Stock Analysis on Net

Linde plc (NASDAQ:LIN)

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 Linde plc common stock.


Rates of Return

Linde plc, monthly rates of return

Microsoft Excel
Linde plc (LIN) Standard & Poor’s 500 (S&P 500)
t Date PriceLIN,t1 DividendLIN,t1 RLIN,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2019 $163.01 2,704.10
1. Feb 28, 2019 $173.24 6.28% 2,784.49 2.97%
2. Mar 31, 2019 $175.93 $0.875 2.06% 2,834.40 1.79%
3. Apr 30, 2019 $180.26 2.46% 2,945.83 3.93%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 $413.77 8.27% 4,567.80 8.92%
59. Dec 31, 2023 $410.71 $1.275 -0.43% 4,769.83 4.42%
Average (R): 1.92% 1.11%
Standard deviation: 6.50% 5.31%
Linde plc (LIN) Standard & Poor’s 500 (S&P 500)
t Date PriceLIN,t1 DividendLIN,t1 RLIN,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2019 $163.01 2,704.10
1. Feb 28, 2019 $173.24 6.28% 2,784.49 2.97%
2. Mar 31, 2019 $175.93 $0.875 2.06% 2,834.40 1.79%
3. Apr 30, 2019 $180.26 2.46% 2,945.83 3.93%
4. May 31, 2019 $180.55 $0.875 0.65% 2,752.06 -6.58%
5. Jun 30, 2019 $200.80 11.22% 2,941.76 6.89%
6. Jul 31, 2019 $191.28 -4.74% 2,980.38 1.31%
7. Aug 31, 2019 $188.91 $0.875 -0.78% 2,926.46 -1.81%
8. Sep 30, 2019 $193.72 2.55% 2,976.74 1.72%
9. Oct 31, 2019 $198.35 2.39% 3,037.56 2.04%
10. Nov 30, 2019 $206.21 3.96% 3,140.98 3.40%
11. Dec 31, 2019 $212.90 $0.875 3.67% 3,230.78 2.86%
12. Jan 31, 2020 $203.13 -4.59% 3,225.52 -0.16%
13. Feb 29, 2020 $191.01 -5.97% 2,954.22 -8.41%
14. Mar 31, 2020 $173.00 $0.963 -8.92% 2,584.59 -12.51%
15. Apr 30, 2020 $183.99 6.35% 2,912.43 12.68%
16. May 31, 2020 $202.34 9.97% 3,044.31 4.53%
17. Jun 30, 2020 $212.11 $0.963 5.30% 3,100.29 1.84%
18. Jul 31, 2020 $245.11 15.56% 3,271.12 5.51%
19. Aug 31, 2020 $249.74 1.89% 3,500.31 7.01%
20. Sep 30, 2020 $238.13 $0.963 -4.26% 3,363.00 -3.92%
21. Oct 31, 2020 $220.34 -7.47% 3,269.96 -2.77%
22. Nov 30, 2020 $256.42 16.37% 3,621.63 10.75%
23. Dec 31, 2020 $263.51 $0.963 3.14% 3,756.07 3.71%
24. Jan 31, 2021 $245.40 -6.87% 3,714.24 -1.11%
25. Feb 28, 2021 $244.27 -0.46% 3,811.15 2.61%
26. Mar 31, 2021 $280.14 $1.06 15.12% 3,972.89 4.24%
27. Apr 30, 2021 $285.84 2.03% 4,181.17 5.24%
28. May 31, 2021 $300.60 5.16% 4,204.11 0.55%
29. Jun 30, 2021 $289.10 $1.06 -3.47% 4,297.50 2.22%
30. Jul 31, 2021 $307.39 6.33% 4,395.26 2.27%
31. Aug 31, 2021 $314.59 2.34% 4,522.68 2.90%
32. Sep 30, 2021 $293.38 $1.06 -6.41% 4,307.54 -4.76%
33. Oct 31, 2021 $319.20 8.80% 4,605.38 6.91%
34. Nov 30, 2021 $318.14 -0.33% 4,567.00 -0.83%
35. Dec 31, 2021 $346.43 $1.06 9.23% 4,766.18 4.36%
36. Jan 31, 2022 $318.68 -8.01% 4,515.55 -5.26%
37. Feb 28, 2022 $293.24 -7.98% 4,373.94 -3.14%
38. Mar 31, 2022 $319.43 $1.17 9.33% 4,530.41 3.58%
39. Apr 30, 2022 $311.96 -2.34% 4,131.93 -8.80%
40. May 31, 2022 $324.68 4.08% 4,132.15 0.01%
41. Jun 30, 2022 $287.53 $1.17 -11.08% 3,785.38 -8.39%
42. Jul 31, 2022 $302.00 5.03% 4,130.29 9.11%
43. Aug 31, 2022 $282.86 -6.34% 3,955.00 -4.24%
44. Sep 30, 2022 $269.59 $1.17 -4.28% 3,585.62 -9.34%
45. Oct 31, 2022 $297.35 10.30% 3,871.98 7.99%
46. Nov 30, 2022 $336.48 13.16% 4,080.11 5.38%
47. Dec 31, 2022 $326.18 $1.17 -2.71% 3,839.50 -5.90%
48. Jan 31, 2023 $330.94 1.46% 4,076.60 6.18%
49. Feb 28, 2023 $348.37 5.27% 3,970.15 -2.61%
50. Mar 31, 2023 $355.44 $1.275 2.40% 4,109.31 3.51%
51. Apr 30, 2023 $369.45 3.94% 4,169.48 1.46%
52. May 31, 2023 $353.66 -4.27% 4,179.83 0.25%
53. Jun 30, 2023 $381.08 $1.275 8.11% 4,376.86 4.71%
54. Jul 31, 2023 $390.67 2.52% 4,588.96 4.85%
55. Aug 31, 2023 $387.04 -0.93% 4,507.66 -1.77%
56. Sep 30, 2023 $372.35 $1.275 -3.47% 4,288.05 -4.87%
57. Oct 31, 2023 $382.16 2.63% 4,193.80 -2.20%
58. Nov 30, 2023 $413.77 8.27% 4,567.80 8.92%
59. Dec 31, 2023 $410.71 $1.275 -0.43% 4,769.83 4.42%
Average (R): 1.92% 1.11%
Standard deviation: 6.50% 5.31%

