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

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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.

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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


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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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)/ ∩Β)/ ∩Β)/ ∩Β)/ P(B)

4.1 If today’s return is 5%-10%, what is the probability that return of after

one month

EventA\Stock 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

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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

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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.

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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

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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

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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


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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

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8.2 SBI



K1 -0.00044628 0.217760019 0.478367427

K2 0.001376515 0.253822884 0.523202431

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

K1 Proportion cannot be less than 0 .This

result can come because sample

proportion is very small

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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

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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

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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/χ

2α/2) < σ < √((n-1)s

2/χ

21-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

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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

QM1 Assignment

44 | P a g e

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).

QM1 Assignment

45 | P a g e

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


months when |VaR| 0 0 0

QM1 Assignment

46 | P a g e

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

χ2

calc =∑(Oi – Ei)2 /Ei

Reject H0 if χ2

calc > χ2

0.05,n-1

QM1 Assignment

47 | P a g e

13.1 RIL

13.1.1 RIL Daily returns

Bin Freq

Mod Obs

freq(O) Exp Cumulative Exp daily

Mod Expected

freq(E) (O-E)2/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

QM1 Assignment

48 | P a g e

13.1.2 RIL Monthly returns

Bin monthly returns

Freq(monthly

ret)

Expected

cumulative

monthly

returns

Exp. Monthly

returns

Mod obs

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


QM1 Assignment

49 | P a g e

13.1.3 RIL yearly returns

Bin(Yearly

returns)

Frequency(yearly

returns)

Exp Cumu Yearly

returns

Exp Yearly

returns

Mod obs

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


QM1 Assignment

50 | P a g e

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


QM1 Assignment

51 | P a g e

13.2.2 SBI monthly return

Bin monthly returns

Freq(month

ly ret)

Expected

cumulative

monthly returns

Exp.

Monthly returns

Mod obs


-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


QM1 Assignment

52 | P a g e

13.2.3 SBI yearly returns

Bin

(Yearly returns)

Frequency

(yearly returns)

Exp Cumu

Yearly returns Exp Yearly returns Mod obs freq

mod

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

QM1 Assignment

53 | P a g e

13.3 Dr Reddy’s

13.3.1 Dr Reddy’s daily returns

Bin (Daily

returns) freq

mod

obs freq

exp

cumulative exp daily

mod

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


QM1 Assignment

54 | P a g e

13.3.2 Dr Reddy’s monthly returns

Bin monthly returns

Freq

(monthly ret)

Expected cumulative

monthly returns

Exp. Monthly

returns Mod obs freq

Mod

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


QM1 Assignment

55 | P a g e

13.3.3 Dr. Reddy’s yearly returns

Bin(Yearly returns)

Frequency

(yearly returns)

Exp Cumu

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


QM1 Assignment

56 | P a g e

13.4 Hindalco

13.4.1 Hindalco daily returns

Bin (Daily returns) freq

mod obs

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



QM1 Assignment

57 | P a g e

13.4.2 Hindalco monthly returns

Bin monthly returns Freq(monthly ret)

Expected

cumulative

monthly returns

Exp.

Monthly

returns

Mod

obs


-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


QM1 Assignment

58 | P a g e

13.4.3 Hindalco Yearly returns

Bin

(Yearly returns)

Frequency

(yearly returns)

Exp Cumu


-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


QM1 Assignment

59 | P a g e

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



QM1 Assignment

60 | P a g e

13.5.2 Satyam monthly returns

Bin monthly returns

Freq

(monthly returns)

Expected cumulative

monthly returns

Exp. Monthly

returns

Mod

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


QM1 Assignment

61 | P a g e

13.5.3 Satyam Yearly returns

Bin(Yearly returns)

Frequency

(yearly returns)

Exp Cumu


-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


QM1 Assignment

62 | P a g e

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



QM1 Assignment

63 | P a g e

13.6.2 Nifty monthly returns

Bin monthly returns Freq(monthly ret)

Expected

cumulative

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

QM1 Assignment

64 | P a g e

13.6.3 Nifty yearly returns

Bin

(Yearly returns)

Frequency

(yearly returns)

