Quantitative Methods Project

Indian Institute of Management, Bangalore

Dharmesh Gandhi
PGSEM – Section ‘A’
Quantitative Methods 1
Final Assignment
Stocks Analyzed : RIL, SBI, Dr Reddy’s, Hindalco, Satyam
and Nifty

QM1 Assignment

All the data are adjusted for stock/splits and bonuses .Dividends are ignored

The returns are in %

1. Descriptive Statistics

1.1 Daily returns
Stock RIL SBI Dr Reddy Hindalco Satyam Nifty

Mean 0.099013838 0.069136782 0.120480846 0.0345841 0.28548121 0.033745968

Median 0.005703856 0 0 0 0 0.046533869

Mode 0 0 0 0 0 0

Skewness 0.444522438 0.175873627 0.075526213 -0.65485711 0.201215992 -0.12423968

Kurtosis 2.854520157 2.547972933 2.890787744 14.94130293 0.994890493 5.049793853

Max 15.1026393 16.81338028 12.69599441 16.56072265 16.4893617 10.91974165

Min -15.352349 -14.7669895 -18.1323334 -31.1499631 -15.9923237 -12.2377401

SD 2.723 2.704 2.9 2.43 4.17 1.691

Analysis

RIL: Mean, median and mode are all quite close to zero. Min, max and mean values suggest
symmetricity. However Range is approx 30 which is much more than 6σ .It is not a normal distribution.
Kurtosis is more than 0 implying a leptokurtic curve. It is a positively skewed curve.

SBI: Mean, median and mode are all quite close to zero. Min, max and mean values suggest
symmetricity. However Range is approx 30 which is much more than 6σ . It is not a normal distribution.

Dr Reddy’s : Mean is not equal to median and mode.Min and max values suggest a non-symmetric
curve.Range is approx 30 which is much more than 6σ. It is not a normal distribution. Kurtosis is more
than 0 implying a leptokurtic curve. It is a positively skewed curve.

Hindalco: Mean, median and mode are quite close. Min and max values suggest a non-symmetric
curve.Range is approx 47 which is much more than 6σ. It is not a normal distribution. Kurtosis is much
more than 0 implying a leptokurtic curve. It is a negatively skewed curve.

2|Page

QM1 Assignment

Satyam: Mean, median and mode are not quite close. Min and max values suggest a symmetric
curve.Range is approx 32 which is more than 6σ. It is not a normal distribution. Kurtosis is much more

Nifty: Mean, median and mode are quite close. Min and max values suggest a symmetric curve. Range is
approx 33 which is more than 6σ. It is not a normal distribution. Kurtosis is much more than 0 implying
a leptokurtic curve. It is a positively skewed curve.

1.2 Monthly return


Mean 2.259506206 1.743758789 2.861548397 1.033867437 7.12144637 0.87903147

Median 1.114649682 1.037089119 1.453488372 0.706190061 3.035032952 0.589599845

Mode 0 0 0 0 0 #N/A

Skewness 0.544226315 0.639824424 0.343847796 0.224917217 1.349531713 0.028199808

Kurtosis 1.217994303 1.727850253 0.057784501 0.614954091 3.802653999 -0.313170521

Max 57.98462852 72.26070529 46.57008948 52.23140496 160.4017217 26.07249791

Min -44.13177 -33.15266486 -36.78387097 -41.17212509 -49.3184466 -26.0693657

SD 13.03 13.42 13.56 12.82 24.88 8.32

Analysis

RIL: Mean, median and mode are not close. Min and max values suggest a non-symmetric curve. Range
is approx 102 which is more than 6σ. It is not a normal distribution. Kurtosis is much more than 0
implying a leptokurtic curve. It is a positively skewed curve.

SBI: Mean, median and mode are not close. Min and max values suggest a highly non-symmetric curve.
Range is approx 105 which is more than 6σ. It is not a normal distribution. Kurtosis is much more than 0

Dr Reddy: Mean, median and mode are not close. Min and max values suggest a non-symmetric curve.
Range is approx 83 which is more than 6σ. It is not a normal distribution. Kurtosis is slightly more than 0
implying a slight leptokurtic curve. It is a positively skewed curve.

Hindalco: Mean, median and mode are not close. Min and max values suggest a non-symmetric curve.
Range is approx 93 which is more than 6σ. It is not a normal distribution. Kurtosis is more than 0

3|Page

QM1 Assignment

Satyam: Mean, median and mode are quite far apart. Min and max values suggest a highly non-
symmetric curve. Range is approx 210 which is more than 6σ. It is not a normal distribution. Kurtosis is
more than 0 implying a leptokurtic curve. It is a positively skewed curve.

Nifty: Mean, median and mode are reasonably close. Min and max values suggest a symmetric curve.
Range is approx 52 which is quite close to 6σ. Kurtosis is slightly less than 0 implying a slightly
platykurtic curve. However, the skewness is almost 0. The curve has lot of properties of a normal
distribution.

1.3 Yearly return


Mean 29.65791997 15.48411764 39.76150302 9.914655201 139.7434961 9.968663069

Median 21.22872801 10.13151486 37.64470783 -7.594285714 54.15122313 -0.950419

Mode 100 5.535714286 -27.76548673 73.91304348 300 #N/A

Skewness 0.619341948 0.87772208 0.991949901 1.187115272 0.988186367 1.026198069

Kurtosis -0.421263142 0.536904004 0.897045857 0.522072956 0.188012776 0.043321

Max 202.5 132.3058378 237.9045529 146.7416667 827.5221652 102.184

Min -48.62697448 -49.07088782 -39.48145025 -59.31397096 -80.76086957 -34.18092156

SD 47.78 37.7 53.82 46.13 190.77 30.77

Analysis

RIL: Mean, median and mode are quite far apart. Min and max values suggest a highly non-symmetric
curve. Range is approx 250 which is less than 6σ(288). It is not a normal distribution. Kurtosis is less
than 0 implying a platykurtic curve. It is a positively skewed curve.

SBI: Mean, median and mode are quite far apart. Min and max values suggest a highly non-symmetric
curve. Range is approx 172 which is less than 6σ(228). It is not a normal distribution. Kurtosis is more

Dr Reddy: Mean, median and mode are quite far apart. Min and max values suggest a highly non-
symmetric curve. Range is approx 277 which is less than 6σ(324). It is not a normal distribution. Kurtosis
is more than 0 implying a leptokurtic curve. It is a positively skewed curve.

4|Page

QM1 Assignment

Hindalco: Mean, median and mode are quite far apart. Min and max values suggest a highly non-
symmetric curve. Range is approx 206 which is less than 6σ(276). It is not a normal distribution. Kurtosis
is more than 0 implying a leptokurtic curve. It is a positively skewed curve.

Satyam: Mean, median and mode are quite far apart. Min and max values suggest a highly non-
symmetric curve. Range is approx 908 which is less than 6σ(1146). It is not a normal distribution.

Nifty: : Mean, median and mode are quite far apart. Min and max values suggest a highly non-symmetric
curve. Range is approx 136 which is less than 6σ(180). It is not a normal distribution. Kurtosis is slightly
more than 0 implying a slightly-leptokurtic curve. It is a positively skewed curve.

