Stock Analysis on Net
Stock Analysis on Net
Microsoft Excel LibreOffice Calc

Vertex Pharmaceuticals Inc. (NASDAQ:VRTX)

Capital Asset Pricing Model (CAPM)

Intermediate level

Rates of Return

Vertex Pharmaceuticals Inc., monthly rates of return

Microsoft Excel LibreOffice Calc
Vertex Pharmaceuticals Inc. (VRTX) Standard & Poor’s 500 (S&P 500)
t Date PriceVRTX,t1 DividendVRTX,t1 RVRTX,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2015 $110.14 1,994.99
1. Feb 28, 2015 $119.43 8.43% 2,104.50 5.49%
2. Mar 31, 2015 $117.97 -1.22% 2,067.89 -1.74%
3. Apr 30, 2015 $123.28 4.50% 2,085.51 0.85%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2019 $221.75 13.44% 3,140.98 3.40%
59. Dec 31, 2019 $218.95 -1.26% 3,230.78 2.86%
Average (R): 1.63% 0.88%
Standard deviation: 9.57% 3.45%
Vertex Pharmaceuticals Inc. (VRTX) Standard & Poor’s 500 (S&P 500)
t Date PriceVRTX,t1 DividendVRTX,t1 RVRTX,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2015 $110.14 1,994.99
1. Feb 28, 2015 $119.43 8.43% 2,104.50 5.49%
2. Mar 31, 2015 $117.97 -1.22% 2,067.89 -1.74%
3. Apr 30, 2015 $123.28 4.50% 2,085.51 0.85%
4. May 31, 2015 $128.29 4.06% 2,107.39 1.05%
5. Jun 30, 2015 $123.48 -3.75% 2,063.11 -2.10%
6. Jul 31, 2015 $135.00 9.33% 2,103.84 1.97%
7. Aug 31, 2015 $127.52 -5.54% 1,972.18 -6.26%
8. Sep 30, 2015 $104.14 -18.33% 1,920.03 -2.64%
9. Oct 31, 2015 $124.74 19.78% 2,079.36 8.30%
10. Nov 30, 2015 $129.36 3.70% 2,080.41 0.05%
11. Dec 31, 2015 $125.83 -2.73% 2,043.94 -1.75%
12. Jan 31, 2016 $90.75 -27.88% 1,940.24 -5.07%
13. Feb 29, 2016 $85.49 -5.80% 1,932.23 -0.41%
14. Mar 31, 2016 $79.49 -7.02% 2,059.74 6.60%
15. Apr 30, 2016 $84.34 6.10% 2,065.30 0.27%
16. May 31, 2016 $93.15 10.45% 2,096.95 1.53%
17. Jun 30, 2016 $86.02 -7.65% 2,098.86 0.09%
18. Jul 31, 2016 $97.00 12.76% 2,173.60 3.56%
19. Aug 31, 2016 $94.51 -2.57% 2,170.95 -0.12%
20. Sep 30, 2016 $87.21 -7.72% 2,168.27 -0.12%
21. Oct 31, 2016 $75.86 -13.01% 2,126.15 -1.94%
22. Nov 30, 2016 $81.61 7.58% 2,198.81 3.42%
23. Dec 31, 2016 $73.67 -9.73% 2,238.83 1.82%
24. Jan 31, 2017 $85.87 16.56% 2,278.87 1.79%
25. Feb 28, 2017 $90.62 5.53% 2,363.64 3.72%
26. Mar 31, 2017 $109.35 20.67% 2,362.72 -0.04%
27. Apr 30, 2017 $118.30 8.18% 2,384.20 0.91%
28. May 31, 2017 $123.60 4.48% 2,411.80 1.16%
29. Jun 30, 2017 $128.87 4.26% 2,423.41 0.48%
30. Jul 31, 2017 $151.82 17.81% 2,470.30 1.93%
31. Aug 31, 2017 $160.54 5.74% 2,471.65 0.05%
32. Sep 30, 2017 $152.04 -5.29% 2,519.36 1.93%
33. Oct 31, 2017 $146.23 -3.82% 2,575.26 2.22%
34. Nov 30, 2017 $144.29 -1.33% 2,647.58 2.81%
35. Dec 31, 2017 $149.86 3.86% 2,673.61 0.98%
36. Jan 31, 2018 $166.87 11.35% 2,823.81 5.62%
37. Feb 28, 2018 $166.03 -0.50% 2,713.83 -3.89%
38. Mar 31, 2018 $162.98 -1.84% 2,640.87 -2.69%
39. Apr 30, 2018 $153.16 -6.03% 2,648.05 0.27%
40. May 31, 2018 $154.00 0.55% 2,705.27 2.16%
41. Jun 30, 2018 $169.96 10.36% 2,718.37 0.48%
42. Jul 31, 2018 $175.05 2.99% 2,816.29 3.60%
43. Aug 31, 2018 $184.40 5.34% 2,901.52 3.03%
44. Sep 30, 2018 $192.74 4.52% 2,913.98 0.43%
45. Oct 31, 2018 $169.46 -12.08% 2,711.74 -6.94%
46. Nov 30, 2018 $180.79 6.69% 2,760.17 1.79%
47. Dec 31, 2018 $165.71 -8.34% 2,506.85 -9.18%
48. Jan 31, 2019 $190.91 15.21% 2,704.10 7.87%
49. Feb 28, 2019 $188.75 -1.13% 2,784.49 2.97%
50. Mar 31, 2019 $183.95 -2.54% 2,834.40 1.79%
51. Apr 30, 2019 $168.98 -8.14% 2,945.83 3.93%
52. May 31, 2019 $166.18 -1.66% 2,752.06 -6.58%
53. Jun 30, 2019 $183.38 10.35% 2,941.76 6.89%
54. Jul 31, 2019 $166.62 -9.14% 2,980.38 1.31%
55. Aug 31, 2019 $180.02 8.04% 2,926.46 -1.81%
56. Sep 30, 2019 $169.42 -5.89% 2,976.74 1.72%
57. Oct 31, 2019 $195.48 15.38% 3,037.56 2.04%
58. Nov 30, 2019 $221.75 13.44% 3,140.98 3.40%
59. Dec 31, 2019 $218.95 -1.26% 3,230.78 2.86%
Average (R): 1.63% 0.88%
Standard deviation: 9.57% 3.45%

