Question

In: Math

Calculate and interpret the three aspects of Descriptive Analysis for weekly return: Location, Shape and Spread....

  1. Calculate and interpret the three aspects of Descriptive Analysis for weekly return: Location, Shape and Spread. Hint: make sure you interpret these measures in the context of the data and pay attention to the unit of measurement in Excel.
  2. Date Weekly Return BIT
    11/3/13 -46.16
    18/3/13 -0.01
    25/3/13 39.23
    1/4/13 13.07
    8/4/13 23.93
    15/4/13 41.36
    22/4/13 26.5
    29/4/13 20.39
    6/5/13 25.5
    13/5/13 42.52
    20/5/13 37.88001
    27/5/13 15.66
    3/6/13 20.98
    10/6/13 25.28
    17/6/13 11.97
    24/6/13 -2.46
    1/7/13 14.95
    8/7/13 -3.5
    15/7/13 -8
    22/7/13 -0.05
    29/7/13 25.49
    5/8/13 4.099998
    12/8/13 9.529999
    19/8/13 58.75
    26/8/13 36.12
    2/9/13 47.87
    9/9/13 43.09
    16/9/13 42.08
    23/9/13 40.24001
    30/9/13 51.77
    7/10/13 93.52
    14/10/13 113.89
    21/10/13 133.5
    28/10/13 231.05
    4/11/13 447.08
    11/11/13 874.55
    18/11/13 1091.99
    25/11/13 916.27
    2/12/13 927.8199
    9/12/13 681.78
    16/12/13 789.11
    23/12/13 899
    30/12/13 937.92
    6/1/14 877.1
    13/1/14 900
    20/1/14 828.99
    27/1/14 750
    3/2/14 640
    10/2/14 628.37
    17/2/14 550
    24/2/14 574.73
    3/3/14 569.53
    10/3/14 546.83
    17/3/14 460
    24/3/14 418.31
    31/3/14 375
    7/4/14 467.54
    14/4/14 369
    21/4/14 402.16
    28/4/14 356
    5/5/14 410.9
    12/5/14 548.66
    19/5/14 652.71
    26/5/14 650
    2/6/14 571.71
    9/6/14 590
    16/6/14 565
    23/6/14 561.2
    30/6/14 592.14
    7/7/14 514.12
    14/7/14 500.84
    21/7/14 565.93
    28/7/14 587.76
    4/8/14 484.97
    11/8/14 443
    18/8/14 410.53
    25/8/14 437.92
    1/9/14 462.43
    8/9/14 324.44
    15/9/14 360.15
    22/9/14 253.36
    29/9/14 381.64
    6/10/14 385.55
    13/10/14 349.98
    20/10/14 319.9
    27/10/14 340.98
    3/11/14 363.96
    10/11/14 348.09
    17/11/14 371.5
    24/11/14 376
    1/12/14 319.55
    8/12/14 334.97
    15/12/14 343.46
    22/12/14 262.8
    29/12/14 250.09
    5/1/15 190.02
    12/1/15 380.51
    19/1/15 189.48
    26/1/15 209.59
    2/2/15 223.9
    9/2/15 223.5
    16/2/15 254.85
    23/2/15 251.34
    2/3/15 305.86
    9/3/15 249.82
    16/3/15 280
    23/3/15 220.56
    30/3/15 279.94
    6/4/15 265
    13/4/15 200
    20/4/15 224.68
    27/4/15 195.91
    4/5/15 245.03
    11/5/15 227.36
    18/5/15 269.69
    25/5/15 228.8
    1/6/15 220.5
    8/6/15 212.87
    15/6/15 225.62
    22/6/15 262.18
    29/6/15 343.58
    6/7/15 312.15
    13/7/15 301.96
    20/7/15 315
    27/7/15 262.04
    3/8/15 229.08
    10/8/15 257.53
    17/8/15 220.4
    24/8/15 249.46
    31/8/15 230.8
    7/9/15 223.27
    14/9/15 246.48
    21/9/15 250.66
    28/9/15 239.59
    5/10/15 273.53
    12/10/15 300.01
    19/10/15 377.69
    26/10/15 451.39
    2/11/15 371.79
    9/11/15 376.89
    16/11/15 418.39
    23/11/15 440.58
    30/11/15 505.46
    7/12/15 516.24
    14/12/15 481.21
    21/12/15 482.38
    28/12/15 542.2
    4/1/16 454.28
    11/1/16 473.92
    18/1/16 432.58
    25/1/16 429.39
    1/2/16 467.05
    8/2/16 509.61
    15/2/16 506.68
    22/2/16 448.07
    29/2/16 443.69
    7/3/16 484.58
    14/3/16 489.97
    21/3/16 485.82
    28/3/16 455.66
    4/4/16 474.93
    11/4/16 516.19
    18/4/16 488.28
