Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like AstraZeneca PLC common stock.
Rates of Return
AstraZeneca PLC (AZN) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceAZN,t1 | DividendAZN,t1 | RAZN,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2010 | $46.49 | 1,073.87 | ||||
1. | Feb 28, 2010 | $44.12 | $1.71 | -1.42% | 1,104.49 | 2.85% |
2. | Mar 31, 2010 | $44.72 | 1.36% | 1,169.43 | 5.88% | |
3. | Apr 30, 2010 | $44.23 | -1.10% | 1,186.69 | 1.48% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
58. | Nov 30, 2014 | $74.17 | 1.69% | 2,067.56 | 2.45% | |
59. | Dec 31, 2014 | $70.38 | -5.11% | 2,058.90 | -0.42% | |
Average (R): | 1.32% | 1.18% | ||||
Standard deviation: | 5.77% | 3.73% |
AstraZeneca PLC (AZN) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceAZN,t1 | DividendAZN,t1 | RAZN,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2010 | $46.49 | 1,073.87 | ||||
1. | Feb 28, 2010 | $44.12 | $1.71 | -1.42% | 1,104.49 | 2.85% |
2. | Mar 31, 2010 | $44.72 | 1.36% | 1,169.43 | 5.88% | |
3. | Apr 30, 2010 | $44.23 | -1.10% | 1,186.69 | 1.48% | |
4. | May 31, 2010 | $42.25 | -4.48% | 1,089.41 | -8.20% | |
5. | Jun 30, 2010 | $47.13 | 11.55% | 1,030.71 | -5.39% | |
6. | Jul 31, 2010 | $50.44 | 7.02% | 1,101.60 | 6.88% | |
7. | Aug 31, 2010 | $49.43 | $0.70 | -0.61% | 1,049.33 | -4.74% |
8. | Sep 30, 2010 | $50.70 | 2.57% | 1,141.20 | 8.76% | |
9. | Oct 31, 2010 | $50.46 | -0.47% | 1,183.26 | 3.69% | |
10. | Nov 30, 2010 | $46.93 | -7.00% | 1,180.55 | -0.23% | |
11. | Dec 31, 2010 | $46.19 | -1.58% | 1,257.64 | 6.53% | |
12. | Jan 31, 2011 | $48.90 | 5.87% | 1,286.12 | 2.26% | |
13. | Feb 28, 2011 | $49.17 | $1.85 | 4.34% | 1,327.22 | 3.20% |
14. | Mar 31, 2011 | $46.12 | -6.20% | 1,325.83 | -0.10% | |
15. | Apr 30, 2011 | $49.83 | 8.04% | 1,363.61 | 2.85% | |
16. | May 31, 2011 | $52.40 | 5.16% | 1,345.20 | -1.35% | |
17. | Jun 30, 2011 | $50.07 | -4.45% | 1,320.64 | -1.83% | |
18. | Jul 31, 2011 | $48.51 | -3.12% | 1,292.28 | -2.15% | |
19. | Aug 31, 2011 | $47.42 | $0.85 | -0.49% | 1,218.89 | -5.68% |
20. | Sep 30, 2011 | $44.36 | -6.45% | 1,131.42 | -7.18% | |
21. | Oct 31, 2011 | $47.91 | 8.00% | 1,253.30 | 10.77% | |
22. | Nov 30, 2011 | $45.98 | -4.03% | 1,246.96 | -0.51% | |
23. | Dec 31, 2011 | $46.29 | 0.67% | 1,257.60 | 0.85% | |
24. | Jan 31, 2012 | $48.15 | 4.02% | 1,312.41 | 4.36% | |
25. | Feb 29, 2012 | $44.89 | $1.95 | -2.72% | 1,365.68 | 4.06% |
26. | Mar 31, 2012 | $44.49 | -0.89% | 1,408.47 | 3.13% | |
27. | Apr 30, 2012 | $43.90 | -1.33% | 1,397.91 | -0.75% | |