2 Frequency distributions and histograms
2.1 Daily returns
2.1.1 RIL daily returns
Bin Freq

-9 4
-7.5 15
-6 13
-4.5 39
-3 144
-1.5 301
0 559
1.5 552
3 296
4.5 107
6 48
7.5 32
9 29
10.5 6
More 5

5|Page

QM1 Assignment

2.1.2 SBI daily returns
Bin Frequency
-9 7
-7.5 14
-6 13
-4.5 42
-3 122
-1.5 345
0 536
1.5 519
3 324
4.5 122
6 48
7.5 24
9 28
10.5 5
More 1

6|Page

QM1 Assignment

2.1.3 Dr Reddy Daily returns
Bin Frequency
-10.5 5
-9 7
-7.5 22
-6 24
-4.5 39
-3 103
-1.5 281
0 626
1.5 540
3 243
4.5 121
6 50
7.5 35
9 44
10.5 7
More 3

7|Page

QM1 Assignment

2.1.4 Hindalco daily returns
Bin Frequency
-9 1
-7.5 10
-6 22
-4.5 34
-3 95
-1.5 264
0 676
1.5 625
3 236
4.5 107
6 46
7.5 16
9 14
10.5 2
More 2

8|Page

QM1 Assignment

2.1.5 Satyam daily returns
Bin Frequency
-12 6
-10.5 6
-9 20
-7.5 46
-6 45
-4.5 89
-3 157
-1.5 303
0 411
1.5 372
3 234
4.5 159
6 99
7.5 67
9 71
10.5 45
12 9
More 11

9|Page

QM1 Assignment

2.1.6 Nifty daily returns
Bin Frequency
-9 2
-7.5 3
-6 3
-4.5 13
-3 44
-1.5 233
0 741
1.5 787
3 254
4.5 50
6 11
7.5 4
9 4
More 1

10 | P a g e

QM1 Assignment

11 | P a g e

QM1 Assignment

2.2 Monthly returns
2.2.1 RIL monthly returns
Bin Frequency
-40 1
-35 3
-30 9
-25 11
-20 50
-15 74
-10 159
-5 295
0 378
5 354
10 302
15 187
20 130
25 71
30 34
35 27
40 15
45 13
50 11
More 5

12 | P a g e

QM1 Assignment

2.2.2 SBI monthly returns
Bin Frequency
-30 8
-25 29
-20 57
-15 94
-10 182
-5 269
0 353
5 347
10 288
15 238
20 99
25 66
30 36
35 21
40 14
45 9
50 8
55 2
60 8
More 1

13 | P a g e

QM1 Assignment

2.2.3 Dr Reddy monthly returns
Bin Frequency
-30 5
-25 26
-20 46
-15 82
-10 173
-5 277
0 348
5 322
10 266
15 202
20 125
25 108
30 83
35 36
40 16
45 8
More 6

14 | P a g e

QM1 Assignment

2.2.4 Hindalco monthly returns
Bin Frequency
-40 1
-35 1
-30 17
-25 35
-20 37
-15 118
-10 187
-5 255
0 360
5 358
10 279
15 230
20 108
25 51
30 46
35 28
40 5
45 10
More 3

15 | P a g e

QM1 Assignment

16 | P a g e

QM1 Assignment

2.2.5 Satyam monthly returns
Bin Frequency
-45 8
-40 8
-35 23
-30 33
-25 35
-20 79
-15 120
-10 160
-5 222
0 249
5 213
10 181
15 177
20 138
25 107
30 89
35 56
40 35
45 41
50 27
55 22
60 24
65 15
70 15
75 8
80 10
85 8
More 26

17 | P a g e

QM1 Assignment

18 | P a g e

QM1 Assignment

2.2.6 Nifty monthly returns
Bin Frequency
-20 4
-17.5 19
-15 38
-12.5 56
-10 88
-7.5 130
-5 181
-2.5 237
0 251
2.5 234
5 208
7.5 208
10 155
12.5 133
15 84
17.5 59
20 29
22.5 10
25 3
More 2

19 | P a g e

QM1 Assignment

20 | P a g e

QM1 Assignment

2.3 Yearly returns

2.3.1 RIL yearly returns
Bin Frequency
-40 16
-30 76
-20 192
-10 210
0 211
10 109
20 123
30 159
40 116
50 90
60 64
70 77
80 106
90 99
100 92
110 68
120 41
130 17
140 16
150 6
160 8
170 5
180 6
More 4

21 | P a g e

QM1 Assignment

22 | P a g e

QM1 Assignment

2.3.2
SBI yearly returns
Bin Frequency
-40 51
-30 144
-20 119
-10 154
0 209
10 277
20 272
30 185
40 115
50 83
60 57
70 44
80 37
90 48
100 32
110 34
120 27
130 22
More 1

23 | P a g e

QM1 Assignment

2.3.3 Dr Reddy’s Yearly returns
Bin Frequency
-30 44
-20 147
-10 198
0 184
10 121
20 88
30 79
40 138
50 220
60 139
70 123
80 66
90 68
100 63
110 31
120 42
130 30
140 21
150 19
160 12
170 8
180 19
190 16
200 11
210 13
More 11

24 | P a g e

QM1 Assignment

25 | P a g e

QM1 Assignment

2.3.4 Hindalco yearly returns
Bin Frequency
-50 22
-40 60
-30 179
-20 237
-10 387
0 247
10 129
20 85
30 69
40 63
50 69
60 53
70 61
80 40
90 31
100 33
110 29
120 35
130 47
140 29
More 6

26 | P a g e

QM1 Assignment

27 | P a g e

QM1 Assignment

2.3.5 Satyam Yearly returns
Bin Frequency
-75 8
-50 179
-25 157
0 203
25 229
50 157
75 119
100 54
125 20
150 23
175 48
200 51
225 49
250 60
275 70
300 71
325 66
350 55
375 33
400 36
425 35
450 45
475 20
500 16
525 16
550 17
575 16
600 10
625 16
More 32

28 | P a g e

QM1 Assignment

29 | P a g e

QM1 Assignment

2.3.6 Nifty Yearly returns
Bin Frequency
-30 5
-20 203
-10 365
0 417
10 217
20 183
30 107
40 43
50 66
60 98
70 91
80 55
90 42
100 15
110 4
More 0

30 | P a g e

QM1 Assignment

3 Using the frequency distribution of daily/monthly/yearly returns,
answer the following questions:
3.1 Probability of a positive return


Daily 0.509302326 0.50744186 0.510232558 0.505116279 0.521860465 0.519534884

Monthly 0.540629403 0.535932363 0.55284171 0.527477689 0.56552372 0.528417097

Yearly 0.631083203 0.64678179 0.700156986 0.407639979 0.714809001 0.481946625

3.2 Probability of a negative return

RIL SBI Dr Reddy Hindalco Satyam Nifty

Daily 0.490697674 0.49255814 0.489767442 0.494883721 0.478139535 0.480465116

Monthly 0.459370597 0.464067637 0.44715829 0.472522311 0.43447628 0.471582903

Yearly 0.368916797 0.35321821 0.299843014 0.592360021 0.285190999 0.518053375

3.3 Probability of a loss of more than 10%


Monthly 0.14372945 0.173790512 0.155941757 0.186002818 0.218882104 0.096289338

Yearly 0.258503401 0.244897959 0.203558346 0.46310832 0.252223967 0.299843014

31 | P a g e

QM1 Assignment

3.4 Probability of a gain of more than 15%


Monthly 0.14372945 0.124001879 0.179426961 0.117895726 0.291686238 0.048379521

Yearly 0.545787546 0.423338566 0.610675039 0.312401884 0.639455782 0.321821036

4 Conditional probability if today’s return is between 5-10%
A= event that return after one month is

B= event that today’s return is between 5-10%

P(A/B)=P(A ∩Β)/ P(B)

4.1 If today’s return is 5%-10%, what is the probability that return of after
one month
EventAStock RIL SBI Dr Reddy Hindalco Satyam Nifty

5%-10% 0.101123596 0.023529412 0.076923077 0 0.131147541 0

>5% 0.101123596 0.023529412 0.076923077 0 0.135245902 0

>10% 0 0 0 0 0.004098361 0

32 | P a g e

QM1 Assignment

one year

5%-10% 0.056818182 0.024691358 0.061403509 0 0.140350877 0

>5% 0.056818182 0.024691358 0.061403509 0 0.162280702 0

>10% 0 0 0 0 0.021929825 0

5 Assuming the distribution of daily return to be normal answer the
above questions and compare and comment

X= return after one month/year

B=event that today’s return is between 5-10%

Assume the conditional variable X/B follows a normal distribution

one month

Mean(X/B) -0.16674872 0.148229898 -0.08257506 -0.5691103 -0.11021055 0.339731985

SD(X/B) 3.295984188 2.735541665 3.671949127 2.318709615 4.617763138 1.924326132

5%-10% 0.057469358 0.037906007 0.080136485 0.00815441 0.119941113 0.007722383

>5% 0.058488535 0.038064263 0.083154319 0.00815699 0.134224375 0.007722642

>10% 0.001019176 0.000158256 0.003017834 2.57986E-06 0.014283261 2.58252E-07

33 | P a g e

QM1 Assignment

Comparison:

RIL: The conditional probabilities are about half of those derived from the data. The assumption of
normality needs to be checked.