Exp Cumu


-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

χ2

calc =∑(Oi – Ei)2 /Ei

QM1 Assignment

65 | P a g e

Reject H0 if χ2

calc > χ2

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

QM1 Assignment

66 | P a g e

χ2

calc 26.1119

degrees of

freedom 28

χ2

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

QM1 Assignment

67 | P a g e

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

χ2

calc 23.4

degrees of

freedom 28

χ2

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

QM1 Assignment

68 | P a g e



[-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

χ2

calc 34.314

degrees of

freedom 28

χ2

cr 41.33714


QM1 Assignment

69 | P a g e

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

QM1 Assignment

70 | P a g e

χ2

calc 15.31

degrees of

freedom 28

χ2

cr 41.33714


14.5 Satyam daily returns

CONTINGENCY TABLE


[-inf,-6] 31 25 30 16 21 123

[-6,-4] 29 35 24 22 31 141

[-4,-2] 55 57 63 76 51 302

[-2,0] 87 95 78 106 96 462

[0,2] 104 97 108 100 105 514

[2,4] 63 51 55 44 49 262

[4,6] 27 31 29 30 26 143

[6,inf] 34 39 43 36 51 203

430 430 430 430 430



[-inf,-6] 24.6 24.6 24.6 24.6 24.6

[-6,-4] 28.2 28.2 28.2 28.2 28.2

[-4,-2] 60.4 60.4 60.4 60.4 60.4

[-2,0] 92.4 92.4 92.4 92.4 92.4

[0,2] 102.8 102.8 102.8 102.8 102.8

[2,4] 52.4 52.4 52.4 52.4 52.4

[4,6] 28.6 28.6 28.6 28.6 28.6

[6,inf] 40.6 40.6 40.6 40.6 40.6

Interim results

1.665041 0.006504 1.185366 3.006504 0.526829

0.022695 1.639716 0.625532 1.363121 0.278014

0.482781 0.191391 0.111921 4.029139 1.462914

0.315584 0.07316 2.244156 2.001732 0.14026

QM1 Assignment

71 | P a g e

0.014008 0.327237 0.263035 0.076265 0.047082

2.144275 0.037405 0.129008 1.346565 0.220611

0.08951 0.201399 0.005594 0.068531 0.236364

1.072906 0.063054 0.141872 0.521182 2.664039

χ2

calc 31.04

degrees of

freedom 28

χ2

cr 41.33714


14.6 Nifty Daily returns

CONTINGENCY TABLE


[-inf,-4] 7 4 7 3 7 28

[-4,-3] 8 7 9 6 7 37

[-3,-2] 29 24 22 21 27 123

[-2,-1] 59 61 63 54 65 302

[-1,0] 118 102 101 110 112 543

[0,1] 122 129 122 134 107 614

[1,2] 54 60 65 53 62 294

[2,3] 26 24 23 33 33 139

[3,inf] 7 19 18 16 10 70

430 430 430 430 430



[-inf,-4] 5.6 5.6 5.6 5.6 5.6

[-4,-3] 7.4 7.4 7.4 7.4 7.4

[-3,-2] 24.6 24.6 24.6 24.6 24.6

[-2,-1] 60.4 60.4 60.4 60.4 60.4

[-1,0] 108.6 108.6 108.6 108.6 108.6

[0,1] 122.8 122.8 122.8 122.8 122.8

[1,2] 58.8 58.8 58.8 58.8 58.8

[2,3] 27.8 27.8 27.8 27.8 27.8

[3,inf] 14 14 14 14 14

QM1 Assignment

72 | P a g e

Interim results

0.35 0.457143 0.35 1.207143 0.35

0.048649 0.021622 0.345946 0.264865 0.021622

0.786992 0.014634 0.274797 0.526829 0.234146

0.03245 0.00596 0.111921 0.678146 0.350331

0.813628 0.401105 0.53186 0.018048 0.106446

0.005212 0.313029 0.005212 1.021498 2.032899

0.391837 0.02449 0.653741 0.572109 0.17415

0.116547 0.519424 0.828777 0.972662 0.972662

3.5 1.785714 1.142857 0.285714 1.142857

χ2

calc 24.77

degrees of

freedom 28

χ2

cr 41.33714


15 Can you develop a model to forecast the daily/monthly/yearly price

of a stock on the basis of the Nifty stock index? Critically comment on

the model you have developed.