28. | May 31, 2012 | $40.41 | -7.95% | 1,310.33 | -6.27% | |
29. | Jun 30, 2012 | $44.75 | 10.74% | 1,362.16 | 3.96% | |
30. | Jul 31, 2012 | $46.81 | 4.60% | 1,379.32 | 1.26% | |
31. | Aug 31, 2012 | $46.79 | $0.90 | 1.88% | 1,406.58 | 1.98% |
32. | Sep 30, 2012 | $47.86 | 2.29% | 1,440.67 | 2.42% | |
33. | Oct 31, 2012 | $46.40 | -3.05% | 1,412.16 | -1.98% | |
34. | Nov 30, 2012 | $47.54 | 2.46% | 1,416.18 | 0.28% | |
35. | Dec 31, 2012 | $47.27 | -0.57% | 1,426.19 | 0.71% | |
36. | Jan 31, 2013 | $48.18 | 1.93% | 1,498.11 | 5.04% | |
37. | Feb 28, 2013 | $45.44 | $1.90 | -1.74% | 1,514.68 | 1.11% |
38. | Mar 31, 2013 | $49.98 | 9.99% | 1,569.19 | 3.60% | |
39. | Apr 30, 2013 | $51.92 | 3.88% | 1,597.57 | 1.81% | |
40. | May 31, 2013 | $51.25 | -1.29% | 1,630.74 | 2.08% | |
41. | Jun 30, 2013 | $47.30 | -7.71% | 1,606.28 | -1.50% | |
42. | Jul 31, 2013 | $50.72 | 7.23% | 1,685.73 | 4.95% | |
43. | Aug 31, 2013 | $49.21 | $0.90 | -1.20% | 1,632.97 | -3.13% |
44. | Sep 30, 2013 | $51.93 | 5.53% | 1,681.55 | 2.97% | |
45. | Oct 31, 2013 | $52.86 | 1.79% | 1,756.54 | 4.46% | |
46. | Nov 30, 2013 | $57.19 | 8.19% | 1,805.81 | 2.80% | |
47. | Dec 31, 2013 | $59.37 | 3.81% | 1,848.36 | 2.36% | |
48. | Jan 31, 2014 | $63.50 | 6.96% | 1,782.59 | -3.56% | |
49. | Feb 28, 2014 | $67.76 | $1.90 | 9.70% | 1,859.45 | 4.31% |
50. | Mar 31, 2014 | $64.88 | -4.25% | 1,872.34 | 0.69% | |
51. | Apr 30, 2014 | $79.05 | 21.84% | 1,883.95 | 0.62% | |
52. | May 31, 2014 | $72.20 | -8.67% | 1,923.57 | 2.10% | |
53. | Jun 30, 2014 | $74.31 | 2.92% | 1,960.23 | 1.91% | |
54. | Jul 31, 2014 | $72.79 | -2.05% | 1,930.67 | -1.51% | |
55. | Aug 31, 2014 | $76.01 | $0.90 | 5.66% | 2,003.37 | 3.77% |
56. | Sep 30, 2014 | $71.44 | -6.01% | 1,972.29 | -1.55% | |
57. | Oct 31, 2014 | $72.94 | 2.10% | 2,018.05 | 2.32% | |
58. | Nov 30, 2014 | $74.17 | 1.69% | 2,067.56 | 2.45% | |
59. | Dec 31, 2014 | $70.38 | -5.11% | 2,058.90 | -0.42% | |
Average (R): | 1.32% | 1.18% | ||||
Standard deviation: | 5.77% | 3.73% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of AZN during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RAZN,t | RS&P 500,t | (RAZN,t–RAZN)2 | (RS&P 500,t–RS&P 500)2 | (RAZN,t–RAZN)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 28, 2010 | -1.42% | 2.85% | 7.50 | 2.80 | -4.58 |
2. | Mar 31, 2010 | 1.36% | 5.88% | 0.00 | 22.11 | 0.19 |
3. | Apr 30, 2010 | -1.10% | 1.48% | 5.83 | 0.09 | -0.72 |
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. | . | . | . | . | . | . |