SBI: The conditional probabilities are quite close to those derived from the data.

Dr Reddy: The conditional probabilities are quite close to those derived from the data.

Hindalco: The conditional probabilities are quite close to those derived from the data.

Satyam: The conditional probabilities are quite close to those derived from the data.

Nifty: The conditional probabilities are quite close to those derived from the data.

one year


Mean(X/B) 3.242826551 3.602205133 7.305029634 0.463840804 9.90210935 1.683467465

SD(X/B) 10.98286795 14.43921291 12.57186648 11.57493635 24.6384195 8.060838659

5%-10% 0.167247701 0.132588216 0.15760646 0.142559148 0.080438796 0.18927429

>5% 0.436443601 0.461440438 0.572737608 0.347567914 0.578853767 0.340375825

>10% 0.2691959 0.328852222 0.415131148 0.205008767 0.498414971 0.151101534

Comparison:

RIL: The conditional probabilities are quite different. The assumption of normality needs to be checked.

SBI: The conditional probabilities are quite different. The assumption of normality needs to be checked.

Dr Reddy: The conditional probabilities are quite different. The assumption of normality needs to be
checked.

Hindalco: The conditional probabilities are quite different. The assumption of normality needs to be
checked.

34 | P a g e

QM1 Assignment

Satyam: The conditional probabilities are quite different. The assumption of normality needs to be
checked.

Nifty: The conditional probabilities are quite different. The assumption of normality needs to be
checked.

6 Estimate a 95% confidence interval for the average
daily/monthly/yearly return.

6.1 RIL
Average daily return Average monthly return Average yearly return

K1 -0.01610043 1.7055041 27.51544905

K2 0.214128104 2.813508313 31.80039089

6.2 SBI

K1 -0.04517166 1.173506538 13.79382365

K2 0.183445227 2.314011041 17.17441162

6.3 Dr. Reddy’s

K1 -0.0021716 2.285435212 37.34823327

K2 0.243133288 3.437661581 42.17477278

6.4 Hindalco

K1 -0.0680646 0.489090237 7.846038599

K2 0.137232799 1.578644638 11.9832718

35 | P a g e

QM1 Assignment

6.5 Satyam

K1 0.10936845 6.064716894 131.1902405

K2 0.46159397 8.178175845 148.2967518

6.6 Nifty

K1 -0.03774256 0.525498641 8.589232903

K2 0.105234498 1.232564299 11.34809323

7 Test the hypothesis that the average daily/monthly/yearly return is
more than 10%.

Test hypothesis

H0: µ >= 10% v/s Ha: µ< 10%

Reject H0 if sample mean < critical value

7.1 RIL
Daily Monthly Yearly

Sample Mean 0.099013838 2.259506206 29.65791997

Critical Value 9.903393063 9.535066776 8.201981723

Decision Reject H0 Reject H0 Accept H0

36 | P a g e

QM1 Assignment

7.2 SBI

Sample Mean 0.069136782 1.743758789 15.48411764

Critical Value 9.904069329 9.521429224 8.581460573


7.3 Dr Reddy’s

Sample Mean 0.120480846 2.861548397 39.76150302

Critical Value 9.897066826 9.516510575 7.974720179


7.4 Hindalco

Sample Mean 0.0345841 1.033867437 9.914655201

Critical Value 9.913854496 9.542808561 8.263962223


7.5 Satyam

Sample Mean 0.28548121 7.12144637 139.7434961

Critical Value 9.852201513 9.113164668 2.821881622


37 | P a g e

QM1 Assignment

7.6 Nifty

Sample Mean 0.033745968 0.87903147 9.968663069

Critical Value 9.940004935 9.703305897 8.842345712


8 Estimate a 95% confidence interval for the proportion of time when
the daily/monthly/yearly return exceeds 10%.

P = (Number of days return > 10%)/Sample Size

Confidence Interval = P^ +/- Zα/2× √ (p (1-p)/n); where n = number of samples

n = 2150 for daily returns, 2129 for monthly returns, 1911 for yearly returns

8.1 RIL

Sample proportion 0.002790698 0.231564115 0.574045003

K1 0.000560833 0.213645695 0.551874651

K2 0.005020562 0.249482534 0.596215354

38 | P a g e

QM1 Assignment

8.2 SBI


K1 -0.00044628 0.217760019 0.478367427

K2 0.001376515 0.253822884 0.523202431

K1 Proportion cannot be less than 0 .This
result can come because sample
proportion is very small

8.3 Dr Reddy


K1 0.000289529 0.255355177 0.615277697

K2 0.004361634 0.293259196 0.658401006

8.4 Hindalco


K1 -0.00035838 0.208163871 0.318895234

K2 0.002218846 0.24369146 0.361376875

39 | P a g e

QM1 Assignment

8.5 Satyam


K1 0.006721823 0.354261401 0.648721233

K2 0.015603759 0.395386321 0.690891536

8.6 Nifty


K1 -0.00044628 0.135125059 0.346766474

K2 0.001376515 0.165485556 0.390020548

9 Test the hypothesis that 90% of the time the daily/monthly/yearly
returns exceeds 10%.

p= (number of times the return exceed 10%)/(sample size)

H0: P=0.9 v/s Ha : P≠0.9

Reject H0 if p<k1 or p>k2; wherein k1 and k2 are the critical values

40 | P a g e

QM1 Assignment

9.1 RIL


K1 0.887319099 0.887256712 0.886549482

K2 0.912680901 0.912743288 0.913450518

Decision Reject H0 Reject H0 Reject H0

9.2 SBI


K1 0.887319099 0.887256712 0.886549482

K2 0.912680901 0.912743288 0.913450518


9.3 Dr Reddy’s


K1 0.887319099 0.887256712 0.886549482

K2 0.912680901 0.912743288 0.913450518


9.4 Hindalco


K1 0.887319099 0.887256712 0.886549482

41 | P a g e

QM1 Assignment

K2 0.912680901 0.912743288 0.913450518


9.5 Satyam


K1 0.887319099 0.887256712 0.886549482

K2 0.912680901 0.912743288 0.913450518


9.6 Nifty


K1 0.887319099 0.887256712 0.886549482

K2 0.912680901 0.912743288 0.913450518


10 Assuming standard deviation to be a measure of risk, compute a 95%
confidence interval for the risk measure for daily/monthly/yearly
returns.

√((n-1)s2/χ2α/2) < σ < √((n-1)s2/χ21-α/2)

χ2 has degrees of freedom n-1.Since n is large χ2 will be a normal distribution

χ2 ~N ( n-1, 2n-2 )

n = 2150 for daily returns, 2129 for monthly returns, 1911 for yearly returns

42 | P a g e

QM1 Assignment

10.1 RIL

Sample SD 2.723330095 13.04220901 47.78561601

K1 2.645391271 12.66719609 46.33873518

K2 2.808590171 13.45263082 49.37708323

10.2 SBI

Sample SD 2.704266289 13.42476675 37.70027324

K1 2.626873051 13.03875384 36.55876232

K2 2.788929528 13.84722716 38.95585503

10.3 Dr. Reddy’s

Sample SD 2.901665448 13.56274367 53.82550615

K1 2.818622855 13.1727634 52.195746

K2 2.99250872 13.98954604 55.61812777

10.4 Hindalco

Sample SD 2.428424398 12.82503808 46.13837114

K1 2.358925463 12.45626964 44.74136656

K2 2.504451777 13.22862579 47.674978

43 | P a g e

QM1 Assignment

10.5 Satyam

Sample SD 4.166409587 24.8773182 190.7715916

K1 4.047171356 24.16200104 184.9952978

K2 4.296848565 25.66017591 197.1251088

10.6 Nifty

Sample SD 1.691248809 8.322800569 30.76677472

K1 1.642847058 8.083488518 29.83520032

K2 1.74419722 8.584708566 31.79144108

11 Compute a 95% VaR for the top three high-risk stocks assuming the
daily/monthly/yearly return distribution to be normal

Compute the mean and variance of negative daily returns .VaR(Value at risk) here would be the
maximum loss faced by the investor 95% of the time given the fact that he faces a loss. Hence we pick all
the negative returns as our data set. 5th percentile of this distribution (assuming it to be normal) would
be the VaR.

