Question: From October 22, 2024 to March 23, 2025, what is Analog Devices's Information Ratio? (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
2024-10-21,225.6699981689453,5853.97998046875
2024-10-22,224.6199951171875,5851.2001953125
2024-10-23,226.8500061035156,5797.419921875
2024-10-24,229.67999267578125,5809.85986328125
2024-10-25,230.1699981689453,5808.1201171875
2024-10-28,230.13999938964844,5823.52001953125
2024-10-29,235.22999572753903,5832.919921875
2024-10-30,230.1199951171875,5813.669921875
2024-10-31,223.1100006103516,5705.4501953125
2024-11-01,225.47999572753903,5728.7998046875
2024-11-04,224.19000244140625,5712.68994140625
2024-11-05,217.6000061035156,5782.759765625
2024-11-06,226.25,5929.0400390625
2024-11-07,227.7700042724609,5973.10009765625
2024-11-08,225.8000030517578,5995.5400390625
2024-11-11,220.47000122070312,6001.35009765625
2024-11-12,219.5500030517578,5983.990234375
2024-11-13,212.83999633789065,5985.3798828125
2024-11-14,212.2400054931641,5949.169921875
2024-11-15,206.3500061035156,5870.6201171875
2024-11-18,209.6499938964844,5893.6201171875
2024-11-19,210.42999267578125,5916.97998046875
2024-11-20,211.00999450683597,5917.10986328125
2024-11-21,213.9600067138672,5948.7099609375
2024-11-22,214.58999633789065,5969.33984375
2024-11-25,223.5800018310547,5987.3701171875
2024-11-26,219.0500030517578,6021.6298828125
2024-11-27,217.1699981689453,5998.740234375
2024-11-29,218.0500030517578,6032.3798828125
2024-12-02,223.1199951171875,6047.14990234375
2024-12-03,221.5399932861328,6049.8798828125
2024-12-04,218.3000030517578,6086.490234375
2024-12-05,214.5500030517578,6075.10986328125
2024-12-06,218.1999969482422,6090.27001953125
2024-12-09,219.0399932861328,6052.85009765625
2024-12-10,215.6100006103516,6034.91015625
2024-12-11,217.1199951171875,6084.18994140625
2024-12-12,217.72000122070312,6051.25
2024-12-13,216.6100006103516,6051.08984375
2024-12-16,216.30999755859372,6074.080078125
2024-12-17,213.82000732421875,6050.60986328125
2024-12-18,207.7700042724609,5872.16015625
2024-12-19,207.77999877929688,5867.080078125
2024-12-20,211.77999877929688,5930.85009765625
2024-12-23,214.88999938964844,5974.06982421875
2024-12-24,218.08999633789065,6040.0400390625
2024-12-26,218.05999755859372,6037.58984375
2024-12-27,216.9900054931641,5970.83984375
2024-12-30,212.55999755859372,5906.93994140625
2024-12-31,212.4600067138672,5881.6298828125
2025-01-02,211.3500061035156,5868.5498046875
2025-01-03,215.3699951171875,5942.47021484375
2025-01-06,218.0,5975.3798828125
2025-01-07,215.8699951171875,5909.02978515625
2025-01-08,220.44000244140625,5918.25
2025-01-10,212.3699951171875,5827.0400390625
2025-01-13,212.9499969482422,5836.22021484375
2025-01-14,214.6499938964844,5842.91015625
2025-01-15,218.22000122070312,5949.91015625
2025-01-16,215.0200042724609,5937.33984375
2025-01-17,219.16000366210935,5996.66015625
2025-01-21,221.4499969482422,6049.240234375
2025-01-22,224.0800018310547,6086.3701171875
2025-01-23,228.3500061035156,6118.7099609375
2025-01-24,217.3699951171875,6101.240234375
2025-01-27,215.4199981689453,6012.27978515625
2025-01-28,209.5200042724609,6067.7001953125
2025-01-29,209.91000366210935,6039.31005859375
2025-01-30,212.3999938964844,6071.169921875
2025-01-31,211.88999938964844,6040.52978515625
2025-02-03,205.2400054931641,5994.56982421875
2025-02-04,206.00999450683597,6037.8798828125
2025-02-05,209.8000030517578,6061.47998046875
2025-02-06,207.8300018310547,6083.56982421875
2025-02-07,205.2100067138672,6025.990234375
2025-02-10,204.8600006103516,6066.43994140625
2025-02-11,203.4600067138672,6068.5
2025-02-12,205.1300048828125,6051.97021484375
2025-02-13,209.33999633789065,6115.06982421875
2025-02-14,214.6100006103516,6114.6298828125
2025-02-18,220.22000122070312,6129.580078125
2025-02-19,241.66000366210935,6144.14990234375
2025-02-20,243.82000732421875,6117.52001953125
2025-02-21,238.91000366210935,6013.1298828125
2025-02-24,236.9900054931641,5983.25
2025-02-25,235.3000030517578,5955.25
2025-02-26,233.72999572753903,5956.06005859375
2025-02-27,223.8500061035156,5861.56982421875
2025-02-28,230.05999755859372,5954.5
2025-03-03,228.52999877929688,5849.72021484375
2025-03-04,226.17999267578125,5778.14990234375
2025-03-05,229.47000122070312,5842.6298828125
2025-03-06,222.7700042724609,5738.52001953125
2025-03-07,225.8600006103516,5770.2001953125
2025-03-10,216.25999450683597,5614.56005859375
2025-03-11,209.0800018310547,5572.06982421875
2025-03-12,206.6199951171875,5599.2998046875
2025-03-13,203.8000030517578,5521.52001953125
2025-03-14,208.75,5638.93994140625
2025-03-17,211.67999267578125,5675.1201171875
2025-03-18,209.16000366210935,5614.66015625
2025-03-19,209.97000122070312,5675.2900390625
2025-03-20,205.8999938964844,5662.89013671875
2025-03-21,204.3999938964844,5667.56005859375

Indicator data:
Answer: -0.4504