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p2-etf-gp-indicator-evolution-results

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1
+ {
2
+ "run_date": "2026-05-01",
3
+ "universes": {
4
+ "EQUITY_SECTORS": {
5
+ "SPY": {
6
+ "formula": "protected_div(mul(ret_lag_2, VIX), mul(protected_div(protected_div(TBILL_3M, 0.0), mul(ret_lag_2, VIX)), add(T10Y2Y, ret_lag_2)))",
7
+ "consensus_votes": 1,
8
+ "total_windows": 15,
9
+ "percentage": 6.666666666666667,
10
+ "all_windows": {
11
+ "2008-2011": "protected_div(mul(ret_lag_2, VIX), mul(protected_div(protected_div(TBILL_3M, 0.0), mul(ret_lag_2, VIX)), add(T10Y2Y, ret_lag_2)))",
12
+ "2009-2012": "protected_div(add(mul(sub(0.5, VIX), sub(TBILL_3M, 0.0)), 1.0), add(protected_div(TBILL_3M, 0.0), add(0.0, -0.1867217695849963)))",
13
+ "2010-2013": "add(protected_div(ret_lag_2, ret_lag_5), sub(-0.886707626221864, 1.0))",
14
+ "2011-2014": "add(protected_div(VIX, add(ret_lag_3, TBILL_3M)), protected_div(mul(VIX, 0.2686320188016187), add(TBILL_3M, ret_lag_5)))",
15
+ "2012-2015": "protected_div(sub(protected_div(add(ret_lag_1, ret_lag_4), -0.6961552670003668), TBILL_3M), TBILL_3M)",
16
+ "2013-2016": "mul(add(add(TBILL_3M, TBILL_3M), T10Y2Y), add(mul(ret_lag_1, T10Y2Y), TBILL_3M))",
17
+ "2014-2017": "mul(protected_div(protected_div(DXY, sub(TBILL_3M, DXY)), 1.0), protected_div(DXY, sub(protected_div(1.0, TBILL_3M), 1.0)))",
18
+ "2015-2018": "add(add(protected_div(0.0, ret_lag_5), add(protected_div(0.0, ret_lag_3), 0.0)), mul(add(ret_lag_1, ret_lag_4), add(ret_lag_1, ret_lag_1)))",
19
+ "2016-2019": "protected_div(protected_div(protected_div(TBILL_3M, mul(TBILL_3M, TBILL_3M)), sub(TBILL_3M, 1.0)), sub(TBILL_3M, 0.5))",
20
+ "2017-2020": "sub(mul(protected_div(add(ret_lag_1, ret_lag_1), add(ret_lag_5, 0.0)), protected_div(TBILL_3M, add(ret_lag_1, 1.0))), protected_div(sub(sub(DXY, VIX), VIX), sub(0.3570120783165629, sub(VIX, 0.0))))",
21
+ "2018-2021": "sub(mul(add(0.5, 0.5), T10Y2Y), protected_div(sub(add(TBILL_3M, T10Y2Y), sub(ret_lag_4, 0.0)), mul(add(0.5, TBILL_3M), protected_div(TBILL_3M, ret_lag_2))))",
22
+ "2019-2022": "protected_div(sub(protected_div(mul(ret_lag_5, ret_lag_2), sub(ret_lag_4, ret_lag_2)), add(ret_lag_2, mul(ret_lag_5, ret_lag_3))), add(ret_lag_2, 0.0))",
23
+ "2020-2023": "sub(add(VIX, T10Y2Y), add(protected_div(add(ret_lag_4, ret_lag_4), protected_div(ret_lag_1, TBILL_3M)), add(0.8933576747622225, 0.5)))",
24
+ "2021-2024": "sub(sub(add(DXY, ret_lag_5), TBILL_3M), mul(protected_div(ret_lag_4, ret_lag_2), sub(0.0, TBILL_3M)))",
25
+ "2022-2025": "protected_div(add(-0.10622338419655408, add(T10Y2Y, add(-0.10622338419655408, -0.10622338419655408))), add(mul(-0.10622338419655408, -0.06257426489815798), add(0.5, -0.10622338419655408)))"
26
+ }
27
+ },
28
+ "QQQ": {
29
+ "formula": "mul(ret_lag_2, sub(sub(ret_lag_3, VIX), protected_div(ret_lag_3, ret_lag_4)))",
30
+ "consensus_votes": 1,
31
+ "total_windows": 15,
32
+ "percentage": 6.666666666666667,
33
+ "all_windows": {
34
+ "2008-2011": "mul(ret_lag_2, sub(sub(ret_lag_3, VIX), protected_div(ret_lag_3, ret_lag_4)))",
35