Here, a negative value would imply a LOSS.

The 3 most volatile stocks are RIL, Satyam and Dr Reddy’s (decided by looking at the SD of yearly return).

44 | P a g e

QM1 Assignment

11.1 RIL

Mean -1.89724528 -8.354053438 -17.47098572

Variance 2.819324919 46.83624966 115.151983

95% VaR -4.65909359 -19.61094061 -35.12172774

Number of days in last 6
months when |VaR|
was exceeded 5 8 0

11.2 Dr Reddy’s

Mean -1.91531609 -8.811026718 -15.90522586

Variance 4.01711585 46.42409842 89.45323824

95% VaR -5.2120541 -20.01827507 -31.46220575

months when |VaR|
was exceeded 4 11 20

11.3 Satyam

Mean -2.94826329 -12.57627678 -37.74318809

Variance 6.42648655 100.4819388 529.7815985

95% VaR -7.11805209 -29.06440135 -75.60275935

0 0 0
months when |VaR|

45 | P a g e

QM1 Assignment

was exceeded

12 Count the number of days when VaR is exceeded during the last six
months in the data set and comment on the effectiveness of the VaR
estimate

12.1 RIL
The VaR is exceeded 5 times for the daily returns which is 3.79% < 5% which is good.

It is exceeded 8 times for the monthly returns which is 6 % > 5% ; not very good.

It is never exceeded for the yearly returns. Excellent.

12.2 Dr Reddy’s
The VaR is exceeded 4 times for the daily returns which is 3% < 5% which is good.

It is exceeded 11 times for the monthly returns which is 8.33 % > 5% ; not very good.

It is exceeded 20 times for the yearly returns which is 15.15% which is really bad.

12.3 Satyam
The VaR estimate is never exceeded for Satyam which is excellent.

13 Test if the assumption of normality of the daily/monthly/yearly
return distribution is valid.

Goodness of fit tests

H0: distribution is Normal v/s Ha : distribution is not normal

χ2calc =∑(Oi – Ei)2 /Ei
2 2
Reject H0 if χ calc > χ 0.05,n-1

46 | P a g e

QM1 Assignment

13.1 RIL
13.1.1 RIL Daily returns
Mod Obs Mod Expected
2
Bin Freq freq(O) Exp Cumulative Exp daily freq(E) (O-E) /E
-9 4 0.896943503 0.896944
-7.5 15 19 5.660186731 4.763243 5.660186731 31.439
-6 13 13 27.00467824 21.34449 21.34449151 3.262225
-4.5 39 39 98.11314674 71.10847 71.1084685 14.49833
-3 144 144 274.2769046 176.1638 176.1637578 5.872419
-1.5 301 301 598.8828895 324.606 324.6059849 1.716674
0 559 559 1043.821985 444.9391 444.9390954 29.23971
1.5 552 552 1497.53373 453.7117 453.7117451 21.29233
3 296 296 1841.722615 344.1889 344.1888849 6.746786
4.5 107 107 2035.955844 194.2332 194.2332294 39.17783
6 48 48 2117.483378 81.52753 81.52753385 13.78793
7.5 32 32 2142.931597 25.44822 25.44821849 1.686792
9 29 40 2148.83739 5.905793 7.068403404 153.4279
10.5 6 2149.856083 1.018693
5 2150 0.143917

df 11
χ2 calc 322.1478843
χ2 critical 19.67513757
Hypothesis decision Reject H0

47 | P a g e

QM1 Assignment

13.1.2 RIL Monthly returns
Expected
Bin cumulative
monthly Freq(monthly monthly Exp. Monthly Mod obs
returns ret) returns returns freq Mod exp freq (O-E)2/E
-40 1 1.271453415 1.271453415
-35 3 4.554796217 3.283342802
-30 9 14.24388556 9.689089342 13 14.24388556 0.108625647
-25 11 38.97019528 24.72630972 11 24.72630972 7.619882654
-20 50 93.5403603 54.57016503 50 54.57016503 0.382744094
-15 74 197.695204 104.1548437 74 104.1548437 8.730411037
-10 159 369.6202217 171.9250177 159 171.9250177 0.971679899
-5 295 615.0570402 245.4368184 295 245.4368184 10.00872233
0 378 918.086891 303.0298509 378 303.0298509 18.54775444
5 354 1241.66459 323.5776989 354 323.5776989 2.86026017
10 302 1540.491686 298.827096 302 298.827096 0.033689448
15 187 1779.167646 238.6759596 187 238.6759596 11.1884113
20 130 1944.037831 164.8701857 130 164.8701857 7.375074193
25 71 2042.533273 98.49544176 71 98.49544176 7.675475168
30 34 2093.42239 50.88911716 34 50.88911716 5.605172467
35 27 2116.160857 22.73846669 27 22.73846669 0.798675937
40 15 2124.947362 8.786504764 44 12.83914314 75.62802198
45 13 2127.883522 2.936159893
50 11 2128.731999 0.848477681
5 2129 0.268000807

χ2 calc 157.5346008
degrees of freedom 14
χ2 critical 23.68479131

48 | P a g e

QM1 Assignment

13.1.3 RIL yearly returns
Bin(Yearly Frequency(yearly Exp Cumu Yearly Exp Yearly Mod obs
returns) returns) returns returns freq mod exp freq (O-E)2/E
-40 16 138.4696045 138.4696045 16 138.4696045 108.3183856
-30 76 202.4384941 63.96888961 76 63.96888961 2.262781456
-20 192 285.4273537 82.98885962 192 82.98885962 143.1930596
-10 210 388.4946282 103.0672745 210 103.0672745 110.9431471
0 211 511.0329313 122.5383031 211 122.5383031 63.86143448
10 109 650.5004455 139.4675143 109 139.4675143 6.655811072
20 123 802.4587456 151.9583 123 151.9583 5.518508302
30 159 960.9575482 158.4988026 159 158.4988026 0.001584863
40 116 1119.21995 158.2624014 116 158.2624014 11.28575425
50 90 1270.499325 151.2793753 90 151.2793753 24.82269527
60 64 1408.929856 138.4305312 64 138.4305312 40.01937963
70 77 1530.194505 121.264649 77 121.264649 16.15771096
80 106 1631.886477 101.6919715 106 101.6919715 0.182503192
90 99 1713.523882 81.63740512 99 81.63740512 3.692666377
100 92 1776.263478 62.73959661 92 62.73959661 13.64642511
110 68 1822.42118 46.15770185 68 46.15770185 10.33599961
120 41 1854.929645 32.50846522 41 32.50846522 2.218073431
130 17 1876.847522 21.91787685 17 21.91787685 1.103460561
140 16 1890.994058 14.14653596 16 14.14653596 0.24283888
150 6 1899.734859 8.740800574 6 8.740800574 0.859416449
160 8 1904.904991 5.170132226 8 5.170132226 1.548925882
170 5 1907.83252 2.927529416 15 6.095009063 13.01045868
180 6 1909.419422 1.586901224
4 1911 1.580578423

