Question: Calculate Paycom's Tracking Error from January 03, 2023 to November 17, 2023. (Annualized; 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: TE = \sigma(r - r_b) * \sqrt{252}; r_b is the benchmark daily return
Data:
date,close,benchmark_close
2022-12-30,310.3099975585937,3839.5
2023-01-03,304.6300048828125,3824.139892578125
2023-01-04,303.8999938964844,3852.969970703125
2023-01-05,294.6199951171875,3808.10009765625
2023-01-06,286.6499938964844,3895.080078125
2023-01-09,292.5899963378906,3892.090087890625
2023-01-10,298.3399963378906,3919.25
2023-01-11,304.25,3969.610107421875
2023-01-12,304.2799987792969,3983.169921875
2023-01-13,304.4599914550781,3999.090087890625
2023-01-17,310.29998779296875,3990.969970703125
2023-01-18,311.7699890136719,3928.860107421875
2023-01-19,304.79998779296875,3898.85009765625
2023-01-20,313.4599914550781,3972.610107421875
2023-01-23,322.07000732421875,4019.81005859375
2023-01-24,319.9200134277344,4016.949951171875
2023-01-25,314.6000061035156,4016.219970703125
2023-01-26,321.4599914550781,4060.429931640625
2023-01-27,322.239990234375,4070.56005859375
2023-01-30,315.760009765625,4017.77001953125
2023-01-31,323.94000244140625,4076.60009765625
2023-02-01,340.7699890136719,4119.2099609375
2023-02-02,352.4100036621094,4179.759765625
2023-02-03,337.44000244140625,4136.47998046875
2023-02-06,329.69000244140625,4111.080078125
2023-02-07,344.5199890136719,4164.0
2023-02-08,321.2099914550781,4117.85986328125
2023-02-09,322.4800109863281,4081.5
2023-02-10,317.0899963378906,4090.4599609375
2023-02-13,322.75,4137.2900390625
2023-02-14,324.69000244140625,4136.1298828125
2023-02-15,320.0,4147.60009765625
2023-02-16,307.45001220703125,4090.409912109375
2023-02-17,303.8900146484375,4079.090087890625
2023-02-21,296.510009765625,3997.340087890625
2023-02-22,298.94000244140625,3991.050048828125
2023-02-23,299.92999267578125,4012.320068359375
2023-02-24,293.4200134277344,3970.0400390625
2023-02-27,294.1199951171875,3982.239990234375
2023-02-28,289.0599975585937,3970.14990234375
2023-03-01,284.510009765625,3951.389892578125
2023-03-02,287.3399963378906,3981.35009765625
2023-03-03,291.5400085449219,4045.639892578125
2023-03-06,292.7300109863281,4048.419921875
2023-03-07,287.3999938964844,3986.3701171875
2023-03-08,288.8299865722656,3992.010009765625
2023-03-09,285.75,3918.320068359375
2023-03-10,273.2799987792969,3861.590087890625
2023-03-13,274.5400085449219,3855.760009765625
2023-03-14,280.510009765625,3919.2900390625
2023-03-15,277.8800048828125,3891.929931640625
2023-03-16,280.0599975585937,3960.280029296875
2023-03-17,276.94000244140625,3916.639892578125
2023-03-20,270.3699951171875,3951.570068359375
2023-03-21,277.3500061035156,4002.8701171875
2023-03-22,266.8500061035156,3936.969970703125
2023-03-23,272.32000732421875,3948.719970703125
2023-03-24,271.5599975585937,3970.989990234375
2023-03-27,272.4800109863281,3977.530029296875
2023-03-28,273.0299987792969,3971.27001953125
2023-03-29,285.8699951171875,4027.81005859375
2023-03-30,296.2900085449219,4050.830078125
2023-03-31,304.010009765625,4109.31005859375
2023-04-03,298.6199951171875,4124.509765625
2023-04-04,292.7799987792969,4100.60009765625
2023-04-05,285.6000061035156,4090.3798828125
2023-04-06,289.45001220703125,4105.02001953125
2023-04-10,294.3800048828125,4109.10986328125
2023-04-11,295.9100036621094,4108.93994140625
2023-04-12,294.2099914550781,4091.949951171875