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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 LIN during period t

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


Variance and Covariance

Linde plc, calculation of variance and covariance of returns

Microsoft Excel
t Date RLIN,t RS&P 500,t (RLIN,tRLIN)2 (RS&P 500,tRS&P 500)2 (RLIN,tRLIN)×(RS&P 500,tRS&P 500)
1. Feb 28, 2019 6.28% 2.97% 18.98 3.49 8.13
2. Mar 31, 2019 2.06% 1.79% 0.02 0.47 0.10
3. Apr 30, 2019 2.46% 3.93% 0.29 7.98 1.53
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 8.27% 8.92% 40.36 61.03 49.63
59. Dec 31, 2023 -0.43% 4.42% 5.52 11.00 -7.80
Total (Σ): 2,453.29 1,634.30 1,499.15
t Date RLIN,t RS&P 500,t (RLIN,tRLIN)2 (RS&P 500,tRS&P 500)2 (RLIN,tRLIN)×(RS&P 500,tRS&P 500)
1. Feb 28, 2019 6.28% 2.97% 18.98 3.49 8.13
2. Mar 31, 2019 2.06% 1.79% 0.02 0.47 0.10
3. Apr 30, 2019 2.46% 3.93% 0.29 7.98 1.53
4. May 31, 2019 0.65% -6.58% 1.62 59.04 9.78
5. Jun 30, 2019 11.22% 6.89% 86.44 33.49 53.80
6. Jul 31, 2019 -4.74% 1.31% 44.35 0.04 -1.38
7. Aug 31, 2019 -0.78% -1.81% 7.29 8.50 7.87
8. Sep 30, 2019 2.55% 1.72% 0.39 0.37 0.38
9. Oct 31, 2019 2.39% 2.04% 0.22 0.88 0.44
10. Nov 30, 2019 3.96% 3.40% 4.18 5.28 4.70
11. Dec 31, 2019 3.67% 2.86% 3.06 3.07 3.07
12. Jan 31, 2020 -4.59% -0.16% 42.35 1.61 8.26
13. Feb 29, 2020 -5.97% -8.41% 62.18 90.57 75.04
14. Mar 31, 2020 -8.92% -12.51% 117.58 185.44 147.66
15. Apr 30, 2020 6.35% 12.68% 19.66 134.06 51.34
16. May 31, 2020 9.97% 4.53% 64.88 11.71 27.57
17. Jun 30, 2020 5.30% 1.84% 11.46 0.54 2.48
18. Jul 31, 2020 15.56% 5.51% 186.03 19.40 60.07
19. Aug 31, 2020 1.89% 7.01% 0.00 34.82 -0.18
20. Sep 30, 2020 -4.26% -3.92% 38.22 25.29 31.09
21. Oct 31, 2020 -7.47% -2.77% 88.16 15.00 36.36
22. Nov 30, 2020 16.37% 10.75% 208.98 93.10 139.48
23. Dec 31, 2020 3.14% 3.71% 1.49 6.79 3.18
24. Jan 31, 2021 -6.87% -1.11% 77.29 4.93 19.51
25. Feb 28, 2021 -0.46% 2.61% 5.66 2.26 -3.58
26. Mar 31, 2021 15.12% 4.24% 174.24 9.85 41.42
27. Apr 30, 2021 2.03% 5.24% 0.01 17.11 0.48
28. May 31, 2021 5.16% 0.55% 10.53 0.31 -1.81
29. Jun 30, 2021 -3.47% 2.22% 29.07 1.24 -6.01
30. Jul 31, 2021 6.33% 2.27% 19.43 1.37 5.15
31. Aug 31, 2021 2.34% 2.90% 0.18 3.22 0.76
32. Sep 30, 2021 -6.41% -4.76% 69.29 34.37 48.80
33. Oct 31, 2021 8.80% 6.91% 47.36 33.74 39.98
34. Nov 30, 2021 -0.33% -0.83% 5.07 3.76 4.36