15.1 RIL regression analysis

Regression Statistics

Multiple R 0.72629368

R Square 0.52750251

Adjusted R Square 0.527282642

Standard Error 73.97871119

Observations 2151

Y=b0 + b1 X ; Y= RIL stock price X = nifty stock price

b0 = -85.47 b1= 0.315

QM1 Assignment

73 | P a g e

Scatter plot

Looking at the scatter plot, there is a linear relationship but there might be other higher order

components.

R2 is 0.528 is quite less compared to 0.7 (thumb rule).Hence there is quite a lot of variation in Y that is

unexplained by the regression model.

Also if one looks at standard error ~ 74 which is quite high compared to mean value of Y i.e 1064.5

.Approx 7% .

H0: b1=0 v/s b1 ≠ 0

tstat= 48.98134655 tcritical = 2.242974478

� Reject H0 i.e. b1 ≠ 0

QM1 Assignment

74 | P a g e

The error variance is not constant for all values .It is heteroscedastic.

Test normality of errors.

Errors are not normally distributed and mean appears to be non-zero.

QM1 Assignment

75 | P a g e

15.2 SBI regression analysis


Multiple R 0.604212

R Square 0.365073

Adjusted R

Square 0.364777


Observations 2151

Y=b0 + b1 X ; Y= SBI stock price X = nifty stock price

b0 = -25.54 b1= 0.254

Scatter plot


components.

R2 is 0.365 which is quite less compared to 0.7 (thumb rule).Hence there is quite a lot of variation in Y

that is unexplained by the regression model.

Also if one looks at standard error ~ 83.04 which is quite high compared to mean value of Y i.e 271

.Approx 30.6%.

QM1 Assignment

76 | P a g e

H0: b1=0 v/s b1 ≠ 0

tstat= 35.15166

tcritical = 2.242974478



QM1 Assignment

77 | P a g e


Errors seem to be normally distributed and mean is approx zero(-4.6267E-16).Both skewness and

kurtosis are close to zero.It is also symmetric.

15.3 Dr Reddy regression analysis

Y=b0 + b1 X ; Y= Dr Reddy stock price X = nifty stock price

b0 = -343 b1= 1



R Square 0.308350237



Observations 2151

QM1 Assignment

78 | P a g e

Scatter plot


components.

R2 is 0.308350237

which is quite less compared to 0.7 (thumb rule).Hence there is quite a lot of variation in Y that is

unexplained by the regression model.

Also if one looks at standard error ~ 372.25 which is quite high compared to mean value of Y i.e 826.381

.Approx 45% .

H0: b1=0 v/s b1 ≠ 0

tstat= 30.95

tcritical = 2.242974478


QM1 Assignment

79 | P a g e


QM1 Assignment

80 | P a g e


Errors are not normally distributed and have a non-zero mean. Hence our basic assumption of normality

of errors fails here.

15.4 Hindalco regression analysis

Y=b0 + b1 X ; Y= Hindalco stock price X = nifty stock price

b0 = 215 b1= 0.5



R Square 0.311520367

Adjusted R

Square 0.311199995


Observations 2151

QM1 Assignment

81 | P a g e

Scatter plot


components.



Also if one looks at standard error ~ 184.32 which is quite high compared to mean value of Y i.e 799.1.

Approx 23%.

H0: b1=0 v/s b1 ≠ 0

tstat= 31.18286

tcritical = 2.242974478


QM1 Assignment

82 | P a g e



Errors are not normally distributed and have a non-zero mean. Hence our basic assumption of normality

of errors fails here.

QM1 Assignment

83 | P a g e

15.5 Satyam regression analysis

Y=b0 + b1 X ; Y= Satyam stock price X = nifty stock price

b0 = -1241 b1= 1.56



R Square 0.175411991



Observations 2151

Scatter plot


components.



QM1 Assignment

84 | P a g e

Also if one looks at standard error ~ 840 which is more than the mean value of Y i.e 583. Approx 144%.

H0: b1=0 v/s b1 ≠ 0

tstat= 21.38

tcritical = 2.242974478



QM1 Assignment

85 | P a g e


Errors are not normally distributed as it is highly positive skewed with skewness of 2.3 and is highly

leptokurtic. Errors are not symmetric too. Hence our basic assumption of normality of errors fails here.

16 Write a brief summary of your findings on the basis of the above

analysis.

The above models are pretty simple and there might be factors other than the nifty stock price at play.

E.g: Company fundamentals, sectoral swings, etc. There might be some higher order factors too in the

equation.

Documents

Quantitative Methods Project