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Quantitative Methods Project

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  • 1. 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
  • 2. 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. Kurtosis is more than 0 implying a leptokurtic curve. It is a positively skewed curve. 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
  • 3. 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 than 0 implying a leptokurtic curve. It is a positively skewed curve. 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 Stock RIL SBI Dr Reddy Hindalco Satyam Nifty 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 implying a leptokurtic curve. It is a positively skewed curve. 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 implying a leptokurtic curve. It is a positively skewed curve. 3|Page
  • 4. 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 Stock RIL SBI Dr Reddy Hindalco Satyam Nifty 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 than 0 implying a leptokurtic curve. It is a positively skewed curve. 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
  • 5. 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. Kurtosis is more than 0 implying a leptokurtic curve. It is a positively skewed curve. 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
  • 6. 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
  • 7. 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
  • 8. 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
  • 9. 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
  • 10. 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
  • 11. QM1 Assignment 11 | P a g e
  • 12. 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
  • 13. 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
  • 14. 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
  • 15. 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
  • 16. QM1 Assignment 16 | P a g e
  • 17. 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
  • 18. QM1 Assignment 18 | P a g e
  • 19. 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
  • 20. QM1 Assignment 20 | P a g e
  • 21. 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
  • 22. QM1 Assignment 22 | P a g e
  • 23. 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
  • 24. 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
  • 25. QM1 Assignment 25 | P a g e
  • 26. 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
  • 27. QM1 Assignment 27 | P a g e
  • 28. 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
  • 29. QM1 Assignment 29 | P a g e
  • 30. 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
  • 31. QM1 Assignment 3 Using the frequency distribution of daily/monthly/yearly returns, answer the following questions: 3.1 Probability of a positive return Stock RIL SBI Dr Reddy Hindalco Satyam Nifty 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% RIL SBI Dr Reddy Hindalco Satyam Nifty 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
  • 32. QM1 Assignment 3.4 Probability of a gain of more than 15% RIL SBI Dr Reddy Hindalco Satyam Nifty 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
  • 33. QM1 Assignment 4.2 If today’s return is 5%-10%, what is the probability that return of after one year RIL SBI Dr Reddy Hindalco Satyam Nifty 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 5.1 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 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
  • 34. 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. 5.2 If today’s return is 5%-10%, what is the probability that return of after one year EventAStock RIL SBI Dr Reddy Hindalco Satyam Nifty 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
  • 35. 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 Average daily return Average monthly return Average yearly return K1 -0.04517166 1.173506538 13.79382365 K2 0.183445227 2.314011041 17.17441162 6.3 Dr. Reddy’s Average daily return Average monthly return Average yearly return K1 -0.0021716 2.285435212 37.34823327 K2 0.243133288 3.437661581 42.17477278 6.4 Hindalco Average daily return Average monthly return Average yearly return K1 -0.0680646 0.489090237 7.846038599 K2 0.137232799 1.578644638 11.9832718 35 | P a g e
  • 36. QM1 Assignment 6.5 Satyam Average daily return Average monthly return Average yearly return K1 0.10936845 6.064716894 131.1902405 K2 0.46159397 8.178175845 148.2967518 6.6 Nifty Average daily return Average monthly return Average yearly return 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
  • 37. QM1 Assignment 7.2 SBI Daily Monthly Yearly Sample Mean 0.069136782 1.743758789 15.48411764 Critical Value 9.904069329 9.521429224 8.581460573 Decision Reject H0 Reject H0 Accept H0 7.3 Dr Reddy’s Daily Monthly Yearly Sample Mean 0.120480846 2.861548397 39.76150302 Critical Value 9.897066826 9.516510575 7.974720179 Decision Reject H0 Reject H0 Accept H0 7.4 Hindalco Daily Monthly Yearly Sample Mean 0.0345841 1.033867437 9.914655201 Critical Value 9.913854496 9.542808561 8.263962223 Decision Reject H0 Reject H0 Accept H0 7.5 Satyam Daily Monthly Yearly Sample Mean 0.28548121 7.12144637 139.7434961 Critical Value 9.852201513 9.113164668 2.821881622 Decision Reject H0 Reject H0 Accept H0 37 | P a g e
