Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like BP PLC common stock.
Rates of Return
BP PLC (BP) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceBP,t1 | DividendBP,t1 | RBP,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2010 | $56.12 | 1,073.87 | ||||
1. | Feb 28, 2010 | $53.21 | $0.84 | -3.69% | 1,104.49 | 2.85% |
2. | Mar 31, 2010 | $57.07 | 7.25% | 1,169.43 | 5.88% | |
3. | Apr 30, 2010 | $52.15 | -8.62% | 1,186.69 | 1.48% | |
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58. | Nov 30, 2014 | $39.32 | $0.60 | -8.15% | 2,067.56 | 2.45% |
59. | Dec 31, 2014 | $38.12 | -3.05% | 2,058.90 | -0.42% | |
Average (R): | 0.14% | 1.18% | ||||
Standard deviation: | 9.50% | 3.73% |
BP PLC (BP) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceBP,t1 | DividendBP,t1 | RBP,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2010 | $56.12 | 1,073.87 | ||||
1. | Feb 28, 2010 | $53.21 | $0.84 | -3.69% | 1,104.49 | 2.85% |
2. | Mar 31, 2010 | $57.07 | 7.25% | 1,169.43 | 5.88% | |
3. | Apr 30, 2010 | $52.15 | -8.62% | 1,186.69 | 1.48% | |
4. | May 31, 2010 | $42.95 | -17.64% | 1,089.41 | -8.20% | |
5. | Jun 30, 2010 | $28.88 | -32.76% | 1,030.71 | -5.39% | |
6. | Jul 31, 2010 | $38.47 | 33.21% | 1,101.60 | 6.88% | |
7. | Aug 31, 2010 | $34.83 | -9.46% | 1,049.33 | -4.74% | |
8. | Sep 30, 2010 | $41.17 | 18.20% | 1,141.20 | 8.76% | |
9. | Oct 31, 2010 | $40.80 | -0.90% | 1,183.26 | 3.69% | |
10. | Nov 30, 2010 | $40.00 | -1.96% | 1,180.55 | -0.23% | |
11. | Dec 31, 2010 | $44.17 | 10.43% | 1,257.64 | 6.53% | |
12. | Jan 31, 2011 | $47.47 | 7.47% | 1,286.12 | 2.26% | |
13. | Feb 28, 2011 | $48.47 | $0.42 | 2.99% | 1,327.22 | 3.20% |
14. | Mar 31, 2011 | $44.14 | -8.93% | 1,325.83 | -0.10% | |
15. | Apr 30, 2011 | $46.14 | 4.53% | 1,363.61 | 2.85% | |
16. | May 31, 2011 | $46.24 | $0.42 | 1.13% | 1,345.20 | -1.35% |
17. | Jun 30, 2011 | $44.29 | -4.22% | 1,320.64 | -1.83% | |
18. | Jul 31, 2011 | $45.44 | 2.60% | 1,292.28 | -2.15% | |
19. | Aug 31, 2011 | $39.39 | $0.42 | -12.39% | 1,218.89 | -5.68% |
20. | Sep 30, 2011 | $36.07 | -8.43% | 1,131.42 | -7.18% | |
21. | Oct 31, 2011 | $44.18 | 22.48% | 1,253.30 | 10.77% | |
22. | Nov 30, 2011 | $43.55 | $0.42 | -0.48% | 1,246.96 | -0.51% |
23. | Dec 31, 2011 | $42.74 | -1.86% | 1,257.60 | 0.85% | |
24. | Jan 31, 2012 | $45.91 | 7.42% | 1,312.41 | 4.36% | |
25. | Feb 29, 2012 | $47.16 | $0.48 | 3.77% | 1,365.68 | 4.06% |
26. | Mar 31, 2012 | $45.00 | -4.58% | 1,408.47 | 3.13% | |
27. | Apr 30, 2012 | $43.41 | -3.53% | 1,397.91 | -0.75% | |
