Stock Analysis on Net

LyondellBasell Industries N.V. (NYSE:LYB)

This company has been moved to the archive! The financial data has not been updated since August 2, 2019.

Capital Asset Pricing Model (CAPM) 

Microsoft Excel

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like LyondellBasell Industries N.V. common stock.


Rates of Return

LyondellBasell Industries N.V., monthly rates of return

Microsoft Excel
LyondellBasell Industries N.V. (LYB) Standard & Poor’s 500 (S&P 500)
t Date PriceLYB,t1 DividendLYB,t1 RLYB,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 $78.76 1,782.59
1. Feb 28, 2014 $88.08 $0.60 12.60% 1,859.45 4.31%
2. Mar 31, 2014 $88.94 0.98% 1,872.34 0.69%
3. Apr 30, 2014 $92.50 $0.70 4.79% 1,883.95 0.62%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2018 $93.31 4.53% 2,760.17 1.79%
59. Dec 31, 2018 $83.16 $1.00 -9.81% 2,506.85 -9.18%
Average (R): 0.66% 0.63%
Standard deviation: 7.34% 3.13%
LyondellBasell Industries N.V. (LYB) Standard & Poor’s 500 (S&P 500)
t Date PriceLYB,t1 DividendLYB,t1 RLYB,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 $78.76 1,782.59
1. Feb 28, 2014 $88.08 $0.60 12.60% 1,859.45 4.31%
2. Mar 31, 2014 $88.94 0.98% 1,872.34 0.69%
3. Apr 30, 2014 $92.50 $0.70 4.79% 1,883.95 0.62%
4. May 31, 2014 $99.57 7.64% 1,923.57 2.10%
5. Jun 30, 2014 $97.65 -1.93% 1,960.23 1.91%
6. Jul 31, 2014 $106.25 8.81% 1,930.67 -1.51%
7. Aug 31, 2014 $114.35 $0.70 8.28% 2,003.37 3.77%
8. Sep 30, 2014 $108.66 -4.98% 1,972.29 -1.55%
9. Oct 31, 2014 $91.63 -15.67% 2,018.05 2.32%
10. Nov 30, 2014 $78.86 $0.70 -13.17% 2,067.56 2.45%
11. Dec 31, 2014 $79.39 0.67% 2,058.90 -0.42%
12. Jan 31, 2015 $79.09 -0.38% 1,994.99 -3.10%
13. Feb 28, 2015 $85.91 $0.70 9.51% 2,104.50 5.49%
14. Mar 31, 2015 $87.80 2.20% 2,067.89 -1.74%
15. Apr 30, 2015 $103.52 17.90% 2,085.51 0.85%
16. May 31, 2015 $101.10 $0.78 -1.58% 2,107.39 1.05%
17. Jun 30, 2015 $103.52 2.39% 2,063.11 -2.10%
18. Jul 31, 2015 $93.83 -9.36% 2,103.84 1.97%
19. Aug 31, 2015 $85.38 $0.78 -8.17% 1,972.18 -6.26%
20. Sep 30, 2015 $83.36 -2.37% 1,920.03 -2.64%
21. Oct 31, 2015 $92.91 11.46% 2,079.36 8.30%
22. Nov 30, 2015 $95.82 $0.78 3.97% 2,080.41 0.05%
23. Dec 31, 2015 $86.90 -9.31% 2,043.94 -1.75%
24. Jan 31, 2016 $77.97 -10.28% 1,940.24 -5.07%
25. Feb 29, 2016 $80.21 $0.78 3.87% 1,932.23 -0.41%
26. Mar 31, 2016 $85.58 6.69% 2,059.74 6.60%
27. Apr 30, 2016 $82.67 -3.40% 2,065.30 0.27%
28. May 31, 2016 $81.36 $0.85 -0.56% 2,096.95 1.53%
29. Jun 30, 2016 $74.42 -8.53% 2,098.86 0.09%
30. Jul 31, 2016 $75.26 1.13% 2,173.60 3.56%
31. Aug 31, 2016 $78.89 $0.85 5.95% 2,170.95 -0.12%
32. Sep 30, 2016 $80.66 2.24% 2,168.27 -0.12%
33. Oct 31, 2016 $79.55 -1.38% 2,126.15 -1.94%
34. Nov 30, 2016 $90.32 $0.85 14.61% 2,198.81 3.42%
35. Dec 31, 2016 $85.78 -5.03% 2,238.83 1.82%
36. Jan 31, 2017 $93.27 8.73% 2,278.87 1.79%
37. Feb 28, 2017 $91.24 -2.18% 2,363.64 3.72%
38. Mar 31, 2017 $91.19 $0.85 0.88% 2,362.72 -0.04%
39. Apr 30, 2017 $84.76 -7.05% 2,384.20 0.91%
40. May 31, 2017 $80.52 -5.00% 2,411.80 1.16%
41. Jun 30, 2017 $84.39 $0.90 5.92% 2,423.41 0.48%
42. Jul 31, 2017 $90.09 6.75% 2,470.30 1.93%
43. Aug 31, 2017 $90.59 0.56% 2,471.65 0.05%
44. Sep 30, 2017 $99.05 $0.90 10.33% 2,519.36 1.93%
45. Oct 31, 2017 $103.53 4.52% 2,575.26 2.22%
46. Nov 30, 2017 $104.70 1.13% 2,647.58 2.81%
47. Dec 31, 2017 $110.32 $0.90 6.23% 2,673.61 0.98%
48. Jan 31, 2018 $119.84 8.63% 2,823.81 5.62%
49. Feb 28, 2018 $108.22 -9.70% 2,713.83 -3.89%
50. Mar 31, 2018 $105.68 $1.00 -1.42% 2,640.87 -2.69%
51. Apr 30, 2018 $105.73 0.05% 2,648.05 0.27%
52. May 31, 2018 $112.12 6.04% 2,705.27 2.16%
53. Jun 30, 2018 $109.85 $1.00 -1.13% 2,718.37 0.48%
54. Jul 31, 2018 $110.79 0.86% 2,816.29 3.60%
55. Aug 31, 2018 $112.78 1.80% 2,901.52 3.03%
56. Sep 30, 2018 $102.51 $1.00 -8.22% 2,913.98 0.43%
57. Oct 31, 2018 $89.27 -12.92% 2,711.74 -6.94%
58. Nov 30, 2018 $93.31 4.53% 2,760.17 1.79%
59. Dec 31, 2018 $83.16 $1.00 -9.81% 2,506.85 -9.18%
Average (R): 0.66% 0.63%
Standard deviation: 7.34% 3.13%