  • 38. QM1 Assignment 7.6 Nifty Daily Monthly Yearly Sample Mean 0.033745968 0.87903147 9.968663069 Critical Value 9.940004935 9.703305897 8.842345712 Decision Reject H0 Reject H0 Accept H0 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 Daily Monthly Yearly 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
  • 39. QM1 Assignment 8.2 SBI Daily Monthly Yearly Sample proportion 0.000465116 0.235791451 0.500784929 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 Daily Monthly Yearly Sample proportion 0.002325581 0.274307186 0.636839351 K1 0.000289529 0.255355177 0.615277697 K2 0.004361634 0.293259196 0.658401006 8.4 Hindalco Daily Monthly Yearly Sample proportion 0.000930233 0.225927666 0.340136054 K1 -0.00035838 0.208163871 0.318895234 K2 0.002218846 0.24369146 0.361376875 39 | P a g e
  • 40. QM1 Assignment 8.5 Satyam Daily Monthly Yearly Sample proportion 0.011162791 0.374823861 0.669806384 K1 0.006721823 0.354261401 0.648721233 K2 0.015603759 0.395386321 0.690891536 8.6 Nifty Daily Monthly Yearly Sample proportion 0.000465116 0.150305308 0.368393511 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
  • 41. QM1 Assignment 9.1 RIL Daily Monthly Yearly Sample proportion 0.002790698 0.231564115 0.574045003 K1 0.887319099 0.887256712 0.886549482 K2 0.912680901 0.912743288 0.913450518 Decision Reject H0 Reject H0 Reject H0 9.2 SBI Daily Monthly Yearly Sample proportion 0.000465116 0.235791451 0.500784929 K1 0.887319099 0.887256712 0.886549482 K2 0.912680901 0.912743288 0.913450518 Decision Reject H0 Reject H0 Reject H0 9.3 Dr Reddy’s Daily Monthly Yearly Sample proportion 0.002325581 0.274307186 0.636839351 K1 0.887319099 0.887256712 0.886549482 K2 0.912680901 0.912743288 0.913450518 Decision Reject H0 Reject H0 Reject H0 9.4 Hindalco Daily Monthly Yearly Sample proportion 0.000930233 0.225927666 0.340136054 K1 0.887319099 0.887256712 0.886549482 41 | P a g e
  • 42. QM1 Assignment K2 0.912680901 0.912743288 0.913450518 Decision Reject H0 Reject H0 Reject H0 9.5 Satyam Daily Monthly Yearly Sample proportion 0.011162791 0.374823861 0.669806384 K1 0.887319099 0.887256712 0.886549482 K2 0.912680901 0.912743288 0.913450518 Decision Reject H0 Reject H0 Reject H0 9.6 Nifty Daily Monthly Yearly Sample proportion 0.000465116 0.150305308 0.368393511 K1 0.887319099 0.887256712 0.886549482 K2 0.912680901 0.912743288 0.913450518 Decision Reject H0 Reject H0 Reject H0 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
  • 43. QM1 Assignment 10.1 RIL Daily Monthly Yearly 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 Daily Monthly Yearly 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 Daily Monthly Yearly 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 Daily Monthly Yearly 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
  • 44. QM1 Assignment 10.5 Satyam Daily Monthly Yearly 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 Daily Monthly Yearly 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
  • 45. QM1 Assignment 11.1 RIL Daily Monthly Yearly 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 Daily Monthly Yearly Mean -1.91531609 -8.811026718 -15.90522586 Variance 4.01711585 46.42409842 89.45323824 95% VaR -5.2120541 -20.01827507 -31.46220575 Number of days in last 6 months when |VaR| was exceeded 4 11 20 11.3 Satyam Daily Monthly Yearly Mean -2.94826329 -12.57627678 -37.74318809 Variance 6.42648655 100.4819388 529.7815985 95% VaR -7.11805209 -29.06440135 -75.60275935 Number of days in last 6 0 0 0 months when |VaR| 45 | P a g e
  • 46. 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
  • 47. 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
  • 48. 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 Hypothesis decision Reject H0 48 | P a g e
  • 49. 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 degrees of freedom 21 χ2 critical 32.67057337 Hypothesis decision Reject H0 49 | P a g e
  • 50. 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 Hypothesis decision Reject H0 50 | P a g e
  • 51. 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 degrees of freedom 14 χ2 critical 23.68479131 Hypothesis decision Reject H0 51 | P a g e
  • 52. 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 degrees of freedom 17 χ2 critical 27.58711164 Hypothesis decision Reject Ho 52 | P a g e
  • 53. 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 Hypothesis decision Reject H0 53 | P a g e
  • 54. 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 degrees of freedom 15 χ2 critical 24.99579013 Hypothesis decision Reject H0 54 | P a g e
  • 55. 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 degrees of freedom 22 χ2 critical 33.92443852 Hypothesis decision Reject Ho 55 | P a g e
  • 56. 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 χ2 critical 16.91898 Hypothesis decision Reject H0 56 | P a g e
  • 57. 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 degrees of freedom 15 χ2 critical 24.99579013 Hypothesis decision Reject H0 57 | P a g e
  • 58. 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 degrees of freedom 19 χ2 critical 30.14352721 Hypothesis decision Reject Ho 58 | P a g e
  • 59. 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 χ2 critical 26.29623 Hypothesis decision Reject H0 59 | P a g e
  • 60. 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 degrees of freedom 25 χ2 critical 37.65248413 Hypothesis decision Reject H0 60 | P a g e
  • 61. 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 degrees of freedom 28 χ2 critical 41.33713813 Hypothesis decision Reject Ho 61 | P a g e
