Regime characterisation — Tier 1¶

Replayed 4278 trading days, 2009-09-18 .. 2026-09-22. 4231 carry both a regime label and a forward outcome.

excluded, no forward outcome (last 30 trading days): 27
excluded, no regime label (fail-closed days, kept in features.jsonl): 20

Outcome is vrp_realised = vix_t/100 - rv_fwd_30: positive means implied exceeded what was realised.

By raw regime label¶

group	n	mean	median	p10	p25	p75	p90	hit rate	worst
`calm-backwardation-vrp+` ⚠ thin	1	0.1005	0.1005	0.1005	0.1005	0.1005	0.1005	1.0	0.1005
`calm-contango-vrp+`	1503	0.0227	0.0386	-0.0383	0.0116	0.0571	0.0738	0.804	-0.6517
`calm-contango-vrp-`	1242	0.0288	0.0354	-0.0055	0.0169	0.0533	0.0681	0.878	-0.2622
`calm-flat-vrp+`	201	0.0206	0.0539	-0.0645	-0.002	0.0759	0.0892	0.746	-0.6279
`calm-flat-vrp-` ⚠ thin	23	0.038	0.0677	-0.0227	0.0454	0.0773	0.0803	0.87	-0.2185
`normal-backwardation-vrp+`	44	0.0117	0.0648	-0.1714	0.0146	0.1192	0.1391	0.818	-0.5645
`normal-contango-vrp+`	489	0.0662	0.0689	0.0028	0.0397	0.1021	0.1232	0.912	-0.0991
`normal-contango-vrp-`	156	0.0534	0.052	-0.0195	0.0307	0.0983	0.1146	0.885	-0.117
`normal-flat-vrp+`	293	0.0511	0.0767	-0.0484	0.0251	0.1031	0.1256	0.833	-0.2303
`normal-flat-vrp-`	38	0.0482	0.0587	-0.0093	0.0142	0.0945	0.1138	0.868	-0.1907
`stressed-backwardation-vrp+`	41	0.0517	0.1311	-0.3917	0.0719	0.1753	0.2104	0.78	-0.4669
`stressed-backwardation-vrp-` ⚠ thin	15	0.0797	0.1077	0.0109	0.0195	0.171	0.2314	0.933	-0.4703
`stressed-contango-vrp+`	36	0.1102	0.114	0.0385	0.0629	0.1606	0.1754	0.972	-0.007
`stressed-contango-vrp-` ⚠ thin	1	0.0339	0.0339	0.0339	0.0339	0.0339	0.0339	1.0	0.0339
`stressed-flat-vrp+`	132	0.0954	0.0889	0.0244	0.0576	0.1294	0.1585	1.0	0.0069
`stressed-flat-vrp-` ⚠ thin	16	0.0896	0.0738	0.0237	0.0367	0.1404	0.1695	1.0	0.0112

By ex-ante VRP size (vol points)¶

group	n	mean	median	p10	p25	p75	p90	hit rate	worst
`[-inf, 0)`	1485	0.0331	0.0375	-0.0056	0.0188	0.057	0.0811	0.879	-0.4703
`[0, 1)`	610	0.0313	0.0416	-0.0247	0.0195	0.0611	0.083	0.849	-0.6354
`[1, 2)`	555	0.024	0.0407	-0.0459	0.0108	0.0631	0.0895	0.813	-0.6464
`[2, 3)`	457	0.0319	0.0451	-0.0378	0.0136	0.069	0.0951	0.792	-0.6517
`[3, 4)`	331	0.0387	0.0539	-0.0264	0.0237	0.0772	0.1039	0.813	-0.6426
`[4, 6)`	385	0.0392	0.0573	-0.0332	0.0124	0.0817	0.1041	0.808	-0.6279
`[6, inf)`	408	0.0746	0.0821	0.0146	0.0497	0.1207	0.1585	0.929	-0.5645