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58. | Nov 30, 2014 | 1.69% | 2.45% | 0.13 | 1.63 | 0.47 |
59. | Dec 31, 2014 | -5.11% | -0.42% | 41.34 | 2.55 | 10.27 |
Total (Σ): | 1,927.83 | 809.11 | 478.66 |
t | Date | RAZN,t | RS&P 500,t | (RAZN,t–RAZN)2 | (RS&P 500,t–RS&P 500)2 | (RAZN,t–RAZN)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 28, 2010 | -1.42% | 2.85% | 7.50 | 2.80 | -4.58 |
2. | Mar 31, 2010 | 1.36% | 5.88% | 0.00 | 22.11 | 0.19 |
3. | Apr 30, 2010 | -1.10% | 1.48% | 5.83 | 0.09 | -0.72 |
4. | May 31, 2010 | -4.48% | -8.20% | 33.60 | 87.90 | 54.34 |
5. | Jun 30, 2010 | 11.55% | -5.39% | 104.67 | 43.11 | -67.17 |
6. | Jul 31, 2010 | 7.02% | 6.88% | 32.53 | 32.49 | 32.51 |
7. | Aug 31, 2010 | -0.61% | -4.74% | 3.74 | 35.08 | 11.46 |
8. | Sep 30, 2010 | 2.57% | 8.76% | 1.56 | 57.42 | 9.47 |
9. | Oct 31, 2010 | -0.47% | 3.69% | 3.21 | 6.29 | -4.50 |
10. | Nov 30, 2010 | -7.00% | -0.23% | 69.14 | 1.98 | 11.70 |
11. | Dec 31, 2010 | -1.58% | 6.53% | 8.39 | 28.65 | -15.50 |
12. | Jan 31, 2011 | 5.87% | 2.26% | 20.68 | 1.18 | 4.94 |
13. | Feb 28, 2011 | 4.34% | 3.20% | 9.09 | 4.07 | 6.09 |
14. | Mar 31, 2011 | -6.20% | -0.10% | 56.59 | 1.64 | 9.65 |
15. | Apr 30, 2011 | 8.04% | 2.85% | 45.22 | 2.79 | 11.24 |
16. | May 31, 2011 | 5.16% | -1.35% | 14.73 | 6.39 | -9.70 |
17. | Jun 30, 2011 | -4.45% | -1.83% | 33.25 | 9.02 | 17.32 |
18. | Jul 31, 2011 | -3.12% | -2.15% | 19.67 | 11.06 | 14.75 |
19. | Aug 31, 2011 | -0.49% | -5.68% | 3.29 | 47.02 | 12.44 |
20. | Sep 30, 2011 | -6.45% | -7.18% | 60.41 | 69.79 | 64.93 |
21. | Oct 31, 2011 | 8.00% | 10.77% | 44.66 | 92.06 | 64.12 |
22. | Nov 30, 2011 | -4.03% | -0.51% | 28.60 | 2.83 | 9.00 |
23. | Dec 31, 2011 | 0.67% | 0.85% | 0.42 | 0.11 | 0.21 |
24. | Jan 31, 2012 | 4.02% | 4.36% | 7.28 | 10.12 | 8.58 |
25. | Feb 29, 2012 | -2.72% | 4.06% | 16.32 | 8.30 | -11.64 |
26. | Mar 31, 2012 | -0.89% | 3.13% | 4.89 | 3.82 | -4.32 |
27. | Apr 30, 2012 | -1.33% | -0.75% | 7.00 | 3.72 | 5.10 |
28. | May 31, 2012 | -7.95% | -6.27% | 85.92 | 55.40 | 68.99 |
29. | Jun 30, 2012 | 10.74% | 3.96% | 88.74 | 7.72 | 26.17 |
30. | Jul 31, 2012 | 4.60% | 1.26% | 10.78 | 0.01 | 0.27 |
31. | Aug 31, 2012 | 1.88% | 1.98% | 0.31 | 0.64 | 0.45 |
32. | Sep 30, 2012 | 2.29% | 2.42% | 0.94 | 1.55 | 1.21 |
33. | Oct 31, 2012 | -3.05% | -1.98% | 19.10 | 9.96 | 13.80 |
34. | Nov 30, 2012 | 2.46% | 0.28% | 1.29 | 0.80 | -1.02 |
35. | Dec 31, 2012 | -0.57% | 0.71% | 3.56 | 0.22 | 0.89 |
36. | Jan 31, 2013 | 1.93% | 5.04% | 0.37 | 14.94 | 2.34 |
37. | Feb 28, 2013 | -1.74% | 1.11% | 9.38 | 0.01 | 0.22 |