  • 62. 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 χ2 critical 14.06714 Hypothesis decision Reject H0 62 | P a g e
  • 63. 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 degrees of freedom 18 χ2 critical 28.86929943 Hypothesis decision Accept H0 63 | P a g e
  • 64. 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 degrees of freedom 13 χ2 critical 22.3620325 Hypothesis decision Reject Ho 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
  • 65. 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 Day0 Day1 Day2 Day3 Day4 [-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
  • 66. 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 Day0 Day1 Day2 Day3 Day4 [-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 Expected frequencies Day0 Day1 Day2 Day3 Day4 [-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
  • 67. 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 Independence test Accept H0 14.3 Dr Reddy’s Daily return CONTINGENCY TABLE Day0 Day1 Day2 Day3 Day4 [-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
  • 68. QM1 Assignment Expected frequencies Day0 Day1 Day2 Day3 Day4 [-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 Independence test Accept H0 68 | P a g e
  • 69. QM1 Assignment 14.4 Hindalco daily returns CONTINGENCY TABLE Day0 Day1 Day2 Day3 Day4 [-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 Expected frequencies Day0 Day1 Day2 Day3 Day4 [-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
  • 70. QM1 Assignment χ2calc 15.31 degrees of freedom 28 2 χ cr 41.33714 Independence test Accept H0 14.5 Satyam daily returns CONTINGENCY TABLE Day0 Day1 Day2 Day3 Day4 [-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 Expected frequencies Day0 Day1 Day2 Day3 Day4 [-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 70 | P a g e
  • 71. QM1 Assignment 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 χ2calc 31.04 degrees of freedom 28 2 χ cr 41.33714 Independence test Accept H0 14.6 Nifty Daily returns CONTINGENCY TABLE Day0 Day1 Day2 Day3 Day4 [-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 Expected frequencies Day0 Day1 Day2 Day3 Day4 [-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 71 | P a g e
  • 72. QM1 Assignment 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 χ2calc 24.77 degrees of freedom 28 2 χ cr 41.33714 Independence test Accept H0 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 72 | P a g e
  • 73. QM1 Assignment 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 73 | P a g e
  • 74. QM1 Assignment 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. 74 | P a g e
  • 75. QM1 Assignment 15.2 SBI regression analysis Regression Statistics Multiple R 0.604212 R Square 0.365073 Adjusted R Square 0.364777 Standard Error 83.04227 Observations 2151 Y=b0 + b1 X ; Y= SBI stock price X = nifty stock price b0 = -25.54 b1= 0.254 Scatter plot Looking at the scatter plot, there is a linear relationship but there might be other higher order 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%. 75 | P a g e
  • 76. QM1 Assignment H0: b1=0 v/s b1 ≠ 0 tstat= 35.15166 tcritical = 2.242974478 Reject H0 i.e. b1 ≠ 0 The error variance is not constant for all values .It is heteroscedastic. 76 | P a g e
  • 77. QM1 Assignment Test normality of errors. 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 Regression Statistics Multiple R 0.555292929 R Square 0.308350237 Adjusted R Square 0.308028389 Standard Error 372.2532366 Observations 2151 77 | P a g e
  • 78. QM1 Assignment Scatter plot Looking at the scatter plot, there is a linear relationship but there might be other higher order 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 Reject H0 i.e. b1 ≠ 0 78 | P a g e
  • 79. QM1 Assignment The error variance is not constant for all values .It is heteroscedastic. 79 | P a g e
  • 80. QM1 Assignment Test normality of errors. 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 Regression Statistics Multiple R 0.558140097 R Square 0.311520367 Adjusted R Square 0.311199995 Standard Error 184.3235188 Observations 2151 80 | P a g e
  • 81. QM1 Assignment Scatter plot Looking at the scatter plot, there is a linear relationship but there might be other higher order components. R2 is 0.312 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 ~ 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 Reject H0 i.e. b1 ≠ 0 81 | P a g e
  • 82. QM1 Assignment The error variance is not constant for all values .It is heteroscedastic. Test normality of errors. Errors are not normally distributed and have a non-zero mean. Hence our basic assumption of normality of errors fails here. 82 | P a g e
  • 83. QM1 Assignment 15.5 Satyam regression analysis Y=b0 + b1 X ; Y= Satyam stock price X = nifty stock price b0 = -1241 b1= 1.56 Regression Statistics Multiple R 0.418822147 R Square 0.175411991 Adjusted R Square 0.175028283 Standard Error 840.0935044 Observations 2151 Scatter plot Looking at the scatter plot, there is a linear relationship but there might be other higher order components. R2 is 0.1754 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. 83 | P a g e
  • 84. QM1 Assignment 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 Reject H0 i.e. b1 ≠ 0 The error variance is not constant for all values .It is heteroscedastic. 84 | P a g e
  • 85. QM1 Assignment Test normality of errors. 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. 85 | P a g e