28. | May 31, 2012 | $36.46 | $0.48 | -14.90% | 1,310.33 | -6.27% |
29. | Jun 30, 2012 | $40.54 | 11.19% | 1,362.16 | 3.96% | |
30. | Jul 31, 2012 | $39.90 | -1.58% | 1,379.32 | 1.26% | |
31. | Aug 31, 2012 | $42.06 | $0.48 | 6.62% | 1,406.58 | 1.98% |
32. | Sep 30, 2012 | $42.36 | 0.71% | 1,440.67 | 2.42% | |
33. | Oct 31, 2012 | $42.89 | 1.25% | 1,412.16 | -1.98% | |
34. | Nov 30, 2012 | $41.76 | $0.54 | -1.38% | 1,416.18 | 0.28% |
35. | Dec 31, 2012 | $41.64 | -0.29% | 1,426.19 | 0.71% | |
36. | Jan 31, 2013 | $44.52 | 6.92% | 1,498.11 | 5.04% | |
37. | Feb 28, 2013 | $40.40 | $0.54 | -8.04% | 1,514.68 | 1.11% |
38. | Mar 31, 2013 | $42.35 | 4.83% | 1,569.19 | 3.60% | |
39. | Apr 30, 2013 | $43.60 | 2.95% | 1,597.57 | 1.81% | |
40. | May 31, 2013 | $42.91 | $0.54 | -0.34% | 1,630.74 | 2.08% |
41. | Jun 30, 2013 | $41.74 | -2.73% | 1,606.28 | -1.50% | |
42. | Jul 31, 2013 | $41.44 | -0.72% | 1,685.73 | 4.95% | |
43. | Aug 31, 2013 | $41.30 | $0.54 | 0.97% | 1,632.97 | -3.13% |
44. | Sep 30, 2013 | $42.03 | 1.77% | 1,681.55 | 2.97% | |
45. | Oct 31, 2013 | $46.50 | 10.64% | 1,756.54 | 4.46% | |
46. | Nov 30, 2013 | $47.01 | $0.57 | 2.32% | 1,805.81 | 2.80% |
47. | Dec 31, 2013 | $48.61 | 3.40% | 1,848.36 | 2.36% | |
48. | Jan 31, 2014 | $46.89 | -3.54% | 1,782.59 | -3.56% | |
49. | Feb 28, 2014 | $50.61 | $0.57 | 9.15% | 1,859.45 | 4.31% |
50. | Mar 31, 2014 | $48.10 | -4.96% | 1,872.34 | 0.69% | |
51. | Apr 30, 2014 | $50.62 | 5.24% | 1,883.95 | 0.62% | |
52. | May 31, 2014 | $50.45 | $0.585 | 0.82% | 1,923.57 | 2.10% |
53. | Jun 30, 2014 | $52.75 | 4.56% | 1,960.23 | 1.91% | |
54. | Jul 31, 2014 | $48.97 | -7.17% | 1,930.67 | -1.51% | |
55. | Aug 31, 2014 | $47.84 | $0.585 | -1.11% | 2,003.37 | 3.77% |
56. | Sep 30, 2014 | $43.95 | -8.13% | 1,972.29 | -1.55% | |
57. | Oct 31, 2014 | $43.46 | -1.11% | 2,018.05 | 2.32% | |
58. | Nov 30, 2014 | $39.32 | $0.60 | -8.15% | 2,067.56 | 2.45% |
59. | Dec 31, 2014 | $38.12 | -3.05% | 2,058.90 | -0.42% | |
Average (R): | 0.14% | 1.18% | ||||
Standard deviation: | 9.50% | 3.73% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of BP during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RBP,t | RS&P 500,t | (RBP,t–RBP)2 | (RS&P 500,t–RS&P 500)2 | (RBP,t–RBP)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 28, 2010 | -3.69% | 2.85% | 14.64 | 2.80 | -6.40 |
2. | Mar 31, 2010 | 7.25% | 5.88% | 50.64 | 22.11 | 33.46 |
3. | Apr 30, 2010 | -8.62% | 1.48% | 76.72 | 0.09 | -2.61 |