χ2 calc 579.8810208
χ2 critical 32.67057337

49 | P a g e

QM1 Assignment

13.2 SBI
13.2.1 SBI daily returns
Bin
(Daily
returns) freq mod obs freq exp cumulative exp daily mod expected (O-E)2/E
-9 7 0.857376236 0.857376
-7.5 14 21 5.511232167 4.653856 5.511232167 43.52964
-6 13 13 26.67531665 21.16408 21.16408448 3.149311
-4.5 42 42 97.93670005 71.26138 71.2613834 12.01532
-3 122 122 275.637689 177.701 177.7009889 17.45967
-1.5 345 345 603.8806737 328.243 328.2429847 0.855456
0 536 536 1053.073923 449.1932 449.1932498 16.77543
1.5 519 519 1508.518618 455.4447 455.4446949 8.868863
3 324 324 1850.658874 342.1403 342.1402558 0.961795
4.5 122 122 2041.07737 190.4185 190.4184961 24.58317
6 48 48 2119.581229 78.50386 78.50385909 11.85273
7.5 24 24 2143.55095 23.96972 23.96972089 3.82E-05
9 28 34 2148.969891 5.418941 6.449049734 117.7003
10.5 5 2149.876699 0.906807
1 2150 0.123301

df 11
χ2 calc 257.751696
χ2 critical 19.67513757

50 | P a g e

QM1 Assignment

13.2.2 SBI monthly return
Expected
Bin monthly Freq(month cumulative Exp. Mod obs
returns ly ret) monthly returns Monthly returns freq Mod exp freq (O-E)2/E
-30 8 19.21546821 19.21546821 8 19.21546821 6.546118252
-25 29 49.34786879 30.13240058 29 30.13240058 0.042556552
-20 57 112.0941002 62.74623145 57 62.74623145 0.526233609
-15 94 226.0077547 113.9136544 94 113.9136544 3.48117734
-10 182 406.3110763 180.3033216 182 180.3033216 0.01596597
-5 269 655.1256562 248.8145799 269 248.8145799 1.637569567
0 353 954.4866105 299.3609543 353 299.3609543 9.610963569
5 347 1268.511081 314.0244704 347 314.0244704 3.462741447
10 288 1555.709006 287.1979251 288 287.1979251 0.002240003
15 238 1784.715455 229.0064492 238 229.0064492 0.353195099
20 99 1943.921871 159.2064157 99 159.2064157 22.76800514
25 66 2040.419444 96.49757257 66 96.49757257 9.638604453
30 36 2091.412431 50.99298759 36 50.99298759 4.408246851
35 21 2114.905342 23.49291049 21 23.49291049 0.264530982
40 14 2124.341351 9.436009584 42 14.0946584 55.24845425
45 9 2127.645479 3.30412815
50 8 2128.654112 1.008632811
55 2 2128.922527 0.268414996
60 8 2128.984795 0.062268274
1 2129 0.015204586

χ2 calc 118.0066031
χ2 critical 23.68479131

51 | P a g e

QM1 Assignment

13.2.3 SBI yearly returns
Bin Frequency Exp Cumu mod
(Yearly returns) (yearly returns) Yearly returns Exp Yearly returns Mod obs freq exp freq (O-E)2/E
-40 51 134.8185899 134.8185899 51 134.8185899 52.11118149
-30 144 217.5077831 82.68919326 144 82.68919326 45.45956824
-20 119 331.1705139 113.6627308 119 113.6627308 0.250622542
-10 154 476.8537256 145.6832117 154 145.6832117 0.474790241
0 209 650.963571 174.1098454 209 174.1098454 6.991694724
10 277 844.9895027 194.0259317 277 194.0259317 35.48338077
20 272 1046.602714 201.613211 272 201.613211 24.57329082
30 185 1241.947131 195.3444177 185 195.3444177 0.547786204
40 115 1418.431316 176.4841848 115 176.4841848 21.42007788
50 83 1567.104699 148.673383 83 148.673383 29.00985467
60 57 1683.888628 116.7839286 57 116.7839286 30.60453748
70 44 1769.425834 85.53720635 44 85.53720635 20.170632
80 37 1827.844116 58.41828168 37 58.41828168 7.852726524
90 48 1865.045899 37.20178302 48 37.20178302 3.134298427
100 32 1887.136088 22.09018911 32 22.09018911 4.445609374
110 34 1899.366897 12.23080865 34 12.23080865 38.74622729
120 27 1905.68127 6.31437318 27 6.31437318 67.76526264
130 22 1908.720922 3.039651893 23 5.318730203 58.77855986
1 1911 2.279078311

χ2 calc 447.8201012
χ2 critical 27.58711164
Hypothesis decision Reject Ho

52 | P a g e

QM1 Assignment

13.3 Dr Reddy’s
13.3.1 Dr Reddy’s daily returns
Bin (Daily mod exp mod
returns) freq obs freq cumulative exp daily expected (O-E)2/E
-10.5 5 0.270991 0.270991
-9 7 1.796522 1.525531
-7.5 22 34 9.280793 7.484272 9.280793302 65.83911
-6 24 24 37.53766 28.25687 28.25687023 0.641293
-4.5 39 39 119.6529 82.11522 82.11522308 22.63798
-3 103 103 303.3554 183.7025 183.7025269 35.4535
-1.5 281 281 619.7658 316.4104 316.4104325 3.962887
0 626 626 1039.396 419.6305 419.6305124 101.4902
1.5 540 540 1467.928 428.5319 428.5318994 28.99466
3 243 243 1804.905 336.9772 336.9772044 26.20864
4.5 121 121 2008.94 204.0341 204.0341017 33.79171
6 50 50 2104.056 95.11657 95.11656736 21.40011
7.5 35 86 2138.192 34.13586 34.13585929 78.79951
9 44 54 2147.622 9.429794 11.80800938 150.759
10.5 7 2149.627 2.004717
3 2150 0.373498

df 11
χ2 calc 569.9786
χ2 critical 19.67514

53 | P a g e

QM1 Assignment

13.3.2 Dr Reddy’s monthly returns
Bin Freq Expected cumulative Exp. Monthly Mod
monthly returns (monthly ret) monthly returns returns Mod obs freq exp freq (O-E)2/E
-30 5 16.3890283 16.3890283 5 16.3890283 7.914439053
-25 26 42.52623049 26.13720219 26 26.13720219 0.000720216
-20 46 97.79583037 55.26959988 46 55.26959988 1.55466083
-15 82 199.9696073 102.1737769 82 102.1737769 3.983226289
-10 173 365.0988082 165.129201 173 165.129201 0.375157616
-5 277 598.4144664 233.3156582 277 233.3156582 8.179141225
0 348 886.6201686 288.2057022 348 288.2057022 12.40557707
5 322 1197.864777 311.2446079 322 311.2446079 0.371664138
10 266 1491.726069 293.8612923 266 293.8612923 2.641557861
15 202 1734.288587 242.5625177 202 242.5625177 6.783067137
20 125 1909.331296 175.0427092 125 175.0427092 14.30663837
25 108 2019.764699 110.4334035 108 110.4334035 0.053620122
30 83 2080.674739 60.9100395 83 60.9100395 8.011263146
35 36 2110.044746 29.37000757 36 29.37000757 1.496656052
40 16 2122.425288 12.38054194 16 12.38054194 1.058150499
45 8 2126.987635 4.562346846 14 6.574711829 8.385904335
6 2129 2.012364982