    25/4/16 555.87
    2/5/16 542.67
    9/5/16 512.75
    16/5/16 601.27
    23/5/16 688.69
    30/5/16 803.09
    6/6/16 953.05
    13/6/16 805.65
    20/6/16 797.08
    27/6/16 771.54
    4/7/16 795.01
    11/7/16 793.52
    18/7/16 723.18
    25/7/16 687.93
    1/8/16 650.5
    8/8/16 660
    15/8/16 670
    22/8/16 715.6
    29/8/16 714
    5/9/16 734.99
    12/9/16 686.2
    19/9/16 719.42
    26/9/16 715.57
    3/10/16 754
    10/10/16 761.02
    17/10/16 825
    24/10/16 825.83
    31/10/16 831.9
    7/11/16 900.52
    14/11/16 902.97
    21/11/16 924.27
    28/11/16 975.2
    5/12/16 1006.2
    12/12/16 1135.94
    19/12/16 1281.4
    26/12/16 1144.41
    2/1/17 995.16
    9/1/17 1123.2
    16/1/17 1138.34
    23/1/17 1247.74
    30/1/17 1241.48
    6/2/17 1275.95
    13/2/17 1453.46
    20/2/17 1590.27
    27/2/17 1549.1
    6/3/17 1262.27
    13/3/17 1177.61
    20/3/17 1372.88
    27/3/17 1512.83
    3/4/17 1488.75
    10/4/17 1583.46
    17/4/17 1681.71
    24/4/17 2096.67
    1/5/17 2495.07
    8/5/17 2760.85
    15/5/17 2994.79
    22/5/17 3393.27
    29/5/17 3789.46
    5/6/17 3488.86
    12/6/17 3403.31
    19/6/17 3242.76
    26/6/17 3315.51
    3/7/17 2410
    10/7/17 3441.5
    17/7/17 3429.74
    24/7/17 3960.53
    31/7/17 5218.14
    7/8/17 5198.76
    14/8/17 5520
    21/8/17 5918.4
    28/8/17 5219.46
    4/9/17 4493.05
    11/9/17 4525.38
    18/9/17 5465.36
    25/9/17 5787.35
    2/10/17 7126.76
    9/10/17 7613.93
    16/10/17 7918.65
    23/10/17 9592.39
    30/10/17 7824.89
    6/11/17 10593.55
    13/11/17 12197.99
    20/11/17 14924.19
    27/11/17 21084.87
    4/12/17 25886.55
    11/12/17 18839.79
    18/12/17 18950.74
    25/12/17 22762.21
    1/1/18 18941.51
    8/1/18 15048.37
    15/1/18 14345.12
    22/1/18 10125.82
    29/1/18 10282.72
    5/2/18 13238.45
    12/2/18 12200.72
    19/2/18 14663.94
    26/2/18 12043.73
    5/3/18 10546.88
    12/3/18 10939.19
    19/3/18 8735.98
    26/3/18 9030.39
    2/4/18 10554.32
    9/4/18 11257.21
    16/4/18 12332.76
    23/4/18 12582.62
    30/4/18 11460.03
    7/5/18 11218.46
    14/5/18 9652.02
    21/5/18 10133.1
    28/5/18 8856.31
    4/6/18 8617.19
    11/6/18 8152.91
    18/6/18 8389.05
    25/6/18 8853.63
    2/7/18 8455.52
    9/7/18 9847.28
    16/7/18 11014.06
    23/7/18 9459.81
    30/7/18 8619.77
    6/8/18 8820.44
    13/8/18 9072.49
    20/8/18 9981.22
    27/8/18 8702.43
    3/9/18 8958.83
    10/9/18 9018.22
    17/9/18 9039.68
    24/9/18 9164.69
    1/10/18 8635.74
    8/10/18 8905.48
    15/10/18 8919.61
    22/10/18 8808.97
    29/10/18 8741.39
    5/11/18 7479.24
    12/11/18 5335.57
    19/11/18 5486.65
    26/11/18 4814.89
    3/12/18 4340.44
    10/12/18 5496.18
    17/12/18 5356.26
    24/12/18 5586.6
    31/12/18 4808.14
    7/1/19 4862.34
    14/1/19 4842.09
    21/1/19 4634.24
    28/1/19 5032.33
    4/2/19 4983.2
    11/2/19 5113.99
    18/2/19 5240.09
    25/2/19 5455.14
    4/3/19 5526.45
    11/3/19 5517.53
    18/3/19 5638.09
    25/3/19 7153.71
    1/4/19 7114.66
    8/4/19 7337.26
    15/4/19 7305.25
    22/4/19 8020.41
    29/4/19 9862.31
    6/5/19 11784.94
    13/5/19 12517.35
    20/5/19 12506.94
    27/5/19 10883.83
    3/6/19 12861.26
    10/6/19 15472.87
    17/6/19 15080.16
    24/6/19 16268.05
    1/7/19 14557.08
    8/7/19 14957.73
    15/7/19 13791.59
    22/7/19 16032.89
    29/7/19 16937.56
    5/8/19 15248.79
    12/8/19

