Hi there, I just got a homework spread sheet and have no idea how to solve...

Hi there, I just got a homework spread sheet and have no idea how to solve it. can you explain it to me? I would really appriciate your help. Here are the questions With a tiny part from the spread sheet.

A) Construct a time series of the ratio of the price of the fifth contract each day to the price of the fourth contract followed through time till the fourth contract expires. Pick a starting year below 2007 and a start date as a trading day closest to your birthday in that year.

B) Compare the standard deviations for the continuously compounded returns on the ratios with the continuously compounded returns on the respective numerators and denominators of the ratio.

C) Comment on the results obtained. In particular explain the di§erences in the standard deviations observed.

	Maturities					Contract Prices
date						1	2	3	4	5
19990601	199907	199910	199912	200003	200005	57.83	57.13	57.68	58.66	59.13
19990602	199907	199910	199912	200003	200005	58.21	57.6	57.69	58.6	59.1
19990603	199907	199910	199912	200003	200005	57.91	57.68	57.36	58.28	58.8
19990604	199907	199910	199912	200003	200005	57.53	57.7	57.48	58.45	58.98
19990607	199907	199910	199912	200003	200005	57.97	58.28	58.1	59	59.5
19990608	199907	199910	199912	200003	200005	57.48	57.7	57.75	58.57	59.15
19990609	199907	199910	199912	200003	200005	57.42	57.48	57.28	58.15	58.5
19990610	199907	199910	199912	200003	200005	56.31	56.91	56.72	57.72	58.25
19990611	199907	199910	199912	200003	200005	55.58	56.18	56.06	57.07	57.6
19990614	199907	199910	199912	200003	200005	56.39	57.19	56.67	57.53	58.03
19990615	199907	199910	199912	200003	200005	56.66	57.2	56.77	57.63	58.2
19990616	199907	199910	199912	200003	200005	55.26	56.37	55.74	56.65	57.33
19990617	199907	199910	199912	200003	200005	54.31	55.18	55.19	56.35	57.09
19990618	199907	199910	199912	200003	200005	55.03	56.16	56.05	57.08	57.7
19990621	199907	199910	199912	200003	200005	55.4	55.9	55.38	56.33	57.03
19990622	199907	199910	199912	200003	200005	54.35	55.88	55.92	56.83	57.55
19990623	199907	199910	199912	200003	200005	51.43	54.74	55.29	56.37	57.05
19990624	199907	199910	199912	200003	200005	52.34	55.34	55.95	56.81	57.48
19990625	199907	199910	199912	200003	200005	51.51	54.74	55.57	56.49	57.1
19990628	199907	199910	199912	200003	200005	50.1	53.58	54.25	55.31	56.13
19990629	199907	199910	199912	200003	200005	50.15	53.35	54	55.01	55.7
19990630	199907	199910	199912	200003	200005	50.1	53.64	54.39	55.18	55.9
19990701	199907	199910	199912	200003	200005	49.5	52.75	53.16	54.2	55.03
19990702	199907	199910	199912	200003	200005	49.7	52.23	52.93	53.95	54.68
19990706	199907	199910	199912	200003	200005	48.9	52.83	53.16	54.11	54.95
19990707	199907	199910	199912	200003	200005	48.75	51.68	52.24	53.26	54.05
19990708	199907	199910	199912	200003	200005	48.37	51.17	51.69	52.75	53.55
19990709	199910	199912	200003	200005	200007	50.01	50.61	51.78	52.6	53.6
19990712	199910	199912	200003	200005	200007	48.45	49.45	50.45	51.35	52.25
19990713	199910	199912	200003	200005	200007	49.53	50.23	51.23	52.03	52.9
19990714	199910	199912	200003	200005	200007	48.55	49.51	50.51	51.25	52.06
19990715	199910	199912	200003	200005	200007	48.95	49.93	50.88	51.53	52.3
19990716	199910	199912	200003	200005	200007	49.52	50.48	51.3	51.9	52.6
19990719	199910	199912	200003	200005	200007	50.44	51.37	52.1	52.78	53.55
19990720	199910	199912	200003	200005	200007	49.89	50.67	51.43	52.2	53
19990721	199910	199912	200003	200005	200007	51.21	51.7	52.45	53.1	54.05
19990722	199910	199912	200003	200005	200007	51.09	51.87	52.85	53.58	54.45
19990723	199910	199912	200003	200005	200007	52.01	52.4	53.43	54.05	54.95
19990726	199910	199912	200003	200005	200007	50.85	51.72	52.7	53.5	54.3
19990727	199910	199912	200003	200005	200007	50.82	51.43	52.35	53.13	53.8
19990728	199910	199912	200003	200005	200007	50.05	50.88	51.86	52.63	53.4
19990729	199910	199912	200003	200005	200007	51.46	52.13	53.08	53.8	54.65
19990730	199910	199912	200003	200005	200007	52.38	53.11	53.93	54.55	55.38
19990802	199910	199912	200003	200005	200007	51.57	52.35	53.12	54	54.63
19990803	199910	199912	200003	200005	200007	51.31	52.16	53	53.75	54.5
19990804	199910	199912	200003	200005	200007	51.59	52.52	53.45	54.15	54.8
19990805	199910	199912	200003	200005	200007	51.48	52.46	53.45	54.15	54.9
19990806	199910	199912	200003	200005	200007	52.09	52.99	53.85	54.8	55.4
19990809	199910	199912	200003	200005	200007	52.89	53.76	54.7	55.45	56.1
19990810	199910	199912	200003	200005	200007	51.81	52.72	53.69	54.53	55.35
19990811	199910	199912	200003	200005	200007	51.75	52.52	53.55	54.45	55.28
19990812	199910	199912	200003	200005	200007	53.15	54.19	55	55.9	56.8