+ "2009-2012": "mul(protected_div(protected_div(sub(1.0, ret_lag_1), add(ret_lag_5, ret_lag_1)), mul(protected_div(1.0, 1.0), mul(ret_lag_1, TBILL_3M))), add(mul(sub(DXY, ret_lag_3), sub(ret_lag_3, T10Y2Y)), mul(mul(ret_lag_3, TBILL_3M), protected_div(VIX, ret_lag_2))))",
36
+ "2010-2013": "sub(sub(protected_div(mul(0.5, 0.2177376843648462), add(ret_lag_3, ret_lag_3)), sub(protected_div(0.5, 0.2177376843648462), protected_div(T10Y2Y, TBILL_3M))), sub(protected_div(protected_div(-0.04273083437745395, ret_lag_2), protected_div(DXY, VIX)), protected_div(ret_lag_1, protected_div(DXY, VIX))))",
37
+ "2011-2014": "sub(sub(add(0.9827348602944816, 0.5), protected_div(ret_lag_2, protected_div(ret_lag_1, ret_lag_3))), protected_div(protected_div(protected_div(T10Y2Y, 0.0), protected_div(TBILL_3M, ret_lag_1)), protected_div(TBILL_3M, ret_lag_1)))",
38
+ "2012-2015": "sub(protected_div(protected_div(protected_div(0.0, ret_lag_1), ret_lag_5), mul(1.0, TBILL_3M)), mul(mul(sub(ret_lag_4, 0.1720736413168562), -0.44750184451610786), 0.0))",
39
+ "2013-2016": "add(sub(mul(DXY, add(ret_lag_5, ret_lag_1)), T10Y2Y), mul(sub(sub(DXY, ret_lag_1), 1.0), add(ret_lag_5, ret_lag_5)))",
40
+ "2014-2017": "add(protected_div(mul(ret_lag_5, ret_lag_3), ret_lag_2), add(protected_div(0.0, ret_lag_2), mul(protected_div(VIX, 0.5), 0.039797604362671324)))",
41
+ "2015-2018": "protected_div(add(mul(VIX, ret_lag_1), add(mul(DXY, ret_lag_1), protected_div(0.5, 1.0))), protected_div(TBILL_3M, protected_div(ret_lag_3, add(DXY, ret_lag_1))))",
42
+ "2016-2019": "add(add(protected_div(-0.15117420203950682, T10Y2Y), mul(T10Y2Y, VIX)), sub(protected_div(protected_div(-0.15117420203950682, T10Y2Y), protected_div(1.0, T10Y2Y)), sub(mul(1.0, TBILL_3M), add(ret_lag_2, ret_lag_2))))",
43
+ "2017-2020": "mul(add(0.8771686784817474, T10Y2Y), sub(VIX, sub(ret_lag_2, protected_div(0.5, ret_lag_4))))",
44
+ "2018-2021": "mul(add(ret_lag_5, add(add(ret_lag_5, ret_lag_5), TBILL_3M)), add(add(sub(T10Y2Y, TBILL_3M), T10Y2Y), T10Y2Y))",
45
+ "2019-2022": "mul(protected_div(mul(-0.4871820291561677, ret_lag_5), mul(ret_lag_2, 1.0)), protected_div(protected_div(DXY, ret_lag_5), protected_div(0.0, protected_div(ret_lag_2, ret_lag_5))))",
46
+ "2020-2023": "protected_div(mul(mul(add(ret_lag_5, TBILL_3M), 0.05832506730581244), mul(add(0.5, T10Y2Y), DXY)), protected_div(protected_div(0.0, ret_lag_1), mul(ret_lag_1, ret_lag_1)))",
47
+ "2021-2024": "sub(mul(add(protected_div(1.0, ret_lag_5), add(DXY, 0.06279813257176237)), T10Y2Y), protected_div(1.0, ret_lag_4))",
48
+ "2022-2025": "add(add(protected_div(sub(ret_lag_2, VIX), sub(0.5, T10Y2Y)), protected_div(mul(ret_lag_4, VIX), protected_div(ret_lag_3, 0.0))), T10Y2Y)"
49
+ }
50
+ },
51
+ "XLK": {
52
+ "formula": "add(mul(sub(ret_lag_4, 1.0), ret_lag_2), mul(ret_lag_3, add(mul(0.0, ret_lag_4), protected_div(ret_lag_2, TBILL_3M))))",
53
+ "consensus_votes": 1,
54
+ "total_windows": 15,
55
+ "percentage": 6.666666666666667,
56
+ "all_windows": {
57
+ "2008-2011": "add(mul(sub(ret_lag_4, 1.0), ret_lag_2), mul(ret_lag_3, add(mul(0.0, ret_lag_4), protected_div(ret_lag_2, TBILL_3M))))",
58
+ "2009-2012": "sub(add(1.0, 0.5), sub(T10Y2Y, mul(1.0, 0.0)))",
59
+ "2010-2013": "mul(sub(add(T10Y2Y, 0.5), sub(0.5, T10Y2Y)), 0.060176951765427145)",