Solutions

Expert Solution

I am assuming the unit of return is %.

The following output is obtained using the 'Descriptive Statistics' tools in Excel.

Steps:

  1. Input the data in Excel.
  2. click the data whose summary has to be obtained. In our case 'Weekly Return'
  3. Click on 'Data' on the toolbar and then select 'Data Analysis' on the top right corner
  4. Select 'Descriptive Statistics' from the options.
  5. Fill the required information and the output will be obtained.
Weekly Return
Mean 3556.180
Standard Error 269.817
Median 734.990
Mode #N/A
Standard Deviation 4938.460
Sample Variance 24388386.970
Kurtosis 2.270
Skewness 1.638
Range 25932.710
Minimum -46.160
Maximum 25886.550
Sum 1191320.170
Count 335.000

The yellow coloured values are the measures of location and the green coloured are the measures of spread. With the help of both of these measures we can interpret the shape of the data.


Measures of location:

Mean tells us on an average what weekly return would be. It is 3556.180%. It is too far from the -46.16% in 2013 and from the 25886.6% in 2019.

This can be greatly affected by the extreme values.

Median is point where below it 50% (half) of the data lies and 50% lies above it. If median is 734.99%, that means 50% of the returns calculated over the 6 years period were below this point and rest above it.

Like mean it is not affected by the extreme values.

Mode is the poit with the highest frequency It is difficult to determine in this data since the returns haven't repeated to calculate the highest frequecny.

Measures of spread: It tells us how much spread, variation is there in the data.

Range is the diffeence between the maximum and the minimum value. It is 25932.710. This is very high but it only measures the absolute difference and ignores the intermediate values.

Standard deviation (square root of variance) is the average deviation of the values from the mean. Each value would deviate from the mean on some level. SD calculates the average deviation. the higher the value the higher would be the variation between the values. It is 4938.460%. On average the values differ by 4938.46% from the mean return.

Interquartile range which is the difference between the 1st and 3rd quartile tells us about the central 50% of the data. it is 5169.73%.

Shape:

It can be determined by the skewness. It is 1.638. This means the data is positively skewed. This means the data has the few high scores shifting towards the mean. It can also be interpreted by looking at the mean and median. Mean > median.

Kurtosis tells us about the shape of the distribution, its tails. High kurtosis have fatter tails means they contain high extreme values and more like a normal distribution. It is 2.27 which is high and closer to kurtosis of normal distribution (3).


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