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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 VRTX during period t

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


Variance and Covariance

Vertex Pharmaceuticals Inc., calculation of variance and covariance of returns

Microsoft Excel LibreOffice Calc
t Date RVRTX,t RS&P 500,t (RVRTX,tRVRTX)2 (RS&P 500,tRS&P 500)2 (RVRTX,tRVRTX)×(RS&P 500,tRS&P 500)
1. Feb 28, 2015 8.43% 5.49% 46.32 21.25 31.38
2. Mar 31, 2015 -1.22% -1.74% 8.13 6.86 7.47
3. Apr 30, 2015 4.50% 0.85% 8.25 0.00 -0.08
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2019 13.44% 3.40% 139.48 6.38 29.83
59. Dec 31, 2019 -1.26% 2.86% 8.36 3.92 -5.72
Total (Σ): 5,307.10 688.77 1,000.85
t Date RVRTX,t RS&P 500,t (RVRTX,tRVRTX)2 (RS&P 500,tRS&P 500)2 (RVRTX,tRVRTX)×(RS&P 500,tRS&P 500)
1. Feb 28, 2015 8.43% 5.49% 46.32 21.25 31.38
2. Mar 31, 2015 -1.22% -1.74% 8.13 6.86 7.47
3. Apr 30, 2015 4.50% 0.85% 8.25 0.00 -0.08
4. May 31, 2015 4.06% 1.05% 5.93 0.03 0.41
5. Jun 30, 2015 -3.75% -2.10% 28.92 8.88 16.03
6. Jul 31, 2015 9.33% 1.97% 59.30 1.20 8.43
7. Aug 31, 2015 -5.54% -6.26% 51.40 50.94 51.17
8. Sep 30, 2015 -18.33% -2.64% 398.52 12.41 70.34
9. Oct 31, 2015 19.78% 8.30% 329.51 55.04 134.68
10. Nov 30, 2015 3.70% 0.05% 4.31 0.69 -1.72
11. Dec 31, 2015 -2.73% -1.75% 18.99 6.93 11.47
12. Jan 31, 2016 -27.88% -5.07% 870.69 35.43 175.65
13. Feb 29, 2016 -5.80% -0.41% 55.13 1.67 9.59
14. Mar 31, 2016 -7.02% 6.60% 74.77 32.72 -49.46
15. Apr 30, 2016 6.10% 0.27% 20.01 0.37 -2.72
16. May 31, 2016 10.45% 1.53% 77.74 0.43 5.76
17. Jun 30, 2016 -7.65% 0.09% 86.17 0.62 7.32
18. Jul 31, 2016 12.76% 3.56% 124.01 7.19 29.86
19. Aug 31, 2016 -2.57% -0.12% 17.60 1.00 4.20
20. Sep 30, 2016 -7.72% -0.12% 87.47 1.01 9.38
21. Oct 31, 2016 -13.01% -1.94% 214.42 7.96 41.32
22. Nov 30, 2016 7.58% 3.42% 35.42 6.44 15.11
23. Dec 31, 2016 -9.73% 1.82% 129.00 0.89 -10.69
24. Jan 31, 2017 16.56% 1.79% 222.96 0.83 13.58
25. Feb 28, 2017 5.53% 3.72% 15.23 8.07 11.09
26. Mar 31, 2017 20.67% -0.04% 362.53 0.84 -17.48
27. Apr 30, 2017 8.18% 0.91% 42.98 0.00 0.20
28. May 31, 2017 4.48% 1.16% 8.13 0.08 0.79
29. Jun 30, 2017 4.26% 0.48% 6.94 0.16 -1.05
30. Jul 31, 2017 17.81% 1.93% 261.79 1.11 17.08
31. Aug 31, 2017 5.74% 0.05% 16.93 0.68 -3.39
32. Sep 30, 2017 -5.29% 1.93% 47.93 1.10 -7.28
33. Oct 31, 2017 -3.82% 2.22% 29.70 1.79 -7.30
34. Nov 30, 2017 -1.33% 2.81% 8.73 3.72 -5.70
35. Dec 31, 2017 3.86% 0.98% 4.98 0.01 0.23
36. Jan 31, 2018 11.35% 5.62% 94.52 22.46 46.07
37. Feb 28, 2018 -0.50% -3.89% 4.55 22.79 10.18
38. Mar 31, 2018 -1.84% -2.69% 12.01 12.73 12.36
39. Apr 30, 2018 -6.03% 0.27% 58.58 0.37 4.65
40. May 31, 2018 0.55% 2.16% 1.17 1.64 -1.38
41. Jun 30, 2018 10.36% 0.48% 76.30 0.16 -3.45
42. Jul 31, 2018 2.99% 3.60% 1.87 7.41 3.72
43. Aug 31, 2018 5.34% 3.03% 13.78 4.61 7.97
44. Sep 30, 2018 4.52% 0.43% 8.38 0.20 -1.30
45. Oct 31, 2018 -12.08% -6.94% 187.88 61.14 107.18
46. Nov 30, 2018 6.69% 1.79% 25.58 0.82 4.59
47. Dec 31, 2018 -8.34% -9.18% 99.40 101.14 100.26
48. Jan 31, 2019 15.21% 7.87% 184.38 48.85 94.91
49. Feb 28, 2019 -1.13% 2.97% 7.62 4.38 -5.78
50. Mar 31, 2019 -2.54% 1.79% 17.40 0.83 -3.81
51. Apr 30, 2019 -8.14% 3.93% 95.39 9.32 -29.81
52. May 31, 2019 -1.66% -6.58% 10.80 55.61 24.50
53. Jun 30, 2019 10.35% 6.89% 76.07 36.17 52.45
54. Jul 31, 2019 -9.14% 1.31% 115.95 0.19 -4.67
55. Aug 31, 2019 8.04% -1.81% 41.13 7.23 -17.24
56. Sep 30, 2019 -5.89% 1.72% 56.50 0.70 -6.31
57. Oct 31, 2019 15.38% 2.04% 189.15 1.36 16.01
58. Nov 30, 2019 13.44% 3.40% 139.48 6.38 29.83
59. Dec 31, 2019 -1.26% 2.86% 8.36 3.92 -5.72
Total (Σ): 5,307.10 688.77 1,000.85