60
+ "2011-2014": "add(mul(add(DXY, 0.5), ret_lag_3), add(T10Y2Y, mul(sub(0.0, ret_lag_4), sub(ret_lag_4, VIX))))",
61
+ "2012-2015": "protected_div(mul(add(ret_lag_1, mul(0.5608539386496569, 1.0)), 0.0), mul(TBILL_3M, protected_div(mul(VIX, ret_lag_5), protected_div(VIX, 1.0))))",
62
+ "2013-2016": "mul(add(mul(add(ret_lag_3, VIX), add(ret_lag_5, TBILL_3M)), sub(1.0, T10Y2Y)), sub(1.0, T10Y2Y))",
63
+ "2014-2017": "add(VIX, protected_div(protected_div(sub(TBILL_3M, 0.5), mul(ret_lag_5, T10Y2Y)), sub(sub(0.29078248846314225, 0.0), mul(TBILL_3M, VIX))))",
64
+ "2015-2018": "mul(sub(sub(DXY, add(1.0, ret_lag_4)), add(1.0, ret_lag_4)), mul(mul(ret_lag_1, ret_lag_4), add(DXY, 0.7010551841490229)))",
65
+ "2016-2019": "sub(add(sub(ret_lag_3, 0.5), add(mul(T10Y2Y, VIX), sub(T10Y2Y, 0.5))), TBILL_3M)",
66
+ "2017-2020": "sub(protected_div(sub(VIX, sub(DXY, VIX)), protected_div(add(ret_lag_2, 0.5), mul(0.5, ret_lag_2))), protected_div(DXY, ret_lag_5))",
67
+ "2018-2021": "mul(mul(ret_lag_2, T10Y2Y), sub(add(DXY, ret_lag_2), protected_div(DXY, ret_lag_4)))",
68
+ "2019-2022": "mul(protected_div(sub(1.0, mul(DXY, -0.16069920315400443)), sub(0.5, TBILL_3M)), add(add(0.5, TBILL_3M), protected_div(mul(ret_lag_2, 1.0), add(-0.16544419720823877, -0.20697937546758194))))",
69
+ "2020-2023": "add(mul(protected_div(DXY, protected_div(ret_lag_1, ret_lag_2)), add(0.5, TBILL_3M)), mul(add(ret_lag_2, VIX), add(DXY, ret_lag_2)))",
70
+ "2021-2024": "mul(sub(DXY, protected_div(add(0.7049583053574981, ret_lag_5), ret_lag_2)), add(T10Y2Y, ret_lag_5))",
71
+ "2022-2025": "sub(mul(mul(T10Y2Y, add(T10Y2Y, T10Y2Y)), mul(add(T10Y2Y, T10Y2Y), add(T10Y2Y, T10Y2Y))), sub(0.5608225047506836, T10Y2Y))"
72
+ }
73
+ },
74
+ "XLF": {
75
+ "formula": "mul(ret_lag_4, sub(sub(mul(VIX, ret_lag_2), add(ret_lag_3, 1.0)), 1.0))",
76
+ "consensus_votes": 1,
77
+ "total_windows": 15,
78
+ "percentage": 6.666666666666667,
79
+ "all_windows": {
80
+ "2008-2011": "mul(ret_lag_4, sub(sub(mul(VIX, ret_lag_2), add(ret_lag_3, 1.0)), 1.0))",
81
+ "2009-2012": "sub(0.9836473860346246, mul(add(ret_lag_3, add(TBILL_3M, ret_lag_1)), VIX))",
82
+ "2010-2013": "mul(sub(mul(VIX, ret_lag_2), add(-0.7878065501460205, VIX)), sub(mul(ret_lag_2, mul(TBILL_3M, 0.5)), mul(protected_div(ret_lag_3, ret_lag_3), mul(0.5, TBILL_3M))))",
83
+ "2011-2014": "add(1.0, protected_div(add(TBILL_3M, ret_lag_2), add(ret_lag_3, TBILL_3M)))",
84
+ "2012-2015": "protected_div(protected_div(protected_div(add(ret_lag_4, ret_lag_4), sub(TBILL_3M, T10Y2Y)), protected_div(ret_lag_5, mul(ret_lag_3, TBILL_3M))), add(TBILL_3M, TBILL_3M))",
85
+ "2013-2016": "mul(protected_div(mul(1.0, ret_lag_5), protected_div(ret_lag_4, 1.0)), mul(add(1.0, add(1.0, VIX)), protected_div(add(TBILL_3M, ret_lag_1), sub(0.5, ret_lag_2))))",
86
+ "2014-2017": "add(sub(add(TBILL_3M, protected_div(TBILL_3M, T10Y2Y)), T10Y2Y), sub(0.5, T10Y2Y))",
87
+ "2015-2018": "mul(sub(mul(DXY, VIX), protected_div(ret_lag_4, protected_div(DXY, 0.0))), protected_div(ret_lag_4, protected_div(add(TBILL_3M, 0.0), ret_lag_3)))",
88
+ "2016-2019": "sub(sub(DXY, protected_div(ret_lag_5, ret_lag_5)), protected_div(VIX, T10Y2Y))",