χ2 calc 69.13553962
χ2 critical 24.99579013

54 | P a g e

QM1 Assignment

13.3.3 Dr. Reddy’s yearly returns
Frequency Exp Cumu
Bin(Yearly returns) (yearly returns) Yearly returns Exp Yearly returns Mod obs freq mod exp freq (O-E)2/E
-30 44 186.2767718 186.2767718 44 186.2767718 108.6699088
-20 147 255.0013823 68.72461042 147 68.72461042 89.15345721
-10 198 339.4201311 84.41874888 198 84.41874888 152.8179555
0 184 439.6087304 100.1885992 184 100.1885992 70.11127962
10 121 554.4903347 114.8816043 121 114.8816043 0.325855179
20 88 681.7631038 127.2727691 88 127.2727691 12.11846338
30 79 817.9932818 136.230178 79 136.230178 24.04234744
40 138 958.8780346 140.8847528 138 140.8847528 0.059068129
50 220 1099.647191 140.7691568 220 140.7691568 44.59447408
60 139 1235.542314 135.8951222 139 135.8951222 0.070939015
70 123 1362.293802 126.7514882 123 126.7514882 0.111033516
80 66 1476.517205 114.2234029 66 114.2234029 20.35919546
90 68 1575.968383 99.45117874 68 99.45117874 9.946354146
100 63 1659.628327 83.65994378 63 83.65994378 5.102002912
110 31 1727.623482 67.99515513 31 67.99515513 20.12851504
120 42 1781.017316 53.39383387 42 53.39383387 2.431356598
130 30 1821.526822 40.50950566 30 40.50950566 2.726513378
140 21 1851.221282 29.6944606 21 29.6944606 2.545715384
150 19 1872.251635 21.03035249 19 21.03035249 0.196018172
160 12 1886.641947 14.39031254 12 14.39031254 0.397044471
170 8 1896.155581 9.513633306 8 9.513633306 0.240821326
180 19 1902.232382 6.076801303 19 6.076801303 27.48305503
190 16 1905.982596 3.750213953 51 8.767617977 203.4274413
200 11 1908.218686 2.23609044
210 13 1909.506862 1.288175158
11 1911 1.493138427

χ2 calc 797.058815
χ2 critical 33.92443852

55 | P a g e

QM1 Assignment

13.4 Hindalco
13.4.1 Hindalco daily returns
mod obs
Bin (Daily returns) freq freq exp cumulative exp daily mod expected (O-E)2/E
-9 1 0.213869499 0.213869
-7.5 10 2.061715406 1.847846
-6 22 33 13.92759327 11.86588 13.92759327 26.1177
-4.5 34 34 66.49997284 52.57238 52.57237957 6.561112
-3 95 95 227.3000907 160.8001 160.8001178 26.9257
-1.5 264 264 566.9929958 339.6929 339.6929051 16.86646
0 676 676 1062.785217 495.7922 495.7922216 65.50091
1.5 625 625 1562.819982 500.0348 500.0347645 31.23045
3 236 236 1911.309434 348.4895 348.4894522 36.31065
4.5 107 107 2079.111443 167.802 167.8020085 22.03123
6 46 46 2134.917837 55.80639 55.80639449 1.723196
7.5 16 34 2147.730875 12.81304 15.08216299 23.72899
9 14 2149.760689 2.029814
10.5 2 2149.982414 0.221726
2 2150 0.017586

df 9
χ2 calc 256.9964

56 | P a g e

QM1 Assignment

13.4.2 Hindalco monthly returns
Bin Expected Exp. Mod
monthly cumulative Monthly obs
returns Freq(monthly ret) monthly returns returns freq Mod exp freq (O-E)2/E
-40 1 1.465393888 1.465393888
-35 1 5.279431561 3.814037673 2 5.279431561 2.037088887
-30 17 16.53123492 11.25180336 17 11.25180336 2.936575012
-25 35 45.09663494 28.56540002 35 28.56540002 1.449448524
-20 37 107.5061085 62.40947351 37 62.40947351 10.34524581
-15 118 224.8504593 117.3443509 118 117.3443509 0.00366337
-10 187 414.732137 189.8816776 187 189.8816776 0.043732845
-5 255 679.16725 264.4351131 255 264.4351131 0.33664727
0 360 996.1054103 316.9381603 360 316.9381603 5.850737695
5 358 1323.033004 326.9275942 358 326.9275942 2.953236195
10 279 1613.268586 290.2355812 279 290.2355812 0.434951097
15 230 1835.021967 221.7533813 230 221.7533813 0.306677263
20 108 1980.838572 145.8166046 108 145.8166046 9.807494752
25 51 2063.357886 82.51931412 51 82.51931412 12.03920771
30 46 2103.547062 40.18917668 46 40.18917668 0.840168186
35 28 2120.391586 16.8445238 28 16.8445238 7.387840157
40 5 2126.467255 6.075669289 18 8.608413841 10.24600957
45 10 2128.353089 1.885833668
3 2129 0.646910885

χ2 calc 64.98163545
χ2 critical 24.99579013

57 | P a g e

QM1 Assignment

13.4.3 Hindalco Yearly returns
Bin Frequency Exp Cumu
(Yearly returns) (yearly returns) Yearly returns Exp Yearly returns Mod obs freq mod exp freq (O-E)2/E
-50 22 185.4491281 185.4491281 22 185.4491281 144.0590083
-40 60 266.8907848 81.44165673 60 81.44165673 5.645079701
-30 179 369.7591393 102.8683545 179 102.8683545 56.34412531
-20 237 493.7515647 123.9924254 237 123.9924254 102.9959038
-10 387 636.3736419 142.6220772 387 142.6220772 418.732992
0 247 792.9249323 156.5512904 247 156.5512904 52.25743622
10 129 956.9102149 163.9852826 129 163.9852826 7.463901519
20 85 1120.830023 163.9198085 85 163.9198085 37.99623869
30 69 1277.193871 156.3638472 69 156.3638472 48.81206194
40 63 1419.531452 142.3375817 63 142.3375817 44.22199534
50 69 1543.177748 123.6462957 69 123.6462957 24.15129074
60 53 1645.677042 102.4992943 53 102.4992943 23.90436106
70 61 1726.761723 81.08468042 61 81.08468042 4.974976599
80 40 1787.973477 61.21175399 40 61.21175399 7.350524661
90 31 1832.070453 44.09697669 31 44.09697669 3.889853937
100 33 1862.385669 30.31521553 33 30.31521553 0.237770623
110 29 1882.273628 19.88795922 29 19.88795922 4.174852047
120 35 1894.724431 12.4508024 35 12.4508024 40.83803567
130 47 1902.16287 7.438439715 47 7.438439715 210.4093213
140 29 1906.403629 4.240758609 35 8.837129655 77.45680005
6 1911 4.596371046

χ2 calc 1315.916529
χ2 critical 30.14352721

58 | P a g e

QM1 Assignment

13.5 Satyam
13.5.1 Satyam daily returns
Bin (Daily returns) freq mod obs freq exp cumulative exp daily mod expected (O-E)2/E
-12 6 3.4305 3.430499624
-10.5 6 12 10.35719 6.926686714 10.35718634 0.260576
-9 20 20 27.77478 17.41759076 17.41759076 0.382879
-7.5 46 46 66.29976 38.52498781 38.52498781 1.450378
-6 45 45 141.2538 74.95399102 74.95399102 11.97056
-4.5 89 89 269.5311 128.2773232 128.2773232 12.02635
-3 157 157 462.6443 193.1132249 193.1132249 6.75337
-1.5 303 303 718.3759 255.7315542 255.7315542 8.736919
0 411 411 1016.275 297.8989603 297.8989603 42.94021
1.5 372 372 1321.533 305.2581178 305.2581178 14.5925
3 234 234 1596.689 275.1561435 275.1561435 6.15588
4.5 159 159 1814.864 218.1745793 218.1745793 16.04967
6 99 99 1967.038 152.1739123 152.1739123 18.58048
7.5 67 67 2060.403 93.36510457 93.36510457 7.445166
9 71 71 2110.791 50.3887431 50.3887431 8.430929
10.5 45 45 2134.713 23.92116441 23.92116441 18.57423
12 9 9 2144.702 9.989076926 9.989076926 0.097934
11 11 2150 5.298339552 5.298339552 6.135683

