Given below are the monthly values of the S P 500 Index Suppose that in each month you had written an out of the money put option on one unit of the index with an exercise price 5 lower than the current value of the index End of month S P 500 End of month S P 500 End of month S P 500 End of month S P 500 Sep 77 96 53 Apr 80 106 29 Nov 82 138 53 Jul 85 191 85 Oct 77 92 34 May 80 111 24 Dec 82 140 64 Aug 85 190 92 Nov 77 94 83 Jun 80 114 24 Jan 83 145 30 Sep 85 188 63 Dec 77 95 10 Jul 80 121 67 Feb 83 148 06 Oct 85 182 08 Jan 78 89 25 Aug 80 122 38 Mar 83 152 96 Nov 85 189 82 Feb 78 87 04 Sep 80 125 46 Apr 83 164 43 Dec 85 202 17 Mar 78 89 21 Oct 80 127 47 May 83 162 39 Jan 86 211 28 Apr 78 96 83 Nov 80 140 52 Jun 83 167 64 Feb 86 226 92 May 78 97 24 Dec 80 135 76 Jul 83 162 56 Mar 86 238 90 Jun 78 95 53 Jan 81 129 55 Aug 83 164 40 Apr 86 235 52 Jul 78 100 68 Feb 81 131 27 Sep 83 166 07 May 86 247 35 Aug 78 103 29 Mar 81 136 00 Oct 83 163 55 Jun 86 250 84 Sep 78 102 54 Apr 81 132 81 Nov 83 166 40 Jul 86 236 12 Oct 78 93 15 May 81 132 59 Dec 83 164 93 Aug 86 252 93 Nov 78 94 70 Jun 81 131 21 Jan 84 163 41 Sep 86 231 32 Dec 78 96 11 Jul 81 130 92 Feb 84 157 06 Oct 86 243 98 Jan 79 99 93 Aug 81 122 79 Mar 84 159 18 Nov 86 249 22 Feb 79 96 28 Sep 81 116 18 Apr 84 160 05 Dec 86 242 17 Mar 79 101 59 Oct 81 121 89 May 84 150 55 Jan 87 274 08 Apr 79 101 76 Nov 81 126 35 Jun 84 153 18 Feb 87 284 20 May 79 99 08 Dec 81 122 55 Jul 84 150 66 Mar 87 291 70 Jun 79 102 91 Jan 82 120 40 Aug 84 166 68 Apr 87 288 36 Jul 79 103 81 Feb 82 113 11 Sep 84 166 10 May 87 290 10 Aug 79 109 32 Mar 82 111 96 Oct 84 166 09 Jun 87 304 00 Sep 79 109 32 Apr 82 116 44 Nov 84 163 58 Jul 87 318 66 Oct 79 101 82 May 82 111 88 Dec 84 167 24 Aug 87 329 80 Nov 79 106 16 Jun 82 109 61 Jan 85 179 63 Sep 87 321 83 Dec 79 107 94 Jul 82 107 09 Feb 85 181 18 Oct 87 251 79 Jan 80 114 16 Aug 82 119 51 Mar 85 180 66 Feb 80 113 66 Sep 82 120 42 Apr 85 179 83 Mar 80 102 09 Oct 82 133 72 May 85 189 55 a 1 What would have been the average value of your gross monthly payouts on the puts over the 10 year period October 1977September 1987 (Round your answer to 4 decimal places ) Average value a 2 The standard deviation (Round your answer to 4 decimal places ) Standard deviation b 1 What would have been the average value of your gross monthly payouts on the puts if you extend the sample by one month to include October 1987 (Round your answer to 4 decimal places ) Average value b 2 The standard deviation (Round your answer to 4 decimal places ) Standard deviation

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Given below are the monthly values of the S&P 500 Index. Suppose that in each month you had written an out-of-the-money put option on one

Given below are the monthly values of the S&P 500 Index. Suppose that in each month you had written an out-of-the-money put option on one unit of the index with an exercise price 5% lower than the current value of the index.

End of month	S&P 500	End of month	S&P 500	End of month	S&P 500	End of month	S&P 500
Sep-77	96.53	Apr-80	106.29	Nov-82	138.53	Jul-85	191.85
Oct-77	92.34	May-80	111.24	Dec-82	140.64	Aug-85	190.92
Nov-77	94.83	Jun-80	114.24	Jan-83	145.30	Sep-85	188.63
Dec-77	95.10	Jul-80	121.67	Feb-83	148.06	Oct-85	182.08
Jan-78	89.25	Aug-80	122.38	Mar-83	152.96	Nov-85	189.82
Feb-78	87.04	Sep-80	125.46	Apr-83	164.43	Dec-85	202.17
Mar-78	89.21	Oct-80	127.47	May-83	162.39	Jan-86	211.28
Apr-78	96.83	Nov-80	140.52	Jun-83	167.64	Feb-86	226.92
May-78	97.24	Dec-80	135.76	Jul-83	162.56	Mar-86	238.90
Jun-78	95.53	Jan-81	129.55	Aug-83	164.40	Apr-86	235.52
Jul-78	100.68	Feb-81	131.27	Sep-83	166.07	May-86	247.35
Aug-78	103.29	Mar-81	136.00	Oct-83	163.55	Jun-86	250.84
Sep-78	102.54	Apr-81	132.81	Nov-83	166.40	Jul-86	236.12
Oct-78	93.15	May-81	132.59	Dec-83	164.93	Aug-86	252.93
Nov-78	94.70	Jun-81	131.21	Jan-84	163.41	Sep-86	231.32
Dec-78	96.11	Jul-81	130.92	Feb-84	157.06	Oct-86	243.98
Jan-79	99.93	Aug-81	122.79	Mar-84	159.18	Nov-86	249.22
Feb-79	96.28	Sep-81	116.18	Apr-84	160.05	Dec-86	242.17
Mar-79	101.59	Oct-81	121.89	May-84	150.55	Jan-87	274.08
Apr-79	101.76	Nov-81	126.35	Jun-84	153.18	Feb-87	284.20
May-79	99.08	Dec-81	122.55	Jul-84	150.66	Mar-87	291.70
Jun-79	102.91	Jan-82	120.40	Aug-84	166.68	Apr-87	288.36
Jul-79	103.81	Feb-82	113.11	Sep-84	166.10	May-87	290.10
Aug-79	109.32	Mar-82	111.96	Oct-84	166.09	Jun-87	304.00
Sep-79	109.32	Apr-82	116.44	Nov-84	163.58	Jul-87	318.66
Oct-79	101.82	May-82	111.88	Dec-84	167.24	Aug-87	329.80
Nov-79	106.16	Jun-82	109.61	Jan-85	179.63	Sep-87	321.83
Dec-79	107.94	Jul-82	107.09	Feb-85	181.18	Oct-87	251.79
Jan-80	114.16	Aug-82	119.51	Mar-85	180.66
Feb-80	113.66	Sep-82	120.42	Apr-85	179.83
Mar-80	102.09	Oct-82	133.72	May-85	189.55

a-1.

What would have been the average value of your gross monthly payouts on the puts over the 10-year period October 1977September 1987? (Round your answer to 4 decimal places.)

Average value

a-2.

The standard deviation? (Round your answer to 4 decimal places.)

Standard deviation

b-1.

What would have been the average value of your gross monthly payouts on the puts if you extend the sample by one month to include October 1987?(Round your answer to 4 decimal places.)

Average value

b-2.

The standard deviation? (Round your answer to 4 decimal places.)

Standard deviation