89
+ "2017-2020": "mul(add(mul(ret_lag_2, mul(ret_lag_1, ret_lag_2)), sub(ret_lag_3, ret_lag_1)), protected_div(sub(ret_lag_1, TBILL_3M), mul(ret_lag_5, ret_lag_5)))",
90
+ "2018-2021": "add(mul(sub(ret_lag_5, VIX), add(ret_lag_1, ret_lag_4)), protected_div(protected_div(protected_div(0.0, ret_lag_5), mul(ret_lag_4, ret_lag_4)), mul(ret_lag_4, sub(TBILL_3M, 0.0))))",
91
+ "2019-2022": "protected_div(mul(protected_div(protected_div(DXY, ret_lag_2), 0.0), sub(ret_lag_5, mul(ret_lag_5, TBILL_3M))), mul(add(ret_lag_5, ret_lag_4), sub(0.5, 1.0)))",
92
+ "2020-2023": "sub(mul(ret_lag_3, sub(VIX, mul(TBILL_3M, ret_lag_5))), protected_div(VIX, sub(protected_div(ret_lag_1, ret_lag_1), VIX)))",
93
+ "2021-2024": "add(protected_div(ret_lag_2, mul(ret_lag_2, T10Y2Y)), sub(VIX, sub(ret_lag_1, TBILL_3M)))",
94
+ "2022-2025": "add(sub(mul(protected_div(TBILL_3M, 0.5), ret_lag_1), protected_div(TBILL_3M, T10Y2Y)), protected_div(add(VIX, TBILL_3M), add(TBILL_3M, ret_lag_4)))"
95
+ }
96
+ },
97
+ "XLE": {
98
+ "formula": "sub(protected_div(protected_div(add(ret_lag_2, 0.9650889924405621), mul(DXY, ret_lag_3)), add(ret_lag_2, add(DXY, DXY))), add(add(sub(ret_lag_4, 1.0), protected_div(1.0, 0.0)), add(ret_lag_2, sub(ret_lag_2, ret_lag_3))))",
99
+ "consensus_votes": 1,
100
+ "total_windows": 15,
101
+ "percentage": 6.666666666666667,
102
+ "all_windows": {
103
+ "2008-2011": "sub(protected_div(protected_div(add(ret_lag_2, 0.9650889924405621), mul(DXY, ret_lag_3)), add(ret_lag_2, add(DXY, DXY))), add(add(sub(ret_lag_4, 1.0), protected_div(1.0, 0.0)), add(ret_lag_2, sub(ret_lag_2, ret_lag_3))))",
104
+ "2009-2012": "sub(mul(sub(ret_lag_5, DXY), mul(ret_lag_2, DXY)), sub(mul(add(T10Y2Y, ret_lag_2), mul(T10Y2Y, DXY)), sub(mul(ret_lag_3, 0.5), mul(TBILL_3M, ret_lag_5))))",
105
+ "2010-2013": "add(mul(ret_lag_3, add(VIX, ret_lag_5)), protected_div(protected_div(ret_lag_3, ret_lag_4), protected_div(T10Y2Y, ret_lag_5)))",
106
+ "2011-2014": "add(sub(mul(-0.0018674400129423674, mul(TBILL_3M, VIX)), mul(1.0, 0.5)), mul(1.0, mul(TBILL_3M, VIX)))",
107
+ "2012-2015": "mul(add(add(T10Y2Y, protected_div(0.0, TBILL_3M)), sub(TBILL_3M, TBILL_3M)), sub(sub(protected_div(0.0, TBILL_3M), add(0.0, ret_lag_4)), ret_lag_3))",
108
+ "2013-2016": "sub(mul(sub(0.5, ret_lag_3), sub(-0.66692693503364, 0.31090181363185065)), sub(mul(add(ret_lag_4, DXY), ret_lag_4), add(0.0, ret_lag_4)))",
109
+ "2014-2017": "mul(add(protected_div(sub(1.0, T10Y2Y), 0.5), sub(protected_div(0.0, DXY), mul(T10Y2Y, ret_lag_3))), add(TBILL_3M, sub(mul(ret_lag_2, TBILL_3M), protected_div(ret_lag_2, VIX))))",
110
+ "2015-2018": "protected_div(add(ret_lag_3, ret_lag_5), mul(mul(ret_lag_3, VIX), mul(DXY, ret_lag_1)))",
111
+ "2016-2019": "protected_div(protected_div(mul(add(0.5, T10Y2Y), mul(1.0, DXY)), mul(mul(-0.16462505562972596, DXY), add(ret_lag_5, ret_lag_5))), protected_div(add(T10Y2Y, mul(0.5, ret_lag_5)), protected_div(ret_lag_5, DXY)))",
112
+ "2017-2020": "add(mul(sub(0.08380699158459493, VIX), sub(ret_lag_5, ret_lag_3)), protected_div(sub(protected_div(ret_lag_3, VIX), VIX), VIX))",
113
+ "2018-2021": "add(sub(protected_div(1.0, add(ret_lag_5, ret_lag_1)), 0.5), add(protected_div(VIX, 0.5), VIX))",