df 16
χ2 calc 180.5837

59 | P a g e

QM1 Assignment

13.5.2 Satyam monthly returns
Bin Freq Expected cumulative Exp. Monthly Mod
monthly returns (monthly returns) monthly returns returns obs freq Mod exp freq (O-E)2/E
-45 8 38.49084422 38.49084422 8 38.49084422 24.1535773
-40 8 61.95891096 23.46806674 8 23.46806674 10.19517676
-35 23 96.25607559 34.29716463 23 34.29716463 3.721180164
-30 33 144.4014068 48.14533124 33 48.14533124 4.764346875
-25 35 209.3194286 64.91802181 35 64.91802181 13.7879745
-20 79 293.3992121 84.07978341 79 84.07978341 0.306901356
-15 120 397.9995676 104.6003555 120 104.6003555 2.267191617
-10 160 522.9938244 124.9942568 160 124.9942568 9.803666872
-5 222 666.4642282 143.4704038 222 143.4704038 42.98376054
0 249 824.6436484 158.1794202 249 158.1794202 52.14570717
5 213 992.1584 167.5147516 213 167.5147516 12.35060076
10 181 1162.559177 170.4007767 181 170.4007767 0.659290041
15 177 1329.055834 166.4966577 177 166.4966577 0.66259708
20 138 1485.318383 156.2625481 138 156.2625481 2.134360839
25 107 1626.188767 140.8703848 107 140.8703848 8.143677395
30 89 1748.171931 121.9831636 89 121.9831636 8.918354379
35 56 1849.632067 101.4601365 56 101.4601365 20.36882739
40 35 1930.692013 81.05994522 35 81.05994522 26.17221795
45 41 1992.898035 62.20602216 41 62.20602216 7.229129275
50 27 2038.751668 45.85363333 27 45.85363333 7.752046324
55 22 2071.217774 32.46610604 22 32.46610604 3.373961004
60 24 2093.297908 22.08013358 24 22.08013358 0.166932282
65 15 2107.721988 14.4240807 15 14.4240807 0.02299509
70 15 2116.77284 9.050851606 15 9.050851606 3.910390773
75 8 2122.227975 5.455134836 8 5.455134836 1.187200481
80 10 2125.38615 3.158174779 44 6.772025118 204.6540126
85 8 2127.142379 1.756229756
26 2129 1.857620583

χ2 calc 471.8360768
χ2 critical 37.65248413

60 | P a g e

QM1 Assignment

13.5.3 Satyam Yearly returns
Frequency Exp Cumu
Bin(Yearly returns) (yearly returns) Yearly returns Exp Yearly returns Mod obs freq mod exp freq (O-E)2/E
-75 8 248.726652 248.726652 8 248.726652 232.9839626
-50 179 305.6888775 56.9622255 179 56.9622255 261.4578043
-25 157 370.5690781 64.88020062 157 64.88020062 130.7957953
0 203 443.2114187 72.64234062 203 72.64234062 233.9285768
25 229 523.1616798 79.95026105 229 79.95026105 277.8705709
50 157 609.658941 86.49726124 157 86.49726124 57.46582148
75 119 701.6482258 91.98928477 119 91.98928477 7.931127405
100 54 797.8148883 96.16666247 54 96.16666247 18.48902081
125 20 896.6393056 98.82441733 20 98.82441733 62.87200001
150 23 996.4682315 99.82892593 23 99.82892593 59.12799126
175 48 1095.597283 99.12905184 48 99.12905184 26.37148135
200 51 1192.357743 96.7604598 51 96.7604598 21.6412746
225 49 1285.200347 92.84260377 49 92.84260377 20.70357603
250 60 1372.76909 87.56874313 60 87.56874313 8.679302349
275 70 1453.959239 81.19014859 70 81.19014859 1.542298266
300 71 1527.955533 73.99629411 71 73.99629411 0.121327406
325 66 1594.248738 66.29320499 66 66.29320499 0.001296802
350 55 1652.63094 58.38220207 55 58.38220207 0.195937982
375 33 1703.171999 50.54105877 33 50.54105877 6.087896659
400 36 1746.181123 43.00912475 36 43.00912475 1.142265276
425 35 1782.158482 35.97735867 35 35.97735867 0.026550864
450 45 1811.742036 29.58355397 45 29.58355397 8.033747683
475 20 1835.654472 23.9124355 20 23.9124355 0.640133522
500 16 1854.654299 18.99982797 16 18.99982797 0.473634175
525 16 1869.494095 14.83979539 16 14.83979539 0.090707095
550 17 1880.887631 11.3935363 17 11.3935363 2.758795374
575 16 1889.486504 8.598873212 16 8.598873212 6.370215768
600 10 1895.865862 6.379357247 10 6.379357247 2.054917673
625 16 1900.518129 4.652267401 48 15.13413838 71.37273581
32 1911 10.48187098

χ2 calc 1390.935427
χ2 critical 41.33713813

61 | P a g e

QM1 Assignment

13.6 Nifty
13.6.1 Nifty Daily returns
Bin (Daily returns) freq mod obs freq exp cumulative exp daily mod expected (O-E)2/E
-9 2 9.91134E-05 9.91E-05
-7.5 3 5 0.009037613 0.008938
-6 3 3 0.387245036 0.378207
-4.5 13 13 7.897634045 7.510389 7.897634045 3.296448
-3 44 44 78.31011779 70.41248 70.41248375 9.907608
-1.5 233 233 391.8101507 313.5 313.5000329 20.67067
0 741 741 1057.886687 666.0765 666.0765361 8.427748
1.5 787 787 1735.091901 677.2052 677.2052142 17.80095
3 254 254 2064.590814 329.4989 329.4989132 17.29926
4.5 50 50 2141.108683 76.51787 76.51786871 9.189976
6 11 20 2149.54941 8.440727 8.44072695 15.83001
7.5 4 2149.989123 0.439713
9 4 2150 0.010877
1

df 7
χ2 calc 102.4227

62 | P a g e

QM1 Assignment

13.6.2 Nifty monthly returns
Expected
Bin cumulative
monthly returns Freq(monthly ret) monthly returns Exp. Monthly returns Mod obs freq Mod exp freq (O-E)2/E
-20 4 12.90088217 12.90088217 4 12.90088217 6.141107436
-17.5 19 28.98113702 16.08025485 19 16.08025485 0.530147803
-15 38 60.04286648 31.06172946 38 31.06172946 1.549804176
-12.5 56 114.9035325 54.86066598 56 54.86066598 0.023661434
-10 88 203.4968013 88.59326888 88 88.59326888 0.003972852
-7.5 130 334.3082739 130.8114726 130 130.8114726 0.005033868
-5 181 510.9110077 176.6027338 181 176.6027338 0.109488397
-2.5 237 728.9109003 217.9998926 237 217.9998926 1.655982838
0 251 974.9606708 246.0497705 251 246.0497705 0.099592744
2.5 234 1228.88119 253.9205189 234 253.9205189 1.562800347
5 208 1468.477906 239.596716 208 239.596716 4.166803623
7.5 208 1675.192911 206.7150053 208 206.7150053 0.007987864
10 155 1838.261695 163.0687834 155 163.0687834 0.399250329
12.5 133 1955.880488 117.6187931 133 117.6187931 2.011426224
15 84 2033.449597 77.56910963 84 77.56910963 0.533154901
17.5 59 2080.223758 46.77416079 59 46.77416079 3.195592222
20 29 2106.012312 25.78855432 29 25.78855432 0.399920959
22.5 10 2119.012519 13.0002064 10 13.0002064 0.692391965
25 3 2125.004549 5.992030367 5 9.987481207 2.490614829
2 2129 3.995450841

χ2 calc 25.57873481
χ2 critical 28.86929943
Hypothesis decision Accept H0

63 | P a g e

QM1 Assignment

13.6.3 Nifty yearly returns
Bin Frequency Exp Cumu
(Yearly returns) (yearly returns) Yearly returns Exp Yearly returns Mod obs freq mod exp freq (O-E)2/E
-30 5 185.2854731 185.2854731 5 185.2854731 175.4204001
-20 203 315.3408902 130.0554171 203 130.0554171 40.91265318
-10 365 493.3407176 177.9998273 365 177.9998273 196.4556095
0 417 712.7384295 219.3977119 417 219.3977119 177.9720668
10 217 956.2765066 243.5380771 217 243.5380771 2.891825151
20 183 1199.734681 243.4581744 183 243.4581744 15.01362958
30 107 1418.916516 219.1818346 107 219.1818346 57.41700282
40 43 1596.624531 177.708015 43 177.708015 102.112723
50 66 1726.381545 129.7570147 66 129.7570147 31.32745412
60 98 1811.706235 85.32468963 98 85.32468963 1.882966039
70 91 1862.234789 50.52855418 91 50.52855418 32.4160854
80 55 1889.182081 26.94729181 55 26.94729181 29.20347031
90 42 1902.124245 12.94216359 42 12.94216359 65.24085802
100 15 1907.721939 5.597694054 19 8.875755457 11.54834967
110 4 1909.90225 2.180311622
0 1911 1.097749782

χ2 calc 939.8150937

14 Construct a two-way table showing the number of days (frequency)
the daily return was within various ranges across five different days
of the week. Using this table, test if the daily return varies across the
days or not.