38. | Mar 31, 2013 | 9.99% | 3.60% | 75.20 | 5.86 | 20.99 |
39. | Apr 30, 2013 | 3.88% | 1.81% | 6.56 | 0.40 | 1.62 |
40. | May 31, 2013 | -1.29% | 2.08% | 6.81 | 0.81 | -2.35 |
41. | Jun 30, 2013 | -7.71% | -1.50% | 81.49 | 7.17 | 24.17 |
42. | Jul 31, 2013 | 7.23% | 4.95% | 34.94 | 14.20 | 22.27 |
43. | Aug 31, 2013 | -1.20% | -3.13% | 6.36 | 18.55 | 10.86 |
44. | Sep 30, 2013 | 5.53% | 2.97% | 17.70 | 3.23 | 7.56 |
45. | Oct 31, 2013 | 1.79% | 4.46% | 0.22 | 10.77 | 1.55 |
46. | Nov 30, 2013 | 8.19% | 2.80% | 47.22 | 2.65 | 11.18 |
47. | Dec 31, 2013 | 3.81% | 2.36% | 6.21 | 1.39 | 2.94 |
48. | Jan 31, 2014 | 6.96% | -3.56% | 31.77 | 22.43 | -26.70 |
49. | Feb 28, 2014 | 9.70% | 4.31% | 70.24 | 9.82 | 26.27 |
50. | Mar 31, 2014 | -4.25% | 0.69% | 31.02 | 0.23 | 2.70 |
51. | Apr 30, 2014 | 21.84% | 0.62% | 421.10 | 0.31 | -11.44 |
52. | May 31, 2014 | -8.67% | 2.10% | 99.70 | 0.86 | -9.24 |
53. | Jun 30, 2014 | 2.92% | 1.91% | 2.57 | 0.53 | 1.17 |
54. | Jul 31, 2014 | -2.05% | -1.51% | 11.32 | 7.21 | 9.04 |
55. | Aug 31, 2014 | 5.66% | 3.77% | 18.84 | 6.70 | 11.23 |
56. | Sep 30, 2014 | -6.01% | -1.55% | 53.76 | 7.45 | 20.01 |
57. | Oct 31, 2014 | 2.10% | 2.32% | 0.61 | 1.31 | 0.89 |
58. | Nov 30, 2014 | 1.69% | 2.45% | 0.13 | 1.63 | 0.47 |
59. | Dec 31, 2014 | -5.11% | -0.42% | 41.34 | 2.55 | 10.27 |
Total (Σ): | 1,927.83 | 809.11 | 478.66 |
Show all
VarianceAZN = Σ(RAZN,t–RAZN)2 ÷ (59 – 1)
= 1,927.83 ÷ (59 – 1)
= 33.24
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 809.11 ÷ (59 – 1)
= 13.95
CovarianceAZN, S&P 500 = Σ(RAZN,t–RAZN)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 478.66 ÷ (59 – 1)
= 8.25
Systematic Risk (β) Estimation
VarianceAZN | 33.24 |
VarianceS&P 500 | 13.95 |
CovarianceAZN, S&P 500 | 8.25 |
Correlation coefficientAZN, S&P 5001 | 0.38 |
βAZN2 | 0.59 |
αAZN3 | 0.62% |
Calculations
1 Correlation coefficientAZN, S&P 500
= CovarianceAZN, S&P 500 ÷ (Standard deviationAZN × Standard deviationS&P 500)
= 8.25 ÷ (5.77% × 3.73%)
= 0.38
2 βAZN
= CovarianceAZN, S&P 500 ÷ VarianceS&P 500
= 8.25 ÷ 13.95
= 0.59
3 αAZN
= AverageAZN – βAZN × AverageS&P 500
= 1.32% – 0.59 × 1.18%
= 0.62%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.43% |
Expected rate of return on market portfolio2 | E(RM) | 13.60% |
Systematic risk (β) of AstraZeneca PLC common stock | βAZN | 0.59 |
Expected rate of return on AstraZeneca PLC common stock3 | E(RAZN) | 9.86% |
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).
3 E(RAZN) = RF + βAZN [E(RM) – RF]
= 4.43% + 0.59 [13.60% – 4.43%]
= 9.86%