114
+ "2019-2022": "sub(sub(protected_div(sub(0.5, 0.5), sub(ret_lag_4, TBILL_3M)), mul(mul(0.27966189180376744, ret_lag_2), TBILL_3M)), protected_div(mul(add(ret_lag_2, VIX), mul(T10Y2Y, VIX)), mul(sub(VIX, T10Y2Y), sub(TBILL_3M, 1.0))))",
115
+ "2020-2023": "add(mul(DXY, sub(0.5, ret_lag_3)), protected_div(T10Y2Y, ret_lag_4))",
116
+ "2021-2024": "sub(mul(T10Y2Y, VIX), protected_div(1.0, add(mul(T10Y2Y, VIX), 1.0)))",
117
+ "2022-2025": "mul(sub(mul(-0.7188441119983029, ret_lag_5), DXY), protected_div(protected_div(protected_div(0.02603630160338355, DXY), 1.0), add(ret_lag_3, ret_lag_2)))"
118
+ }
119
+ },
120
+ "XLV": {
121
+ "formula": "sub(protected_div(mul(ret_lag_1, -0.507102997156381), protected_div(TBILL_3M, 1.0)), add(sub(T10Y2Y, 0.17659846192263662), mul(ret_lag_2, DXY)))",
122
+ "consensus_votes": 1,
123
+ "total_windows": 15,
124
+ "percentage": 6.666666666666667,
125
+ "all_windows": {
126
+ "2008-2011": "sub(protected_div(mul(ret_lag_1, -0.507102997156381), protected_div(TBILL_3M, 1.0)), add(sub(T10Y2Y, 0.17659846192263662), mul(ret_lag_2, DXY)))",
127
+ "2009-2012": "protected_div(sub(sub(VIX, protected_div(ret_lag_2, ret_lag_5)), add(VIX, 0.0)), protected_div(0.0, ret_lag_1))",
128
+ "2010-2013": "add(mul(DXY, protected_div(0.5, sub(T10Y2Y, ret_lag_1))), add(mul(protected_div(0.12710480091394483, ret_lag_3), 1.0), sub(1.0, 0.5)))",
129
+ "2011-2014": "protected_div(protected_div(ret_lag_4, mul(protected_div(ret_lag_2, T10Y2Y), mul(ret_lag_4, TBILL_3M))), add(mul(TBILL_3M, ret_lag_4), 0.0))",
130
+ "2012-2015": "protected_div(VIX, add(mul(protected_div(DXY, TBILL_3M), ret_lag_2), protected_div(add(ret_lag_2, DXY), TBILL_3M)))",
131
+ "2013-2016": "protected_div(protected_div(protected_div(0.5821378270873245, ret_lag_4), T10Y2Y), protected_div(protected_div(0.5, add(ret_lag_5, ret_lag_5)), ret_lag_4))",
132
+ "2014-2017": "protected_div(sub(add(add(-0.30093141038791016, 0.5), protected_div(ret_lag_1, 0.0)), T10Y2Y), sub(1.0, T10Y2Y))",
133
+ "2015-2018": "protected_div(0.0, mul(mul(mul(ret_lag_5, 0.5), 0.5), mul(protected_div(0.5, ret_lag_1), ret_lag_5)))",
134
+ "2016-2019": "sub(sub(VIX, protected_div(TBILL_3M, T10Y2Y)), protected_div(TBILL_3M, 0.5))",
135
+ "2017-2020": "protected_div(add(add(add(0.07010471536598595, ret_lag_3), add(0.07010471536598595, ret_lag_4)), ret_lag_3), add(0.07010471536598595, ret_lag_4))",
136
+ "2018-2021": "mul(sub(DXY, mul(add(ret_lag_3, VIX), protected_div(0.5, 0.0))), sub(DXY, add(mul(DXY, T10Y2Y), 0.5)))",
137
+ "2019-2022": "add(T10Y2Y, protected_div(protected_div(-0.4647599301594385, ret_lag_2), ret_lag_2))",
138
+ "2020-2023": "add(protected_div(VIX, T10Y2Y), add(add(DXY, T10Y2Y), sub(0.23757916443042015, 0.0)))",
139
+ "2021-2024": "protected_div(sub(VIX, protected_div(TBILL_3M, T10Y2Y)), protected_div(1.0, mul(1.0, 0.0)))",
140
+ "2022-2025": "sub(mul(T10Y2Y, T10Y2Y), sub(mul(VIX, ret_lag_3), mul(T10Y2Y, mul(T10Y2Y, T10Y2Y))))"
141
+ }
142
+ },
143
+ "XLI": {
144
+ "formula": "mul(sub(sub(0.5, mul(ret_lag_3, VIX)), 0.0), sub(mul(ret_lag_2, mul(ret_lag_2, VIX)), mul(ret_lag_2, 1.0)))",
145
+ "consensus_votes": 1,
146
+ "total_windows": 15,