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1 Data in US$ per share of common stock, adjusted for splits and stock dividends.

2 Rate of return on common stock of LYB during period t

3 Rate of return on S&P 500 (the market portfolio proxy) during period t


Variance and Covariance

LyondellBasell Industries N.V., calculation of variance and covariance of returns

Microsoft Excel
t Date RLYB,t RS&P 500,t (RLYB,tRLYB)2 (RS&P 500,tRS&P 500)2 (RLYB,tRLYB)×(RS&P 500,tRS&P 500)
1. Feb 28, 2014 12.60% 4.31% 142.37 13.57 43.95
2. Mar 31, 2014 0.98% 0.69% 0.10 0.00 0.02
3. Apr 30, 2014 4.79% 0.62% 17.03 0.00 -0.03
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2018 4.53% 1.79% 14.92 1.34 4.47
59. Dec 31, 2018 -9.81% -9.18% 109.61 96.15 102.66
Total (Σ): 3,127.55 566.60 695.50
t Date RLYB,t RS&P 500,t (RLYB,tRLYB)2 (RS&P 500,tRS&P 500)2 (RLYB,tRLYB)×(RS&P 500,tRS&P 500)
1. Feb 28, 2014 12.60% 4.31% 142.37 13.57 43.95
2. Mar 31, 2014 0.98% 0.69% 0.10 0.00 0.02
3. Apr 30, 2014 4.79% 0.62% 17.03 0.00 -0.03
4. May 31, 2014 7.64% 2.10% 48.72 2.18 10.30
5. Jun 30, 2014 -1.93% 1.91% 6.72 1.63 -3.31
6. Jul 31, 2014 8.81% -1.51% 66.32 4.56 -17.39
7. Aug 31, 2014 8.28% 3.77% 58.05 9.84 23.90
8. Sep 30, 2014 -4.98% -1.55% 31.80 4.75 12.29
9. Oct 31, 2014 -15.67% 2.32% 266.87 2.86 -27.64
10. Nov 30, 2014 -13.17% 2.45% 191.43 3.33 -25.26
11. Dec 31, 2014 0.67% -0.42% 0.00 1.10 -0.01
12. Jan 31, 2015 -0.38% -3.10% 1.08 13.93 3.89
13. Feb 28, 2015 9.51% 5.49% 78.23 23.63 43.00
14. Mar 31, 2015 2.20% -1.74% 2.36 5.61 -3.64
15. Apr 30, 2015 17.90% 0.85% 297.25 0.05 3.86
16. May 31, 2015 -1.58% 1.05% 5.05 0.18 -0.95
17. Jun 30, 2015 2.39% -2.10% 2.99 7.45 -4.72
18. Jul 31, 2015 -9.36% 1.97% 100.48 1.81 -13.49
19. Aug 31, 2015 -8.17% -6.26% 78.11 47.42 60.86
20. Sep 30, 2015 -2.37% -2.64% 9.18 10.71 9.91
21. Oct 31, 2015 11.46% 8.30% 116.49 58.83 82.79
22. Nov 30, 2015 3.97% 0.05% 10.94 0.33 -1.91
23. Dec 31, 2015 -9.31% -1.75% 99.45 5.67 23.74
24. Jan 31, 2016 -10.28% -5.07% 119.68 32.51 62.37
25. Feb 29, 2016 3.87% -0.41% 10.30 1.08 -3.34
26. Mar 31, 2016 6.69% 6.60% 36.38 35.65 36.01
27. Apr 30, 2016 -3.40% 0.27% 16.51 0.13 1.45
28. May 31, 2016 -0.56% 1.53% 1.49 0.82 -1.10
29. Jun 30, 2016 -8.53% 0.09% 84.52 0.29 4.94
30. Jul 31, 2016 1.13% 3.56% 0.22 8.60 1.36
31. Aug 31, 2016 5.95% -0.12% 27.98 0.56 -3.97
32. Sep 30, 2016 2.24% -0.12% 2.50 0.56 -1.19
33. Oct 31, 2016 -1.38% -1.94% 4.16 6.61 5.24
34. Nov 30, 2016 14.61% 3.42% 194.43 7.78 38.90
