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 Sep-77 Oct-77 Nov-77 Dec-77 Jan-78 Feb-78 Mar-78 Apr-78 May-78 Jun-78 Jul-78 Aug-78 Sep-78 Oct-78 Nov-78 Dec-78 Jan-79 Feb-79 Mar-79 Apr-79 May-79 Jun-79 Jul-79 Aug-79 Sep-79 S&P 500 96.53 92.34 94.83 95.10 89.25 87.04 89.21 96.83 97.24 95.53 100.68 103.29 102.54 93.15 94.70 96.11 99.93 96.28 101.59 101.76 99.08 102.91 103.81 109.32 109.32 End of month Apr-80 May-80 Jun-80 Jul-80 Aug-80 Sep-80 Oct-80 Nov-80 Dec-80 Jan-81 Feb-81 Mar-81 Apr-81 May-81 Jun-81 Jul-81 Aug-81 Sep-81 Oct-81 Nov-81 Dec-81 Jan-82 Feb-82 Mar-82 Apr-82 S&P 500 106.29 111.24 114.24 121.67 122.38 125.46 127.47 140.52 135.76 129.55 131.27 136.00 132.81 132.59 131.21 130.92 122.79 116.18 121.89 126.35 122.55 120.40 113. 11 111.96 116.44 End of month Nov-82 Dec-82 Jan-83 Feb-83 Mar-83 Apr-83 May-83 Jun-83 Jul-83 Aug-83 Sep-83 Oct-83 Nov-83 Dec-83 Jan-84 Feb-84 Mar-84 Apr-84 May-84 Jun-84 Jul-84 Aug-84 Sep-84 Oct-84 Nov-84 S&P 500 138.53 140.64 145.30 148.06 152.96 164.43 162.39 167.64 162.56 164.40 166.07 163.55 166.40 164.93 163.41 157.06 159.18 160.05 150.55 153.18 150.66 166.68 166.10 166.09 163.58 End of month Jul-85 Aug-85 Sep-85 Oct-85 Nov-85 Dec-85 Jan-86 Feb-86 Mar-86 Apr-86 May-86 Jun-86 Jul-86 Aug-86 Sep-86 Oct-86 Nov-86 Dec-86 Jan-87 Feb-87 Mar-87 Apr-87 May-87 Jun-87 Jul-87 S&P 500 191.85 190.92 188.63 182.08 189.82 202.17 211.28 226.92 238.90 235.52 247.35 250.84 236.12 252.93 231.32 243.98 249.22 242.17 274.08 284.20 291.70 288.36 290.10 304.00 318.66 Sep-79 Oct-79 Nov-79 Dec-79 Jan-80 Feb-80 Mar-80 109.32 101.82 106.16 107.94 114.16 113.66 102.09 Apr-82 May-82 Jun-82 Jul-82 Aug-82 Sep-82 Oct-82 116.44 111.88 109.61 107.09 119.51 120.42 133.72 Nov-84 Dec-84 Jan-85 Feb-85 Mar-85 Apr-85 May-85 163.58 167.24 179.63 181.18 180.66 179.83 189.55 Jul-87 Aug-87 Sep-87 Oct-87 318.66 329.80 321.83 251.79 a-1. What would have been the average value of your gross monthly payouts on the puts over the 10-year period October 1977 September 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 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 Sep-77 Oct-77 Nov-77 Dec-77 Jan-78 Feb-78 Mar-78 Apr-78 May-78 Jun-78 Jul-78 Aug-78 Sep-78 Oct-78 Nov-78 Dec-78 Jan-79 Feb-79 Mar-79 Apr-79 May-79 Jun-79 Jul-79 Aug-79 Sep-79 S&P 500 96.53 92.34 94.83 95.10 89.25 87.04 89.21 96.83 97.24 95.53 100.68 103.29 102.54 93.15 94.70 96.11 99.93 96.28 101.59 101.76 99.08 102.91 103.81 109.32 109.32 End of month Apr-80 May-80 Jun-80 Jul-80 Aug-80 Sep-80 Oct-80 Nov-80 Dec-80 Jan-81 Feb-81 Mar-81 Apr-81 May-81 Jun-81 Jul-81 Aug-81 Sep-81 Oct-81 Nov-81 Dec-81 Jan-82 Feb-82 Mar-82 Apr-82 S&P 500 106.29 111.24 114.24 121.67 122.38 125.46 127.47 140.52 135.76 129.55 131.27 136.00 132.81 132.59 131.21 130.92 122.79 116.18 121.89 126.35 122.55 120.40 113. 11 111.96 116.44 End of month Nov-82 Dec-82 Jan-83 Feb-83 Mar-83 Apr-83 May-83 Jun-83 Jul-83 Aug-83 Sep-83 Oct-83 Nov-83 Dec-83 Jan-84 Feb-84 Mar-84 Apr-84 May-84 Jun-84 Jul-84 Aug-84 Sep-84 Oct-84 Nov-84 S&P 500 138.53 140.64 145.30 148.06 152.96 164.43 162.39 167.64 162.56 164.40 166.07 163.55 166.40 164.93 163.41 157.06 159.18 160.05 150.55 153.18 150.66 166.68 166.10 166.09 163.58 End of month Jul-85 Aug-85 Sep-85 Oct-85 Nov-85 Dec-85 Jan-86 Feb-86 Mar-86 Apr-86 May-86 Jun-86 Jul-86 Aug-86 Sep-86 Oct-86 Nov-86 Dec-86 Jan-87 Feb-87 Mar-87 Apr-87 May-87 Jun-87 Jul-87 S&P 500 191.85 190.92 188.63 182.08 189.82 202.17 211.28 226.92 238.90 235.52 247.35 250.84 236.12 252.93 231.32 243.98 249.22 242.17 274.08 284.20 291.70 288.36 290.10 304.00 318.66 Sep-79 Oct-79 Nov-79 Dec-79 Jan-80 Feb-80 Mar-80 109.32 101.82 106.16 107.94 114.16 113.66 102.09 Apr-82 May-82 Jun-82 Jul-82 Aug-82 Sep-82 Oct-82 116.44 111.88 109.61 107.09 119.51 120.42 133.72 Nov-84 Dec-84 Jan-85 Feb-85 Mar-85 Apr-85 May-85 163.58 167.24 179.63 181.18 180.66 179.83 189.55 Jul-87 Aug-87 Sep-87 Oct-87 318.66 329.80 321.83 251.79 a-1. What would have been the average value of your gross monthly payouts on the puts over the 10-year period October 1977 September 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