By regime x VRP bucket¶

group	n	mean	median	p10	p25	p75	p90	hit rate	worst
`calm-backwardation-vrp+ \| [1, 2)` ⚠ thin	1	0.1005	0.1005	0.1005	0.1005	0.1005	0.1005	1.0	0.1005
`calm-contango-vrp+ \| [0, 1)`	477	0.0265	0.0373	-0.0167	0.0199	0.0538	0.0701	0.862	-0.6354
`calm-contango-vrp+ \| [1, 2)`	410	0.0178	0.0376	-0.0443	0.0101	0.056	0.0718	0.81	-0.6464
`calm-contango-vrp+ \| [2, 3)`	312	0.0187	0.0399	-0.0508	0.0064	0.0559	0.0745	0.763	-0.6517
`calm-contango-vrp+ \| [3, 4)`	169	0.0267	0.0449	-0.035	0.0053	0.0664	0.0806	0.757	-0.6426
`calm-contango-vrp+ \| [4, 6)`	120	0.0293	0.0461	-0.0339	-0.0016	0.0613	0.0794	0.742	-0.113
`calm-contango-vrp+ \| [6, inf)` ⚠ thin	15	0.0244	0.022	-0.0214	-0.0167	0.0679	0.073	0.667	-0.0337
`calm-contango-vrp- \| [-inf, 0)`	1239	0.0288	0.0354	-0.0056	0.0169	0.0533	0.0683	0.877	-0.2622
`calm-contango-vrp- \| [0, 1)` ⚠ thin	3	0.0326	0.0283	0.0091	0.0091	0.0602	0.0602	1.0	0.0091
`calm-flat-vrp+ \| [0, 1)` ⚠ thin	16	0.0133	0.057	-0.2346	-0.0227	0.077	0.0809	0.688	-0.2377
`calm-flat-vrp+ \| [1, 2)` ⚠ thin	26	0.0263	0.0536	0.0037	0.034	0.071	0.0948	0.923	-0.5363
`calm-flat-vrp+ \| [2, 3)`	31	0.0361	0.0414	-0.0216	-0.002	0.0671	0.0863	0.71	-0.0542
`calm-flat-vrp+ \| [3, 4)`	40	0.0309	0.0571	-0.0172	0.0371	0.0717	0.0969	0.825	-0.3611
`calm-flat-vrp+ \| [4, 6)`	63	-0.0067	0.0497	-0.105	-0.0198	0.0762	0.0869	0.603	-0.6279
`calm-flat-vrp+ \| [6, inf)` ⚠ thin	25	0.0527	0.0687	-0.0221	0.0472	0.0782	0.0909	0.88	-0.0892
`calm-flat-vrp- \| [-inf, 0)` ⚠ thin	23	0.038	0.0677	-0.0227	0.0454	0.0773	0.0803	0.87	-0.2185
`normal-backwardation-vrp+ \| [1, 2)` ⚠ thin	3	0.0183	0.0893	-0.1714	-0.1714	0.1371	0.1371	0.667	-0.1714
`normal-backwardation-vrp+ \| [2, 3)` ⚠ thin	3	0.0104	0.1018	-0.1875	-0.1875	0.1168	0.1168	0.667	-0.1875
`normal-backwardation-vrp+ \| [3, 4)` ⚠ thin	2	-0.0293	-0.0293	-0.1709	-0.1709	0.1123	0.1123	0.5	-0.1709
`normal-backwardation-vrp+ \| [4, 6)` ⚠ thin	7	0.042	0.0334	0.0095	0.0182	0.0694	0.0951	1.0	0.0095
`normal-backwardation-vrp+ \| [6, inf)` ⚠ thin	29	0.0067	0.0666	-0.5314	0.0146	0.1207	0.1462	0.828	-0.5645
`normal-contango-vrp+ \| [0, 1)`	76	0.0627	0.0647	-0.0162	0.0409	0.1054	0.1174	0.842	-0.097
`normal-contango-vrp+ \| [1, 2)`	83	0.0442	0.0605	-0.0435	0.0037	0.0986	0.1166	0.783	-0.0991
`normal-contango-vrp+ \| [2, 3)`	83	0.0741	0.0752	0.0113	0.0505	0.1151	0.1309	0.928	-0.0637
`normal-contango-vrp+ \| [3, 4)`	75	0.0652	0.062	0.0065	0.0383	0.1007	0.1244	0.933	-0.0657
`normal-contango-vrp+ \| [4, 6)`	97	0.0731	0.0776	0.0319	0.0557	0.0951	0.1161	0.99	-0.029
`normal-contango-vrp+ \| [6, inf)`	75	0.0776	0.0678	0.0238	0.0386	0.1092	0.1606	0.987	-0.0198
`normal-contango-vrp- \| [-inf, 0)`	155	0.0537	0.052	-0.0195	0.0307	0.0983	0.1146	0.884	-0.117
`normal-contango-vrp- \| [0, 1)` ⚠ thin	1	0.0032	0.0032	0.0032	0.0032	0.0032	0.0032	1.0	0.0032
`normal-flat-vrp+ \| [0, 1)` ⚠ thin	26	0.0186	0.0616	-0.1987	-0.0025	0.083	0.1315	0.731	-0.2303
`normal-flat-vrp+ \| [1, 2)` ⚠ thin	24	0.0499	0.0889	-0.1867	0.0508	0.1237	0.1488	0.833	-0.2179
`normal-flat-vrp+ \| [2, 3)` ⚠ thin	19	0.0463	0.0784	-0.1861	0.0136	0.0978	0.1411	0.789	-0.2224
`normal-flat-vrp+ \| [3, 4)`	32	0.0519	0.0755	-0.0468	0.03	0.1051	0.1321	0.781	-0.2212
`normal-flat-vrp+ \| [4, 6)`	67	0.0336	0.0566	-0.0742	0.001	0.0979	0.1242	0.761	-0.2236
`normal-flat-vrp+ \| [6, inf)`	125	0.0679	0.0816	0.0052	0.0507	0.107	0.1235	0.912	-0.2214
`normal-flat-vrp- \| [-inf, 0)`	36	0.0438	0.0563	-0.0093	0.0142	0.0923	0.103	0.861	-0.1907
`normal-flat-vrp- \| [0, 1)` ⚠ thin	2	0.1263	0.1263	0.0992	0.0992	0.1535	0.1535	1.0	0.0992
`stressed-backwardation-vrp+ \| [0, 1)` ⚠ thin	6	0.0669	0.1217	-0.0821	-0.0797	0.1402	0.1799	0.667	-0.0821
`stressed-backwardation-vrp+ \| [1, 2)` ⚠ thin	2	-0.1343	-0.1343	-0.3917	-0.3917	0.1232	0.1232	0.5	-0.3917
`stressed-backwardation-vrp+ \| [3, 4)` ⚠ thin	2	-0.1511	-0.1511	-0.4669	-0.4669	0.1647	0.1647	0.5	-0.4669
`stressed-backwardation-vrp+ \| [4, 6)` ⚠ thin	3	0.0527	0.0376	-0.1137	-0.1137	0.2344	0.2344	0.667	-0.1137
`stressed-backwardation-vrp+ \| [6, inf)` ⚠ thin	28	0.0761	0.1454	-0.405	0.1061	0.1826	0.216	0.857	-0.4309
`stressed-backwardation-vrp- \| [-inf, 0)` ⚠ thin	15	0.0797	0.1077	0.0109	0.0195	0.171	0.2314	0.933	-0.4703
`stressed-contango-vrp+ \| [2, 3)` ⚠ thin	2	0.028	0.028	-0.007	-0.007	0.0629	0.0629	0.5	-0.007
`stressed-contango-vrp+ \| [3, 4)` ⚠ thin	3	0.1174	0.1267	0.0385	0.0385	0.1871	0.1871	1.0	0.0385
`stressed-contango-vrp+ \| [4, 6)` ⚠ thin	6	0.0989	0.1032	0.0136	0.0329	0.1693	0.1713	1.0	0.0136
`stressed-contango-vrp+ \| [6, inf)` ⚠ thin	25	0.1187	0.1207	0.049	0.0882	0.1491	0.1754	1.0	0.0429
`stressed-contango-vrp- \| [-inf, 0)` ⚠ thin	1	0.0339	0.0339	0.0339	0.0339	0.0339	0.0339	1.0	0.0339
`stressed-flat-vrp+ \| [0, 1)` ⚠ thin	3	0.069	0.049	0.0481	0.0481	0.11	0.11	1.0	0.0481
`stressed-flat-vrp+ \| [1, 2)` ⚠ thin	6	0.0951	0.0726	0.0206	0.0553	0.1177	0.232	1.0	0.0206
`stressed-flat-vrp+ \| [2, 3)` ⚠ thin	7	0.0743	0.0689	0.007	0.0357	0.1199	0.1382	1.0	0.007
`stressed-flat-vrp+ \| [3, 4)` ⚠ thin	8	0.0666	0.0573	0.023	0.0464	0.094	0.1488	1.0	0.023
`stressed-flat-vrp+ \| [4, 6)` ⚠ thin	22	0.0737	0.074	0.0244	0.0498	0.0987	0.1177	1.0	0.0103
`stressed-flat-vrp+ \| [6, inf)`	86	0.1062	0.103	0.0326	0.0678	0.142	0.182	1.0	0.0069
`stressed-flat-vrp- \| [-inf, 0)` ⚠ thin	16	0.0896	0.0738	0.0237	0.0367	0.1404	0.1695	1.0	0.0112