2023-04-13,302.92999267578125,4146.22021484375
2023-04-14,303.1499938964844,4137.64013671875
2023-04-17,307.25,4151.31982421875
2023-04-18,305.260009765625,4154.8701171875
2023-04-19,304.9599914550781,4154.52001953125
2023-04-20,299.82000732421875,4129.7900390625
2023-04-21,300.54998779296875,4133.52001953125
2023-04-24,298.5400085449219,4137.0400390625
2023-04-25,288.7099914550781,4071.6298828125
2023-04-26,285.70001220703125,4055.989990234375
2023-04-27,288.8999938964844,4135.35009765625
2023-04-28,290.3699951171875,4169.47998046875
2023-05-01,297.54998779296875,4167.8701171875
2023-05-02,288.75,4119.580078125
2023-05-03,293.70001220703125,4090.75
2023-05-04,279.989990234375,4061.219970703125
2023-05-05,272.6300048828125,4136.25
2023-05-08,274.3800048828125,4138.1201171875
2023-05-09,268.739990234375,4119.169921875
2023-05-10,273.17999267578125,4137.64013671875
2023-05-11,265.3099975585937,4130.6201171875
2023-05-12,268.510009765625,4124.080078125
2023-05-15,271.7200012207031,4136.27978515625
2023-05-16,265.2900085449219,4109.89990234375
2023-05-17,272.8099975585937,4158.77001953125
2023-05-18,282.25,4198.0498046875
2023-05-19,285.3599853515625,4191.97998046875
2023-05-22,289.20001220703125,4192.6298828125
2023-05-23,283.9700012207031,4145.580078125
2023-05-24,280.8399963378906,4115.240234375
2023-05-25,279.0199890136719,4151.27978515625
2023-05-26,280.95001220703125,4205.4501953125
2023-05-30,279.82000732421875,4205.52001953125
2023-05-31,280.1300048828125,4179.830078125
2023-06-01,281.1099853515625,4221.02001953125
2023-06-02,293.32000732421875,4282.3701171875
2023-06-05,305.92999267578125,4273.7900390625
2023-06-06,307.44000244140625,4283.85009765625
2023-06-07,302.95001220703125,4267.52001953125
2023-06-08,305.010009765625,4293.93017578125
2023-06-09,304.70001220703125,4298.85986328125
2023-06-12,312.57000732421875,4338.93017578125
2023-06-13,322.739990234375,4369.009765625
2023-06-14,319.9100036621094,4372.58984375
2023-06-15,323.95001220703125,4425.83984375
2023-06-16,319.9200134277344,4409.58984375
2023-06-20,322.4599914550781,4388.7099609375
2023-06-21,312.44000244140625,4365.68994140625
2023-06-22,306.75,4381.89013671875
2023-06-23,306.20001220703125,4348.330078125
2023-06-26,310.79998779296875,4328.81982421875
2023-06-27,313.9700012207031,4378.41015625
2023-06-28,312.2300109863281,4376.85986328125
2023-06-29,313.67999267578125,4396.43994140625
2023-06-30,321.239990234375,4450.3798828125
2023-07-03,319.6199951171875,4455.58984375
2023-07-05,317.8900146484375,4446.81982421875
2023-07-06,323.8800048828125,4411.58984375
2023-07-07,324.510009765625,4398.9501953125
2023-07-10,334.8699951171875,4409.52978515625
2023-07-11,338.8099975585937,4439.259765625
2023-07-12,340.8999938964844,4472.16015625
2023-07-13,349.6499938964844,4510.0400390625
2023-07-14,355.010009765625,4505.419921875
2023-07-17,358.989990234375,4522.7900390625
2023-07-18,363.75,4554.97998046875
2023-07-19,365.4700012207031,4565.72021484375
2023-07-20,357.6099853515625,4534.8701171875
2023-07-21,350.17999267578125,4536.33984375
2023-07-24,350.9800109863281,4554.64013671875
2023-07-25,353.82000732421875,4567.4599609375
2023-07-26,358.0,4566.75
2023-07-27,361.0899963378906,4537.41015625
2023-07-28,368.4599914550781,4582.22998046875
2023-07-31,368.760009765625,4588.9599609375
2023-08-01,370.7799987792969,4576.72998046875
2023-08-02,299.6199951171875,4513.39013671875