35. Dec 31, 2016 -5.03% 1.82% 32.38 1.42 -6.78
36. Jan 31, 2017 8.73% 1.79% 65.10 1.35 9.36
37. Feb 28, 2017 -2.18% 3.72% 8.07 9.56 -8.78
38. Mar 31, 2017 0.88% -0.04% 0.05 0.44 -0.14
39. Apr 30, 2017 -7.05% 0.91% 59.52 0.08 -2.17
40. May 31, 2017 -5.00% 1.16% 32.10 0.28 -3.00
41. Jun 30, 2017 5.92% 0.48% 27.67 0.02 -0.77
42. Jul 31, 2017 6.75% 1.93% 37.10 1.71 7.96
43. Aug 31, 2017 0.56% 0.05% 0.01 0.33 0.06
44. Sep 30, 2017 10.33% 1.93% 93.49 1.70 12.59
45. Oct 31, 2017 4.52% 2.22% 14.90 2.53 6.14
46. Nov 30, 2017 1.13% 2.81% 0.22 4.75 1.02
47. Dec 31, 2017 6.23% 0.98% 30.96 0.13 1.98
48. Jan 31, 2018 8.63% 5.62% 63.46 24.90 39.75
49. Feb 28, 2018 -9.70% -3.89% 107.32 20.45 46.85
50. Mar 31, 2018 -1.42% -2.69% 4.35 11.00 6.92
51. Apr 30, 2018 0.05% 0.27% 0.38 0.13 0.22
52. May 31, 2018 6.04% 2.16% 28.95 2.35 8.25
53. Jun 30, 2018 -1.13% 0.48% 3.23 0.02 0.26
54. Jul 31, 2018 0.86% 3.60% 0.04 8.85 0.57
55. Aug 31, 2018 1.80% 3.03% 1.28 5.75 2.72
56. Sep 30, 2018 -8.22% 0.43% 78.91 0.04 1.76
57. Oct 31, 2018 -12.92% -6.94% 184.40 57.28 102.77
58. Nov 30, 2018 4.53% 1.79% 14.92 1.34 4.47
59. Dec 31, 2018 -9.81% -9.18% 109.61 96.15 102.66
Total (Σ): 3,127.55 566.60 695.50

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VarianceLYB = Σ(RLYB,tRLYB)2 ÷ (59 – 1)
= 3,127.55 ÷ (59 – 1)
= 53.92

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 566.60 ÷ (59 – 1)
= 9.77

CovarianceLYB, S&P 500 = Σ(RLYB,tRLYB)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 695.50 ÷ (59 – 1)
= 11.99


Systematic Risk (β) Estimation

Microsoft Excel
VarianceLYB 53.92
VarianceS&P 500 9.77
CovarianceLYB, S&P 500 11.99
Correlation coefficientLYB, S&P 5001 0.52
βLYB2 1.23
αLYB3 -0.11%

Calculations

1 Correlation coefficientLYB, S&P 500
= CovarianceLYB, S&P 500 ÷ (Standard deviationLYB × Standard deviationS&P 500)
= 11.99 ÷ (7.34% × 3.13%)
= 0.52

2 βLYB
= CovarianceLYB, S&P 500 ÷ VarianceS&P 500
= 11.99 ÷ 9.77
= 1.23

3 αLYB
= AverageLYB – βLYB × AverageS&P 500
= 0.66%1.23 × 0.63%
= -0.11%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.67%
Expected rate of return on market portfolio2 E(RM) 13.79%
Systematic risk (β) of LyondellBasell Industries N.V. common stock βLYB 1.23
 
Expected rate of return on LyondellBasell Industries N.V. common stock3 E(RLYB) 15.86%

1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).

2 See details »

3 E(RLYB) = RF + βLYB [E(RM) – RF]
= 4.67% + 1.23 [13.79%4.67%]
= 15.86%