Transition vs settled¶

group	n	mean	median	p10	p25	p75	p90	hit rate	worst
`settled`	2001	0.0304	0.0387	-0.0294	0.014	0.0611	0.0872	0.825	-0.6517
`transition`	2230	0.042	0.0491	-0.0142	0.0233	0.0774	0.1095	0.872	-0.6354

Limitations — these bound every number above¶

One underlying. Forward realised vol is SPY's. Seventeen years of a single correlated series is one sample, not N independent ones. Effective sample size is far below the row counts; treat n as an upper bound on evidence, not a measure of it.
Post-2008 sample. VIX3M's Cboe history starts 2009-09-18, so 2008 is excluded. Later stress (2010, 2011, 2015, 2018, 2020, 2022) is present but the stressed-day count is small relative to calm.
VIX is the IV30 proxy. VRP uses the production proxy, carrying the same caveat the live records carry. When canonical IV30 arrives the level shifts systematically by an estimated 1-2 vol points and every conclusion about theta here must be recomputed.
No data-outage incidence. FRED's archive is complete for past dates, so the replay sees timely data on days that may in reality have been late. This measures what the gate would have done GIVEN timely inputs, not how often inputs arrived.
Tier 2 is blocked. Nothing here speaks to EV, edge, or ladder quality: that needs historical option chains we do not have.