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58. | Nov 30, 2014 | -8.15% | 2.45% | 68.62 | 1.63 | -10.57 |
59. | Dec 31, 2014 | -3.05% | -0.42% | 10.18 | 2.55 | 5.09 |
Total (Σ): | 5,237.74 | 809.11 | 1,597.65 |
t | Date | RBP,t | RS&P 500,t | (RBP,t–RBP)2 | (RS&P 500,t–RS&P 500)2 | (RBP,t–RBP)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 28, 2010 | -3.69% | 2.85% | 14.64 | 2.80 | -6.40 |
2. | Mar 31, 2010 | 7.25% | 5.88% | 50.64 | 22.11 | 33.46 |
3. | Apr 30, 2010 | -8.62% | 1.48% | 76.72 | 0.09 | -2.61 |
4. | May 31, 2010 | -17.64% | -8.20% | 316.12 | 87.90 | 166.69 |
5. | Jun 30, 2010 | -32.76% | -5.39% | 1,082.23 | 43.11 | 216.00 |
6. | Jul 31, 2010 | 33.21% | 6.88% | 1,093.50 | 32.49 | 188.49 |
7. | Aug 31, 2010 | -9.46% | -4.74% | 92.16 | 35.08 | 56.86 |
8. | Sep 30, 2010 | 18.20% | 8.76% | 326.32 | 57.42 | 136.88 |
9. | Oct 31, 2010 | -0.90% | 3.69% | 1.08 | 6.29 | -2.60 |
10. | Nov 30, 2010 | -1.96% | -0.23% | 4.41 | 1.98 | 2.95 |
11. | Dec 31, 2010 | 10.43% | 6.53% | 105.82 | 28.65 | 55.06 |
12. | Jan 31, 2011 | 7.47% | 2.26% | 53.77 | 1.18 | 7.97 |
13. | Feb 28, 2011 | 2.99% | 3.20% | 8.14 | 4.07 | 5.76 |
14. | Mar 31, 2011 | -8.93% | -0.10% | 82.29 | 1.64 | 11.63 |
15. | Apr 30, 2011 | 4.53% | 2.85% | 19.30 | 2.79 | 7.34 |
16. | May 31, 2011 | 1.13% | -1.35% | 0.98 | 6.39 | -2.50 |
17. | Jun 30, 2011 | -4.22% | -1.83% | 18.97 | 9.02 | 13.08 |
18. | Jul 31, 2011 | 2.60% | -2.15% | 6.04 | 11.06 | -8.17 |
19. | Aug 31, 2011 | -12.39% | -5.68% | 156.96 | 47.02 | 85.90 |
20. | Sep 30, 2011 | -8.43% | -7.18% | 73.39 | 69.79 | 71.57 |
21. | Oct 31, 2011 | 22.48% | 10.77% | 499.34 | 92.06 | 214.40 |
22. | Nov 30, 2011 | -0.48% | -0.51% | 0.38 | 2.83 | 1.03 |
23. | Dec 31, 2011 | -1.86% | 0.85% | 3.99 | 0.11 | 0.65 |
24. | Jan 31, 2012 | 7.42% | 4.36% | 52.98 | 10.12 | 23.15 |
25. | Feb 29, 2012 | 3.77% | 4.06% | 13.18 | 8.30 | 10.46 |
26. | Mar 31, 2012 | -4.58% | 3.13% | 22.26 | 3.82 | -9.23 |
27. | Apr 30, 2012 | -3.53% | -0.75% | 13.48 | 3.72 | 7.08 |
28. | May 31, 2012 | -14.90% | -6.27% | 226.28 | 55.40 | 111.96 |
29. | Jun 30, 2012 | 11.19% | 3.96% | 122.15 | 7.72 | 30.70 |
30. | Jul 31, 2012 | -1.58% | 1.26% | 2.95 | 0.01 | -0.14 |
31. | Aug 31, 2012 | 6.62% | 1.98% | 41.97 | 0.64 | 5.17 |
32. | Sep 30, 2012 | 0.71% | 2.42% | 0.33 | 1.55 | 0.72 |
33. | Oct 31, 2012 | 1.25% | -1.98% | 1.24 | 9.96 | -3.51 |
34. | Nov 30, 2012 | -1.38% | 0.28% | 2.29 | 0.80 | 1.35 |
35. | Dec 31, 2012 | -0.29% | 0.71% | 0.18 | 0.22 | 0.20 |
36. | Jan 31, 2013 | 6.92% | 5.04% | 45.94 | 14.94 | 26.20 |
37. | Feb 28, 2013 | -8.04% | 1.11% | 66.91 | 0.01 | 0.59 |