Chi-Square test of independence

H0: Daily return does not vary across weekdays v/s Ha: Daily return varies across days

χ2calc =∑(Oi – Ei)2 /Ei

64 | P a g e

QM1 Assignment
2 2
Reject H0 if χ calc > χ 0.05,(p-1)(q-1)

14.1 RIL daily returns
CONTINGENCY TABLE
Day0 Day1 Day2 Day3 Day4

[-inf,-6] 4 8 6 6 8 32
[-6,-4] 11 11 12 15 22 71
[-4,-2] 61 61 66 51 49 288
[-2,0] 140 134 133 130 127 664
[0,2] 134 149 130 142 149 704
[2,4] 48 45 60 47 46 246
[4,6] 16 9 10 21 17 73
[6,inf] 16 13 13 18 12 72

430 430 430 430 430

Expected frequencies

[-inf,-6] 6.4 6.4 6.4 6.4 6.4
[-6,-4] 14.2 14.2 14.2 14.2 14.2
[-4,-2] 57.6 57.6 57.6 57.6 57.6
[-2,0] 132.8 132.8 132.8 132.8 132.8
[0,2] 140.8 140.8 140.8 140.8 140.8
[2,4] 49.2 49.2 49.2 49.2 49.2
[4,6] 14.6 14.6 14.6 14.6 14.6
[6,inf] 14.4 14.4 14.4 14.4 14.4

Interim results
0.9 0.4 0.025 0.025 0.4
0.721127 0.721127 0.340845 0.04507 4.284507
0.200694 0.200694 1.225 0.75625 1.284028
0.390361 0.010843 0.000301 0.059036 0.253313
0.328409 0.477557 0.828409 0.010227 0.477557
0.029268 0.358537 2.370732 0.098374 0.20813
0.134247 2.147945 1.449315 2.805479 0.394521
0.177778 0.136111 0.136111 0.9 0.4

65 | P a g e

QM1 Assignment

χ2calc 26.1119
degrees of
freedom 28
2
χ cr 41.33714
Independence test Accept H0

14.2 SBI daily returns
CONTINGENCY TABLE

[-inf,-6] 8 6 10 3 7 34
[-6,-4] 15 18 10 13 17 73
[-4,-2] 63 54 55 56 61 289
[-2,0] 137 141 123 134 128 663
[0,2] 121 128 141 142 138 670
[2,4] 63 46 67 55 52 283
[4,6] 16 20 15 15 14 80
[6,inf] 7 17 9 12 13 58

430 430 430 430 430


[-inf,-6] 6.8 6.8 6.8 6.8 6.8
[-6,-4] 14.6 14.6 14.6 14.6 14.6
[-4,-2] 57.8 57.8 57.8 57.8 57.8
[-2,0] 132.6 132.6 132.6 132.6 132.6
[0,2] 134 134 134 134 134
[2,4] 56.6 56.6 56.6 56.6 56.6
[4,6] 16 16 16 16 16
[6,inf] 11.6 11.6 11.6 11.6 11.6

66 | P a g e

QM1 Assignment

Interim results
0.211765 0.094118 1.505882 2.123529 0.005882
0.010959 0.791781 1.449315 0.175342 0.394521
0.46782 0.249827 0.13564 0.056055 0.177163
0.146003 0.532127 0.695023 0.014781 0.159578
1.261194 0.268657 0.365672 0.477612 0.119403
0.723675 1.985159 1.910954 0.04523 0.373852
0 1 0.0625 0.0625 0.25
1.824138 2.513793 0.582759 0.013793 0.168966

χ2calc 23.4
degrees of
freedom 28
2
χ cr 41.33714

14.3 Dr Reddy’s Daily return
CONTINGENCY TABLE

[-inf,-6] 10 11 11 14 12 58
[-6,-4] 15 19 18 6 9 67
[-4,-2] 34 46 37 51 62 230
[-2,0] 142 130 151 146 129 698
[0,2] 150 144 141 131 136 702
[2,4] 48 44 34 48 48 222
[4,6] 20 15 19 14 15 83
[6,inf] 11 21 19 20 19 90

430 430 430 430 430

67 | P a g e

QM1 Assignment


[-inf,-6] 11.6 11.6 11.6 11.6 11.6
[-6,-4] 13.4 13.4 13.4 13.4 13.4
[-4,-2] 46 46 46 46 46
[-2,0] 139.6 139.6 139.6 139.6 139.6
[0,2] 140.4 140.4 140.4 140.4 140.4
[2,4] 44.4 44.4 44.4 44.4 44.4
[4,6] 16.6 16.6 16.6 16.6 16.6
[6,inf] 18 18 18 18 18

Interim results
0.22069 0.031034 0.031034 0.496552 0.013793
0.191045 2.340299 1.579104 4.086567 1.444776
3.130435 0 1.76087 0.543478 5.565217
0.041261 0.660172 0.930946 0.29341 0.804871
0.65641 0.092308 0.002564 0.629345 0.137892
0.291892 0.003604 2.436036 0.291892 0.291892
0.696386 0.154217 0.346988 0.407229 0.154217
2.722222 0.5 0.055556 0.222222 0.055556

χ2calc 34.314
degrees of
freedom 28
2
χ cr 41.33714

68 | P a g e

QM1 Assignment

14.4 Hindalco daily returns
CONTINGENCY TABLE

[-inf,-6] 7 6 8 5 7 33
[-6,-4] 8 11 11 15 10 55
[-4,-2] 43 39 43 42 53 220
[-2,0] 147 149 159 151 150 756
[0,2] 152 157 151 153 147 760
[2,4] 52 49 36 46 37 220
[4,6] 16 14 14 10 18 72
[6,inf] 5 5 8 8 8 34

430 430 430 430 430


[-inf,-6] 6.6 6.6 6.6 6.6 6.6
[-6,-4] 11 11 11 11 11
[-4,-2] 44 44 44 44 44
[-2,0] 151.2 151.2 151.2 151.2 151.2
[0,2] 152 152 152 152 152
[2,4] 44 44 44 44 44
[4,6] 14.4 14.4 14.4 14.4 14.4
[6,inf] 6.8 6.8 6.8 6.8 6.8

Interim results
0.024242 0.054545 0.29697 0.387879 0.024242
0.818182 0 0 1.454545 0.090909
0.022727 0.568182 0.022727 0.090909 1.840909
0.116667 0.032011 0.402381 0.000265 0.009524
0 0.164474 0.006579 0.006579 0.164474
1.454545 0.568182 1.454545 0.090909 1.113636
0.177778 0.011111 0.011111 1.344444 0.9
0.476471 0.476471 0.211765 0.211765 0.211765

69 | P a g e

Quantitative Methods Project

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (17)

Similar to Quantitative Methods Project

Similar to Quantitative Methods Project (14)

More from Dharmesh Gandhi

More from Dharmesh Gandhi (7)

Quantitative Methods Project