147
+ "percentage": 6.666666666666667,
148
+ "all_windows": {
149
+ "2008-2011": "mul(sub(sub(0.5, mul(ret_lag_3, VIX)), 0.0), sub(mul(ret_lag_2, mul(ret_lag_2, VIX)), mul(ret_lag_2, 1.0)))",
150
+ "2009-2012": "sub(add(sub(add(T10Y2Y, TBILL_3M), T10Y2Y), sub(protected_div(ret_lag_5, ret_lag_3), sub(ret_lag_4, ret_lag_2))), protected_div(add(mul(ret_lag_5, 0.5), mul(TBILL_3M, TBILL_3M)), protected_div(protected_div(0.1872780126839768, DXY), sub(0.5, ret_lag_5))))",
151
+ "2010-2013": "sub(TBILL_3M, add(add(sub(1.0, T10Y2Y), mul(VIX, ret_lag_2)), 1.0))",
152
+ "2011-2014": "mul(protected_div(add(T10Y2Y, 0.5), add(0.0, ret_lag_3)), sub(add(ret_lag_1, DXY), protected_div(1.0, ret_lag_1)))",
153
+ "2012-2015": "protected_div(protected_div(0.0, 1.0), mul(TBILL_3M, sub(ret_lag_1, TBILL_3M)))",
154
+ "2013-2016": "mul(protected_div(ret_lag_5, protected_div(ret_lag_4, ret_lag_1)), add(mul(protected_div(ret_lag_4, ret_lag_1), mul(VIX, 1.0)), VIX))",
155
+ "2014-2017": "sub(sub(add(sub(0.9553260076238788, T10Y2Y), TBILL_3M), sub(T10Y2Y, ret_lag_4)), sub(sub(0.9553260076238788, add(ret_lag_1, 1.0)), TBILL_3M))",
156
+ "2015-2018": "protected_div(protected_div(0.0, mul(ret_lag_1, ret_lag_5)), sub(mul(ret_lag_5, protected_div(ret_lag_4, ret_lag_3)), ret_lag_5))",
157
+ "2016-2019": "add(mul(sub(DXY, protected_div(T10Y2Y, TBILL_3M)), protected_div(T10Y2Y, TBILL_3M)), sub(mul(TBILL_3M, 0.5586056894016409), protected_div(TBILL_3M, T10Y2Y)))",
158
+ "2017-2020": "add(protected_div(-0.28770944395383125, sub(add(T10Y2Y, ret_lag_5), 0.5)), mul(mul(protected_div(1.0, VIX), 1.0), protected_div(0.0, T10Y2Y)))",
159
+ "2018-2021": "mul(add(mul(add(T10Y2Y, ret_lag_5), sub(ret_lag_5, 0.5)), 0.5), mul(sub(mul(ret_lag_5, VIX), mul(VIX, TBILL_3M)), sub(sub(ret_lag_5, 0.5), ret_lag_1)))",
160
+ "2019-2022": "protected_div(sub(protected_div(1.0, TBILL_3M), sub(TBILL_3M, ret_lag_1)), sub(protected_div(ret_lag_2, ret_lag_5), ret_lag_2))",
161
+ "2020-2023": "add(mul(add(DXY, DXY), protected_div(protected_div(ret_lag_5, -0.22848851339885634), protected_div(0.0, ret_lag_4))), add(0.9585947339608321, sub(TBILL_3M, sub(DXY, DXY))))",
162
+ "2021-2024": "protected_div(sub(sub(ret_lag_2, 0.40339010458146674), ret_lag_3), mul(DXY, protected_div(protected_div(0.0, T10Y2Y), ret_lag_1)))",
163
+ "2022-2025": "add(ret_lag_5, sub(mul(T10Y2Y, TBILL_3M), protected_div(0.5, T10Y2Y)))"
164
+ }
165
+ },
166
+ "XLY": {
167
+ "formula": "mul(mul(mul(0.5, add(0.5, 1.0)), 1.0), sub(ret_lag_1, mul(ret_lag_2, VIX)))",
168
+ "consensus_votes": 1,
169
+ "total_windows": 15,
170
+ "percentage": 6.666666666666667,
171
+ "all_windows": {
172
+ "2008-2011": "mul(mul(mul(0.5, add(0.5, 1.0)), 1.0), sub(ret_lag_1, mul(ret_lag_2, VIX)))",
173
+ "2009-2012": "add(sub(1.0, 0.5), protected_div(sub(ret_lag_2, T10Y2Y), add(ret_lag_2, add(ret_lag_3, ret_lag_4))))",
174
+ "2010-2013": "protected_div(0.5, sub(add(protected_div(ret_lag_4, T10Y2Y), T10Y2Y), add(add(1.0, 0.5), sub(0.5723921915934733, ret_lag_4))))",
175
+ "2011-2014": "protected_div(protected_div(add(sub(0.0, TBILL_3M), 0.5), T10Y2Y), sub(T10Y2Y, add(0.0, 1.0)))",
176
