sig(ret_lag_5))), -1.7308324173127763)), sub(mul(VIX, TBILL_3M), add(ret_lag_5, sig(ret_lag_5))))",
305
+ "2018-2021": "mul(protected_div(mul(protected_div(mul(VIX, protected_div(0.0, ret_lag_5)), add(T10Y2Y, neg(ret_lag_2))), protected_div(0.0, ret_lag_5)), add(T10Y2Y, protected_div(add(1.0, 1.0), add(VIX, ret_lag_1)))), sub(mul(protected_sqrt(add(neg(ret_lag_1), ret_lag_4)), protected_div(add(1.0, 1.0), add(VIX, ret_lag_1))), ret_lag_2))",
306
+ "2019-2022": "protected_div(add(add(-1.0, add(-1.0, mul(T10Y2Y, TBILL_3M))), mul(add(add(-1.0, mul(T10Y2Y, TBILL_3M)), mul(add(T10Y2Y, -1.0), TBILL_3M)), TBILL_3M)), add(sig(T10Y2Y), mul(mul(protected_div(protected_sqrt(ret_lag_1), mul(ret_lag_3, T10Y2Y)), protected_div(ret_lag_1, mul(ret_lag_3, ret_lag_1))), T10Y2Y)))",
307
+ "2020-2023": "add(add(sub(sub(T10Y2Y, protected_sqrt(ret_lag_3)), protected_div(mul(sub(-1.0, 0.0), protected_div(ret_lag_1, ret_lag_4)), protected_div(add(-1.8360063305477294, ret_lag_1), sig(1.0)))), protected_sqrt(sub(ret_lag_3, add(sub(T10Y2Y, ret_lag_5), protected_sqrt(-1.0))))), add(sub(-1.0, protected_sqrt(sub(T10Y2Y, ret_lag_5))), add(-1.8360063305477294, ret_lag_1)))",
308
+ "2021-2024": "add(add(TBILL_3M, neg(sub(sub(1.8020277213212772, sub(ret_lag_1, 0.5)), sub(neg(VIX), T10Y2Y)))), protected_sqrt(DXY))",
309
+ "2022-2025": "add(add(add(-1.2237736131333081, T10Y2Y), protected_div(add(mul(protected_div(1.0, VIX), neg(ret_lag_3)), mul(ret_lag_2, add(-1.2237736131333081, T10Y2Y))), ret_lag_2)), mul(T10Y2Y, mul(neg(protected_div(1.0, VIX)), protected_div(protected_sqrt(T10Y2Y), add(ret_lag_1, ret_lag_1)))))"
310
+ },
311
+ "rank": 2,
312
+ "signal_strength": "STRONG"
313
+ }
314
+ }
315
+ }
316
+ }
317
+ }