38. | Mar 31, 2013 | 4.83% | 3.60% | 21.98 | 5.86 | 11.35 |
39. | Apr 30, 2013 | 2.95% | 1.81% | 7.91 | 0.40 | 1.77 |
40. | May 31, 2013 | -0.34% | 2.08% | 0.23 | 0.81 | -0.43 |
41. | Jun 30, 2013 | -2.73% | -1.50% | 8.21 | 7.17 | 7.67 |
42. | Jul 31, 2013 | -0.72% | 4.95% | 0.73 | 14.20 | -3.23 |
43. | Aug 31, 2013 | 0.97% | -3.13% | 0.68 | 18.55 | -3.56 |
44. | Sep 30, 2013 | 1.77% | 2.97% | 2.65 | 3.23 | 2.93 |
45. | Oct 31, 2013 | 10.64% | 4.46% | 110.19 | 10.77 | 34.45 |
46. | Nov 30, 2013 | 2.32% | 2.80% | 4.77 | 2.65 | 3.55 |
47. | Dec 31, 2013 | 3.40% | 2.36% | 10.66 | 1.39 | 3.85 |
48. | Jan 31, 2014 | -3.54% | -3.56% | 13.52 | 22.43 | 17.41 |
49. | Feb 28, 2014 | 9.15% | 4.31% | 81.20 | 9.82 | 28.24 |
50. | Mar 31, 2014 | -4.96% | 0.69% | 25.99 | 0.23 | 2.47 |
51. | Apr 30, 2014 | 5.24% | 0.62% | 26.02 | 0.31 | -2.84 |
52. | May 31, 2014 | 0.82% | 2.10% | 0.46 | 0.86 | 0.63 |
53. | Jun 30, 2014 | 4.56% | 1.91% | 19.54 | 0.53 | 3.22 |
54. | Jul 31, 2014 | -7.17% | -1.51% | 53.35 | 7.21 | 19.62 |
55. | Aug 31, 2014 | -1.11% | 3.77% | 1.57 | 6.70 | -3.24 |
56. | Sep 30, 2014 | -8.13% | -1.55% | 68.38 | 7.45 | 22.57 |
57. | Oct 31, 2014 | -1.11% | 2.32% | 1.57 | 1.31 | -1.43 |
58. | Nov 30, 2014 | -8.15% | 2.45% | 68.62 | 1.63 | -10.57 |
59. | Dec 31, 2014 | -3.05% | -0.42% | 10.18 | 2.55 | 5.09 |
Total (Σ): | 5,237.74 | 809.11 | 1,597.65 |
Show all
VarianceBP = Σ(RBP,t–RBP)2 ÷ (59 – 1)
= 5,237.74 ÷ (59 – 1)
= 90.31
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 809.11 ÷ (59 – 1)
= 13.95
CovarianceBP, S&P 500 = Σ(RBP,t–RBP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,597.65 ÷ (59 – 1)
= 27.55
Systematic Risk (β) Estimation
VarianceBP | 90.31 |
VarianceS&P 500 | 13.95 |
CovarianceBP, S&P 500 | 27.55 |
Correlation coefficientBP, S&P 5001 | 0.78 |
βBP2 | 1.97 |
αBP3 | -2.19% |
Calculations
1 Correlation coefficientBP, S&P 500
= CovarianceBP, S&P 500 ÷ (Standard deviationBP × Standard deviationS&P 500)
= 27.55 ÷ (9.50% × 3.73%)
= 0.78
2 βBP
= CovarianceBP, S&P 500 ÷ VarianceS&P 500
= 27.55 ÷ 13.95
= 1.97
3 αBP
= AverageBP – βBP × AverageS&P 500
= 0.14% – 1.97 × 1.18%
= -2.19%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.83% |
Expected rate of return on market portfolio2 | E(RM) | 13.48% |
Systematic risk (β) of BP PLC common stock | βBP | 1.97 |
Expected rate of return on BP PLC common stock3 | E(RBP) | 21.90% |
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).
3 E(RBP) = RF + βBP [E(RM) – RF]
= 4.83% + 1.97 [13.48% – 4.83%]
= 21.90%