End of month S&P 500 End of month S&P 500 End of month S&P 500 End of month S&P 500 September-77 96.53 April-80 106.29 November-82 138.53 July-85 191.85 October-77 92.34 May-80 111.24 December-82 140.64 August-85 190.92 November-77 94.83 June-80 114.24 January-83 145.30 September-85 188.63 December-77 95.10 July-80 121.67 February-83 148.06 October-85 182.08 January-78 89.25 August-80 122.38 March-83 152.96 November-85 189.82 February-78 87.04 September-80 125.46 April-83 164.43 December-85 202.17 March-78 89.21 October-80 127.47 May-83 162.39 January-86 211.28 April-78 96.83 November-80 140.52 June-83 167.64 February-86 226.92 May-78 97.24 December-80 135.76 July-83 162.56 March-86 238.90 June-78 95.53 January-81 129.55 August-83 164.40 April-86 235.52 July-78 100.68 February-81 131.27 September-83 166.07 May-86 247.35 August-78 103.29 March-81 136.00 October-83 163.55 June-86 250.84 September-78 102.54 April-81 132.81 November-83 166.40 July-86 236.12 October-78 93.15 May-81 132.59 December-83 164.93 August-86 252.93 November-78 94.70 June-81 131.21 January-84 163.41 September-86 231.32 December-78 96.11 July-81 130.92 February-84 157.06 October-86 243.98 January-79 99.93 August-81 122.79 March-84 159.18 November-86 249.22 February-79 96.28 September-81 116.18 April-84 160.05 December-86 242.17 March-79 101.59 October-81 121.89 May-84 150.55 January-87 274.08 April-79 101.76 November-81 126.35 June-84 153.18 February-87 284.20 May-79 99.08 December-81 122.55 July-84 150.66 March-87 291.70 June-79 102.91 January-82 120.40 August-84 166.68 April-87 288.36 July-79 103.81 February-82 113.11 September-84 166.10 May-87 290.10 August-79 109.32 March-82 111.96 October-84 166.09 June-87 304.00 September-79 109.32 April-82 116.44 November-84 163.58 July-87 318.66 October-79 101.82 May-82 111.88 December-84 167.24 August-87 329.80 November-79 106.16 June-82 109.61 January-85 179.63 September-87 321.83 December-79 107.94 July-82 107.09 February-85 181.18 October-87 251.79 January-80 114.16 August-82 119.51 March-85 180.66     February-80 113.66 September-82 120.42 April-85 179.83     March-80 102.09 October-82 133.72 May-85 189.55       Required: 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? (Do not round intermediate calculations. Round your answer to 4 decimal places.)   a-2. The standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)   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? (Do not round intermediate calculations. Round your answer to 4 decimal places.)   b-2. The standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)