Expert Solution


Date	Contract 4	Contract 5	Contract (5) / Contract (4)	Return (Contract 5/ Contract 4)	Return (Contract 5)	Return (Contract 4)
19990601	58.66	59.13	1.0080
19990602	58.6	59.1	1.0085	0.0005	-0.0005	-0.0010
19990603	58.28	58.8	1.0089	0.0004	-0.0051	-0.0055
19990604	58.45	58.98	1.0091	0.0001	0.0031	0.0029
19990607	59	59.5	1.0085	-0.0006	0.0088	0.0094
19990608	58.57	59.15	1.0099	0.0014	-0.0059	-0.0073
19990609	58.15	58.5	1.0060	-0.0038	-0.0110	-0.0072
19990610	57.72	58.25	1.0092	0.0031	-0.0043	-0.0074
19990611	57.07	57.6	1.0093	0.0001	-0.0112	-0.0113
19990614	57.53	58.03	1.0087	-0.0006	0.0075	0.0081
19990615	57.63	58.2	1.0099	0.0012	0.0029	0.0017
19990616	56.65	57.33	1.0120	0.0021	-0.0149	-0.0170
19990617	56.35	57.09	1.0131	0.0011	-0.0042	-0.0053
19990618	57.08	57.7	1.0109	-0.0022	0.0107	0.0130
19990621	56.33	57.03	1.0124	0.0015	-0.0116	-0.0131
19990622	56.83	57.55	1.0127	0.0002	0.0091	0.0089
19990623	56.37	57.05	1.0121	-0.0006	-0.0087	-0.0081
19990624	56.81	57.48	1.0118	-0.0003	0.0075	0.0078
19990625	56.49	57.1	1.0108	-0.0010	-0.0066	-0.0056
19990628	55.31	56.13	1.0148	0.0040	-0.0170	-0.0209
19990629	55.01	55.7	1.0125	-0.0022	-0.0077	-0.0054
19990630	55.18	55.9	1.0130	0.0005	0.0036	0.0031
19990701	54.2	55.03	1.0153	0.0022	-0.0156	-0.0178
19990702	53.95	54.68	1.0135	-0.0018	-0.0064	-0.0046
19990706	54.11	54.95	1.0155	0.0020	0.0049	0.0030
19990707	53.26	54.05	1.0148	-0.0007	-0.0164	-0.0157
19990708	52.75	53.55	1.0152	0.0003	-0.0093	-0.0096
19990709	52.6	53.6	1.0190	0.0038	0.0009	-0.0028
19990712	51.35	52.25	1.0175	-0.0015	-0.0252	-0.0238
19990713	52.03	52.9	1.0167	-0.0008	0.0124	0.0132
19990714	51.25	52.06	1.0158	-0.0009	-0.0159	-0.0150
19990715	51.53	52.3	1.0149	-0.0008	0.0046	0.0055
19990716	51.9	52.6	1.0135	-0.0014	0.0057	0.0072
19990719	52.78	53.55	1.0146	0.0011	0.0181	0.0170
19990720	52.2	53	1.0153	0.0007	-0.0103	-0.0110
19990721	53.1	54.05	1.0179	0.0025	0.0198	0.0172
19990722	53.58	54.45	1.0162	-0.0016	0.0074	0.0090
19990723	54.05	54.95	1.0167	0.0004	0.0092	0.0088
19990726	53.5	54.3	1.0150	-0.0017	-0.0118	-0.0102
19990727	53.13	53.8	1.0126	-0.0023	-0.0092	-0.0069
19990728	52.63	53.4	1.0146	0.0020	-0.0074	-0.0094
19990729	53.8	54.65	1.0158	0.0012	0.0234	0.0222
19990730	54.55	55.38	1.0152	-0.0006	0.0134	0.0139
19990802	54	54.63	1.0117	-0.0035	-0.0135	-0.0101
19990803	53.75	54.5	1.0140	0.0023	-0.0024	-0.0046
19990804	54.15	54.8	1.0120	-0.0019	0.0055	0.0074
19990805	54.15	54.9	1.0139	0.0018	0.0018	0.0000
19990806	54.8	55.4	1.0109	-0.0029	0.0091	0.0120
19990809	55.45	56.1	1.0117	0.0008	0.0126	0.0119
19990810	54.53	55.35	1.0150	0.0033	-0.0134	-0.0166
19990811	54.45	55.28	1.0152	0.0002	-0.0013	-0.0015
19990812	55.9	56.8	1.0161	0.0008	0.0275	0.0266

Return = (Present Price / Previous Price) - 1

Contract	Standard Deviation
Ratio (Contract 5 / Contract 4)	0.001823
Contract 5	0.011564
Contract 4	0.011656

It is evident that the standard deviation value of Contract (5) and Contract (4) is almost same. While the standard deviation value of Ratio 5 / Ratio 4 is very less. Two contracts which have similar standard deviations around their expected value, when put in the form of one divided by the other, produce a set of values that has much lesser standard deviation when compared with that of the original contracts.

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