+ "2012-2015": "sub(mul(sub(add(ret_lag_4, ret_lag_4), 1.0), add(ret_lag_1, add(ret_lag_4, ret_lag_4))), mul(ret_lag_2, 1.0))",
177
+ "2013-2016": "sub(add(add(sub(ret_lag_4, ret_lag_4), add(T10Y2Y, VIX)), T10Y2Y), sub(protected_div(-0.8859804631629291, mul(VIX, ret_lag_4)), VIX))",
178
+ "2014-2017": "add(sub(0.5, T10Y2Y), protected_div(sub(sub(TBILL_3M, 0.3526465385591284), ret_lag_3), protected_div(T10Y2Y, sub(TBILL_3M, 0.3526465385591284))))",
179
+ "2015-2018": "add(sub(protected_div(VIX, 0.5), mul(DXY, 0.5)), add(-0.4466050060902327, sub(sub(0.5, ret_lag_4), TBILL_3M)))",
180
+ "2016-2019": "add(protected_div(TBILL_3M, sub(-0.8248675648153927, ret_lag_4)), add(mul(T10Y2Y, VIX), protected_div(ret_lag_1, 1.0)))",
181
+ "2017-2020": "sub(add(mul(VIX, ret_lag_1), mul(TBILL_3M, VIX)), mul(add(1.0, VIX), mul(add(T10Y2Y, 1.0), ret_lag_5)))",
182
+ "2018-2021": "sub(T10Y2Y, add(sub(TBILL_3M, ret_lag_5), protected_div(0.0, mul(ret_lag_5, ret_lag_2))))",
183
+ "2019-2022": "sub(sub(T10Y2Y, add(mul(0.5, ret_lag_2), VIX)), protected_div(protected_div(protected_div(ret_lag_3, T10Y2Y), TBILL_3M), ret_lag_4))",
184
+ "2020-2023": "sub(add(protected_div(add(ret_lag_4, TBILL_3M), add(T10Y2Y, 0.557831529499391)), TBILL_3M), protected_div(T10Y2Y, ret_lag_4))",
185
+ "2021-2024": "add(sub(sub(VIX, T10Y2Y), mul(0.5, DXY)), protected_div(add(TBILL_3M, 1.0), T10Y2Y))",
186
+ "2022-2025": "sub(-0.27238362381682557, sub(sub(sub(ret_lag_2, T10Y2Y), -0.48353514726267455), T10Y2Y))"
187
+ }
188
+ },
189
+ "XLP": {
190
+ "formula": "add(mul(add(protected_div(1.0, -0.8099664170732903), mul(ret_lag_2, DXY)), mul(ret_lag_2, DXY)), add(0.5, sub(mul(ret_lag_2, DXY), T10Y2Y)))",
191
+ "consensus_votes": 1,
192
+ "total_windows": 15,
193
+ "percentage": 6.666666666666667,
194
+ "all_windows": {
195
+ "2008-2011": "add(mul(add(protected_div(1.0, -0.8099664170732903), mul(ret_lag_2, DXY)), mul(ret_lag_2, DXY)), add(0.5, sub(mul(ret_lag_2, DXY), T10Y2Y)))",
196
+ "2009-2012": "mul(add(mul(0.0, ret_lag_5), mul(DXY, ret_lag_2)), protected_div(protected_div(0.5, ret_lag_1), protected_div(0.9268774733035168, ret_lag_4)))",
197
+ "2010-2013": "add(VIX, protected_div(protected_div(ret_lag_2, 0.5), ret_lag_5))",
198
+ "2011-2014": "add(sub(protected_div(ret_lag_4, 0.20999912483555794), mul(TBILL_3M, T10Y2Y)), protected_div(-0.6522952275011717, add(mul(VIX, ret_lag_2), sub(-0.3021880606321481, ret_lag_4))))",
199
+ "2012-2015": "protected_div(mul(DXY, protected_div(1.0, TBILL_3M)), protected_div(protected_div(protected_div(1.0, TBILL_3M), ret_lag_5), TBILL_3M))",
200
+ "2013-2016": "mul(add(1.0, 1.0), sub(T10Y2Y, 1.0))",
201
+ "2014-2017": "sub(sub(mul(TBILL_3M, 0.5), T10Y2Y), sub(0.5, protected_div(add(0.5, ret_lag_1), T10Y2Y)))",
202
+ "2015-2018": "sub(add(add(DXY, VIX), protected_div(protected_div(T10Y2Y, ret_lag_1), VIX)), sub(protected_div(VIX, T10Y2Y), sub(mul(ret_lag_5, VIX), ret_lag_5)))",
203
+ "2016-2019": "add(protected_div(TBILL_3M, protected_div(add(TBILL_3M, ret_lag_5), -0.5238399993979941)), TBILL_3M)",
204
+ "2017-2020": "add(sub(protected_div(ret_lag_5, ret_lag_4), mul(ret_lag_2, -0.5500654126181095)), sub(sub(protected_div(ret_lag_5, ret_lag_4), 0.8305755650064102), ret_lag_1))",
205