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VarianceVRTX = Σ(RVRTX,tRVRTX)2 ÷ (59 – 1)
= 5,307.10 ÷ (59 – 1)
= 91.50

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 688.77 ÷ (59 – 1)
= 11.88

CovarianceVRTX, S&P 500 = Σ(RVRTX,tRVRTX)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,000.85 ÷ (59 – 1)
= 17.26


Systematic Risk (β) Estimation

Microsoft Excel LibreOffice Calc
VarianceVRTX 91.50
VarianceS&P 500 11.88
CovarianceVRTX, S&P 500 17.26
Correlation coefficientVRTX, S&P 5001 0.52
βVRTX2 1.45
αVRTX3 0.35%

Calculations

1 Correlation coefficientVRTX, S&P 500
= CovarianceVRTX, S&P 500 ÷ (Standard deviationVRTX × Standard deviationS&P 500)
= 17.26 ÷ (9.57% × 3.45%)
= 0.52

2 βVRTX
= CovarianceVRTX, S&P 500 ÷ VarianceS&P 500
= 17.26 ÷ 11.88
= 1.45

3 αVRTX
= AverageVRTX – βVRTX × AverageS&P 500
= 1.63%1.45 × 0.88%
= 0.35%


Expected Rate of Return

Microsoft Excel LibreOffice Calc
Assumptions
Rate of return on LT Treasury Composite1 RF 1.65%
Expected rate of return on market portfolio2 E(RM) 12.15%
Systematic risk (β) of Vertex Pharmaceuticals Inc.’s common stock βVRTX 1.45
 
Expected rate of return on Vertex Pharmaceuticals Inc.’s common stock3 E(RVRTX) 16.90%

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(RVRTX) = RF + βVRTX [E(RM) – RF]
= 1.65% + 1.45 [12.15%1.65%]
= 16.90%