Futures Hedges under Basis Heteroscedasticity

Table 1

Simulation results.

Simulation	Number of	Input parameters						Simulation statistics		Equation (4)		Equation (5)		Difference	Difference
no.	obs.	𝐸(𝑆1)	𝜎(𝑆1)	𝐸(𝑒)	𝜎(𝑒)	𝐸(𝜀)	𝜎(𝜀)	𝜌(𝑆1,𝑒)	𝜌(𝑆1,𝜀)	𝑥^∗	𝜎^2(𝑊)	𝑥^∗	𝜎^2(𝑊)	in 𝑥^∗	in 𝜎^2(𝑊)
l	100,000	1.0	1.0	0.0	0.5	0.0	0.5	0.0005	0.0093	0.6656	0.3336	0.8027	0.3617	0.1371	0.0282
2	100,000	1.0	1.0	0.0	1.0	0.0	1.0	−0.0014	0.0053	0.3355	0.6681	0.5035	0.7527	0.1680	0.0845
3	100,000	1.0	1.0	0.0	1.5	0.0	1.5	0.0026	0.0024	0.1802	0.8197	0.3075	0.9096	0.1273	0.0900
4	100,000	1.0	1.0	0.0	2.0	0.0	2.0	−0.0003	−0.0009	0.1109	0.8863	0.2006	0.9587	0.0897	0.0723
5	100,000	1.0	1.0	0.0	2.5	0.0	2.5	−0.0040	−0.0035	0.0741	0.9272	0.1381	0.9827	0.0640	0.0555
6	100,000	2.0	1.5	0.0	0.5	0.0	0.5	0.0015	0.0052	0.5903	0.9211	0.9017	1.2903	0.3113	0.3691
7	100,000	2.0	1.5	0.0	1.0	0.0	1.0	0.0043	−0.0005	0.2659	1.6603	0.6939	3.2182	0.4280	1.5578
8	100,000	2.0	1.5	0.0	1.5	0.0	1.5	−0.0045	−0.0001	0.1392	1.9379	0.4991	4.0324	0.3599	2.0945
9	100,000	2.0	1.5	0.0	2.0	0.0	2.0	0.0027	−0.0041	0.0831	2.0833	0.3643	4.2470	0.2813	2.1637
10	100,000	2.0	1.5	0.0	2.5	0.0	2.5	0.0011	0.0053	0.0543	2.1330	0.2647	3.9708	0.2104	1.8378
11	100,000	3.0	2.0	0.0	0.5	0.0	0.5	−0.0021	−0.0044	0.5513	1.8066	0.9403	2.9120	0.3891	1.1054
12	100,000	3.0	2.0	0.0	1.0	0.0	1.0	−0.0010	0.0001	0.2349	3.0587	0.7993	8.4808	0.5644	5.4221
13	100,000	3.0	2.0	0.0	1.5	0.0	1.5	−0.0005	−0.0042	0.1191	3.5087	0.6364	12.4608	0.5173	8.9520
14	100,000	3.0	2.0	0.0	2.0	0.0	2.0	0.0049	0.0019	0.0717	3.7208	0.5007	14.0061	0.4290	10.2853
15	100,000	3.0	2.0	0.0	2.5	0.0	2.5	−0.0043	0.0072	0.0474	3.8234	0.3898	13.7559	0.3424	9.9325
16	100,000	4.0	2.5	0.0	0.5	0.0	0.5	−0.0015	0.0020	0.5315	2.9587	0.9622	5.1629	0.4307	2.2042
17	100,000	4.0	2.5	0.0	1.0	0.0	1.0	−0.0020	−0.0002	0.2190	4.8682	0.8613	16.6077	0.6422	11.7395
18	100,000	4.0	2.5	0.0	1.5	0.0	1.5	−0.0010	0.0021	0.1101	5.5462	0.7353	27.6705	0.6252	22.1243
19	100,000	4.0	2.5	0.0	2.0	0.0	2.0	−0.0016	0.0002	0.0655	5.8076	0.6096	33.9231	0.5442	28.1155
20	100,000	4.0	2.5	0.0	2.5	0.0	2.5	0.0002	−0.0027	0.0429	5.9652	0.5004	36.3498	0.4574	30.3845
21	100,000	5.0	3.0	0.0	0.5	0.0	0.5	0.0037	0.0037	0.5125	4.3721	0.9735	8.0919	0.4611	3.7198
22	100,000	5.0	3.0	0.0	1.0	0.0	1.0	−0.0007	−0.0014	0.2085	7.1458	0.8994	27.8115	0.6909	20.6656
23	100,000	5.0	3.0	0.0	1.5	0.0	1.5	0.0046	−0.0012	0.1046	8.0387	0.7979	49.3004	0.6933	41.2617
24	100,000	5.0	3.0	0.0	2.0	0.0	2.0	−0.0018	0.0021	0.0620	8.3823	0.6901	65.2245	0.6281	56.8423
25	100,000	5.0	3.0	0.0	2.5	0.0	2.5	0.0051	0.0003	0.0404	8.6664	0.5915	76.6045	0.5512	67.9381