+ "2018-2021": "sub(add(TBILL_3M, 1.0), mul(mul(T10Y2Y, T10Y2Y), mul(add(TBILL_3M, 1.0), T10Y2Y)))",
206
+ "2019-2022": "sub(protected_div(sub(TBILL_3M, 1.0), sub(ret_lag_3, TBILL_3M)), protected_div(ret_lag_1, TBILL_3M))",
207
+ "2020-2023": "sub(sub(add(ret_lag_4, add(ret_lag_4, VIX)), add(ret_lag_4, 0.5)), add(protected_div(ret_lag_2, ret_lag_4), protected_div(ret_lag_3, ret_lag_2)))",
208
+ "2021-2024": "add(sub(protected_div(1.0, 1.0), add(sub(0.0, DXY), protected_div(DXY, T10Y2Y))), protected_div(sub(0.0, 0.5), add(mul(VIX, ret_lag_4), ret_lag_1)))",
209
+ "2022-2025": "sub(sub(mul(VIX, ret_lag_2), mul(DXY, ret_lag_3)), add(protected_div(ret_lag_1, -0.42446392574877234), protected_div(1.0, VIX)))"
210
+ }
211
+ },
212
+ "XLU": {
213
+ "formula": "sub(mul(protected_div(ret_lag_5, TBILL_3M), add(ret_lag_4, ret_lag_4)), add(ret_lag_2, add(ret_lag_4, ret_lag_4)))",
214
+ "consensus_votes": 1,
215
+ "total_windows": 15,
216
+ "percentage": 6.666666666666667,
217
+ "all_windows": {
218
+ "2008-2011": "sub(mul(protected_div(ret_lag_5, TBILL_3M), add(ret_lag_4, ret_lag_4)), add(ret_lag_2, add(ret_lag_4, ret_lag_4)))",
219
+ "2009-2012": "protected_div(protected_div(sub(ret_lag_1, T10Y2Y), 0.0), mul(add(add(ret_lag_5, ret_lag_2), mul(ret_lag_1, ret_lag_4)), mul(add(VIX, T10Y2Y), protected_div(0.0, ret_lag_1))))",
220
+ "2010-2013": "add(mul(T10Y2Y, protected_div(0.0, ret_lag_2)), protected_div(0.0, ret_lag_3))",
221
+ "2011-2014": "sub(protected_div(0.0, ret_lag_1), mul(mul(sub(VIX, DXY), protected_div(ret_lag_1, ret_lag_4)), mul(protected_div(1.0, VIX), ret_lag_5)))",
222
+ "2012-2015": "mul(protected_div(ret_lag_1, add(ret_lag_1, TBILL_3M)), protected_div(ret_lag_2, mul(0.5, 1.0)))",
223
+ "2013-2016": "protected_div(mul(mul(ret_lag_3, mul(VIX, T10Y2Y)), mul(ret_lag_3, 0.5)), protected_div(sub(TBILL_3M, 0.5), add(TBILL_3M, VIX)))",
224
+ "2014-2017": "sub(sub(T10Y2Y, sub(TBILL_3M, TBILL_3M)), sub(sub(add(TBILL_3M, ret_lag_1), protected_div(0.0, ret_lag_3)), T10Y2Y))",
225
+ "2015-2018": "add(add(mul(mul(1.0, ret_lag_5), add(T10Y2Y, DXY)), sub(sub(0.5, 0.5), 1.0)), mul(mul(1.0, ret_lag_5), add(-0.42602776224488537, DXY)))",
226
+ "2016-2019": "add(protected_div(ret_lag_2, ret_lag_5), add(VIX, T10Y2Y))",
227
+ "2017-2020": "protected_div(sub(add(ret_lag_4, sub(ret_lag_2, ret_lag_2)), sub(protected_div(TBILL_3M, -0.060163192259545584), protected_div(ret_lag_5, VIX))), sub(0.5, T10Y2Y))",
228
+ "2018-2021": "sub(protected_div(TBILL_3M, DXY), sub(T10Y2Y, protected_div(protected_div(T10Y2Y, T10Y2Y), sub(1.0, T10Y2Y))))",
229
+ "2019-2022": "add(sub(protected_div(ret_lag_1, mul(ret_lag_1, ret_lag_2)), mul(0.0, ret_lag_2)), sub(protected_div(ret_lag_1, mul(ret_lag_3, ret_lag_2)), ret_lag_5))",
230
+ "2020-2023": "add(add(1.0, add(add(ret_lag_2, T10Y2Y), T10Y2Y)), add(add(1.0, add(0.0, T10Y2Y)), T10Y2Y))",
231
+ "2021-2024": "sub(protected_div(TBILL_3M, add(1.0, sub(0.0, ret_lag_3))), mul(mul(add(1.0, TBILL_3M), TBILL_3M), mul(T10Y2Y, T10Y2Y)))",
232
+ "2022-2025": "sub(add(add(protected_div(ret_lag_1, ret_lag_3), ret_lag_4), protected_div(0.0, 0.5)), add(add(1.0, ret_lag_3), mul(ret_lag_1, DXY)))"
233
+ }
234
+ }
235
+ }
236
+ }
237
+ }