2023-08-03,296.95001220703125,4501.89013671875
2023-08-04,290.4200134277344,4478.02978515625
2023-08-07,293.1099853515625,4518.43994140625
2023-08-08,291.5599975585937,4499.3798828125
2023-08-09,286.8800048828125,4467.7099609375
2023-08-10,291.510009765625,4468.830078125
2023-08-11,292.0,4464.0498046875
2023-08-14,294.25,4489.72021484375
2023-08-15,291.9599914550781,4437.85986328125
2023-08-16,290.8099975585937,4404.330078125
2023-08-17,280.3999938964844,4370.35986328125
2023-08-18,281.32000732421875,4369.7099609375
2023-08-21,283.6499938964844,4399.77001953125
2023-08-22,286.8599853515625,4387.5498046875
2023-08-23,289.8699951171875,4436.009765625
2023-08-24,284.5799865722656,4376.31005859375
2023-08-25,286.3900146484375,4405.7099609375
2023-08-28,287.6499938964844,4433.31005859375
2023-08-29,293.0400085449219,4497.6298828125
2023-08-30,293.6600036621094,4514.8701171875
2023-08-31,294.8399963378906,4507.66015625
2023-09-01,295.7900085449219,4515.77001953125
2023-09-05,294.1199951171875,4496.830078125
2023-09-06,293.1400146484375,4465.47998046875
2023-09-07,288.6000061035156,4451.14013671875
2023-09-08,284.3099975585937,4457.490234375
2023-09-11,285.95001220703125,4487.4599609375
2023-09-12,284.1400146484375,4461.89990234375
2023-09-13,279.3999938964844,4467.43994140625
2023-09-14,280.3399963378906,4505.10009765625
2023-09-15,277.9200134277344,4450.31982421875
2023-09-18,276.1000061035156,4453.52978515625
2023-09-19,276.9100036621094,4443.9501953125
2023-09-20,268.4800109863281,4402.2001953125
2023-09-21,261.69000244140625,4330.0
2023-09-22,257.1600036621094,4320.06005859375
2023-09-25,258.32000732421875,4337.43994140625
2023-09-26,253.6000061035156,4273.52978515625
2023-09-27,257.0799865722656,4274.509765625
2023-09-28,257.4599914550781,4299.7001953125
2023-09-29,259.2699890136719,4288.0498046875
2023-10-02,260.0400085449219,4288.39013671875
2023-10-03,261.5400085449219,4229.4501953125
2023-10-04,261.1700134277344,4263.75
2023-10-05,262.6000061035156,4258.18994140625
2023-10-06,270.2799987792969,4308.5
2023-10-09,275.69000244140625,4335.66015625
2023-10-10,275.0,4358.240234375
2023-10-11,278.0899963378906,4376.9501953125
2023-10-12,268.5400085449219,4349.60986328125
2023-10-13,264.9700012207031,4327.77978515625
2023-10-16,270.1300048828125,4373.6298828125
2023-10-17,275.2300109863281,4373.2001953125
2023-10-18,268.2300109863281,4314.60009765625
2023-10-19,265.5,4278.0
2023-10-20,259.0899963378906,4224.16015625
2023-10-23,257.6499938964844,4217.0400390625
2023-10-24,261.45001220703125,4247.68017578125
2023-10-25,248.0800018310547,4186.77001953125
2023-10-26,244.94000244140625,4137.22998046875
2023-10-27,240.33999633789065,4117.3701171875
2023-10-30,240.05999755859372,4166.81982421875
2023-10-31,244.97000122070312,4193.7998046875
2023-11-01,150.69000244140625,4237.85986328125
2023-11-02,162.66000366210938,4317.77978515625
2023-11-03,159.02000427246094,4358.33984375
2023-11-06,160.88999938964844,4365.97998046875
2023-11-07,167.83999633789062,4378.3798828125
2023-11-08,167.52000427246094,4382.77978515625
2023-11-09,167.75999450683594,4347.35009765625
2023-11-10,171.16000366210938,4415.240234375
2023-11-13,172.0,4411.5498046875
2023-11-14,176.27999877929688,4495.7001953125
2023-11-15,177.11000061035156,4502.8798828125
2023-11-16,173.64999389648438,4508.240234375
2023-11-17,177.5,4514.02001953125

Indicator data:
Answer: 0.5276