35. Dec 31, 2021 9.23% 4.36% 53.39 10.60 23.79
36. Jan 31, 2022 -8.01% -5.26% 98.58 40.51 63.19
37. Feb 28, 2022 -7.98% -3.14% 98.04 17.99 42.00
38. Mar 31, 2022 9.33% 3.58% 54.93 6.11 18.32
39. Apr 30, 2022 -2.34% -8.80% 18.12 98.04 42.15
40. May 31, 2022 4.08% 0.01% 4.66 1.21 -2.38
41. Jun 30, 2022 -11.08% -8.39% 169.01 90.21 123.48
42. Jul 31, 2022 5.03% 9.11% 9.70 64.09 24.93
43. Aug 31, 2022 -6.34% -4.24% 68.17 28.62 44.17
44. Sep 30, 2022 -4.28% -9.34% 38.40 109.11 64.72
45. Oct 31, 2022 10.30% 7.99% 70.20 47.34 57.65
46. Nov 30, 2022 13.16% 5.38% 126.36 18.23 47.99
47. Dec 31, 2022 -2.71% -5.90% 21.46 49.04 32.44
48. Jan 31, 2023 1.46% 6.18% 0.21 25.70 -2.33
49. Feb 28, 2023 5.27% -2.61% 11.21 13.82 -12.45
50. Mar 31, 2023 2.40% 3.51% 0.23 5.76 1.14
51. Apr 30, 2023 3.94% 1.46% 4.09 0.13 0.72
52. May 31, 2023 -4.27% 0.25% 38.35 0.74 5.31
53. Jun 30, 2023 8.11% 4.71% 38.38 13.02 22.35
54. Jul 31, 2023 2.52% 4.85% 0.36 13.99 2.24
55. Aug 31, 2023 -0.93% -1.77% 8.11 8.28 8.19
56. Sep 30, 2023 -3.47% -4.87% 29.00 35.73 32.19
57. Oct 31, 2023 2.63% -2.20% 0.51 10.92 -2.37
58. Nov 30, 2023 8.27% 8.92% 40.36 61.03 49.63
59. Dec 31, 2023 -0.43% 4.42% 5.52 11.00 -7.80
Total (Σ): 2,453.29 1,634.30 1,499.15

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VarianceLIN = Σ(RLIN,tRLIN)2 ÷ (59 – 1)
= 2,453.29 ÷ (59 – 1)
= 42.30

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18

CovarianceLIN, S&P 500 = Σ(RLIN,tRLIN)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,499.15 ÷ (59 – 1)
= 25.85


Systematic Risk (β) Estimation

Microsoft Excel
VarianceLIN 42.30
VarianceS&P 500 28.18
CovarianceLIN, S&P 500 25.85
Correlation coefficientLIN, S&P 5001 0.75
βLIN2 0.92
αLIN3 0.90%

Calculations

1 Correlation coefficientLIN, S&P 500
= CovarianceLIN, S&P 500 ÷ (Standard deviationLIN × Standard deviationS&P 500)
= 25.85 ÷ (6.50% × 5.31%)
= 0.75

2 βLIN
= CovarianceLIN, S&P 500 ÷ VarianceS&P 500
= 25.85 ÷ 28.18
= 0.92

3 αLIN
= AverageLIN – βLIN × AverageS&P 500
= 1.92%0.92 × 1.11%
= 0.90%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.65%
Expected rate of return on market portfolio2 E(RM) 13.79%
Systematic risk (β) of Linde plc common stock βLIN 0.92
 
Expected rate of return on Linde plc common stock3 E(RLIN) 13.03%

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(RLIN) = RF + βLIN [E(RM) – RF]
= 4.65% + 0.92 [13.79%4.65%]
= 13.03%