Question: What was Ingersoll Rand's Information Ratio during the period September 15, 2019 to February 04, 2020? (Annualized (US standard uses arithmetic mean excess return); 252 trading days per year) Using unadjusted prices, write down the indicator formula, collect the raw data, calculate the answer, and keep four decimal places. Please list the raw data and key calculation process.
Formula: IR = E[r - r_b] * 252 / TE; TE = \sigma(r - r_b) * \sqrt{252}; r_b is the benchmark daily return
Data:
date,close,benchmark_close
2019-09-13,31.229999542236328,3007.389892578125
2019-09-16,31.850000381469727,2997.9599609375
2019-09-17,31.059999465942383,3005.699951171875
2019-09-18,30.75,3006.72998046875
2019-09-19,30.030000686645508,3006.7900390625
2019-09-20,29.5,2992.070068359375
2019-09-23,29.299999237060547,2991.780029296875
2019-09-24,28.93000030517578,2966.60009765625
2019-09-25,29.309999465942383,2984.8701171875
2019-09-26,29.18000030517578,2977.6201171875
2019-09-27,28.68000030517578,2961.7900390625
2019-09-30,28.290000915527344,2976.739990234375
2019-10-01,27.059999465942383,2940.25
2019-10-02,27.1200008392334,2887.610107421875
2019-10-03,27.82999992370605,2910.6298828125
2019-10-04,28.21999931335449,2952.010009765625
2019-10-07,27.56999969482422,2938.7900390625
2019-10-08,27.01000022888184,2893.06005859375
2019-10-09,27.32999992370605,2919.39990234375
2019-10-10,28.1299991607666,2938.1298828125
2019-10-11,29.56999969482422,2970.27001953125
2019-10-14,29.06999969482422,2966.14990234375
2019-10-15,29.38999938964844,2995.679931640625
2019-10-16,29.450000762939453,2989.68994140625
2019-10-17,29.65999984741211,2997.949951171875
2019-10-18,30.850000381469727,2986.199951171875
2019-10-21,31.11000061035156,3006.719970703125
2019-10-22,31.979999542236328,2995.989990234375
2019-10-23,32.560001373291016,3004.52001953125
2019-10-24,32.2599983215332,3010.2900390625
2019-10-25,32.790000915527344,3022.550048828125
2019-10-28,32.31999969482422,3039.419921875
2019-10-29,33.02000045776367,3036.889892578125
2019-10-30,32.11000061035156,3046.77001953125
2019-10-31,31.82999992370605,3037.56005859375
2019-11-01,32.849998474121094,3066.909912109375
2019-11-04,33.439998626708984,3078.27001953125
2019-11-05,32.63999938964844,3074.6201171875
2019-11-06,32.72999954223633,3076.780029296875
2019-11-07,33.2400016784668,3085.179931640625
2019-11-08,33.72999954223633,3093.080078125
2019-11-11,33.81999969482422,3087.010009765625
2019-11-12,33.630001068115234,3091.840087890625
2019-11-13,33.380001068115234,3094.0400390625
2019-11-14,33.0,3096.6298828125
2019-11-15,33.650001525878906,3120.4599609375
2019-11-18,33.7400016784668,3122.030029296875
2019-11-19,33.65999984741211,3120.179931640625
2019-11-20,33.58000183105469,3108.4599609375
2019-11-21,33.20000076293945,3103.5400390625
2019-11-22,33.65999984741211,3110.2900390625
2019-11-25,33.95000076293945,3133.639892578125
2019-11-26,33.939998626708984,3140.52001953125
2019-11-27,34.119998931884766,3153.6298828125
2019-11-29,33.869998931884766,3140.97998046875
2019-12-02,33.540000915527344,3113.8701171875
2019-12-03,33.27000045776367,3093.199951171875
2019-12-04,33.380001068115234,3112.760009765625
2019-12-05,33.52000045776367,3117.429931640625
2019-12-06,34.09000015258789,3145.909912109375
2019-12-09,33.849998474121094,3135.9599609375
2019-12-10,33.439998626708984,3132.52001953125
2019-12-11,34.290000915527344,3141.6298828125
2019-12-12,35.02000045776367,3168.570068359375
2019-12-13,35.540000915527344,3168.800048828125
2019-12-16,36.18000030517578,3191.449951171875
2019-12-17,36.08000183105469,3192.52001953125
2019-12-18,36.15999984741211,3191.139892578125
2019-12-19,36.4900016784668,3205.3701171875
2019-12-20,36.63999938964844,3221.219970703125
2019-12-23,36.880001068115234,3224.010009765625
2019-12-24,36.77999877929688,3223.3798828125
2019-12-26,36.95000076293945,3239.909912109375
2019-12-27,36.95000076293945,3240.02001953125
2019-12-30,36.4900016784668,3221.2900390625
2019-12-31,36.68000030517578,3230.780029296875
2020-01-02,36.880001068115234,3257.85009765625
2020-01-03,36.720001220703125,3234.85009765625
2020-01-06,36.27999877929688,3246.280029296875
2020-01-07,36.0099983215332,3237.179931640625
2020-01-08,35.75,3253.050048828125
2020-01-09,35.79999923706055,3274.699951171875
2020-01-10,35.13999938964844,3265.35009765625
2020-01-13,35.439998626708984,3288.1298828125
2020-01-14,34.93000030517578,3283.14990234375
2020-01-15,34.5,3289.2900390625
2020-01-16,35.11000061035156,3316.81005859375
2020-01-17,35.47999954223633,3329.6201171875
2020-01-21,34.560001373291016,3320.7900390625
2020-01-22,34.5,3321.75
2020-01-23,34.869998931884766,3325.5400390625
2020-01-24,34.65999984741211,3295.469970703125
2020-01-27,34.52000045776367,3243.6298828125
2020-01-28,35.58000183105469,3276.239990234375
2020-01-29,36.09999847412109,3273.39990234375
2020-01-30,36.209999084472656,3283.659912109375
2020-01-31,35.310001373291016,3225.52001953125
2020-02-03,35.77000045776367,3248.919921875
2020-02-04,36.560001373291016,3297.590087890625

Indicator data:
Answer: 0.8899