Capital Asset Pricing Model (CAPM)
Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Carnival Corp. & plc common stock.
Rates of Return
Carnival Corp. & plc, monthly rates of return
| Carnival Corp. & plc (CCL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCCL,t1 | DividendCCL,t1 | RCCL,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Dec 31, 2017 | $66.37 | 2,673.61 | ||||
| 1. | Jan 31, 2018 | $71.61 | 7.90% | 2,823.81 | 5.62% | |
| 2. | Feb 28, 2018 | $66.91 | $0.45 | -5.93% | 2,713.83 | -3.89% |
| 3. | Mar 31, 2018 | $65.58 | -1.99% | 2,640.87 | -2.69% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Oct 31, 2023 | $11.46 | -16.47% | 4,193.80 | -2.20% | |
| 71. | Nov 30, 2023 | $15.06 | 31.41% | 4,567.80 | 8.92% | |
| Average (R): | -0.14% | 0.89% | ||||
| Standard deviation: | 18.84% | 5.22% | ||||
| Carnival Corp. & plc (CCL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCCL,t1 | DividendCCL,t1 | RCCL,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Dec 31, 2017 | $66.37 | 2,673.61 | ||||
| 1. | Jan 31, 2018 | $71.61 | 7.90% | 2,823.81 | 5.62% | |
| 2. | Feb 28, 2018 | $66.91 | $0.45 | -5.93% | 2,713.83 | -3.89% |
| 3. | Mar 31, 2018 | $65.58 | -1.99% | 2,640.87 | -2.69% | |
| 4. | Apr 30, 2018 | $63.06 | -3.84% | 2,648.05 | 0.27% | |
| 5. | May 31, 2018 | $62.28 | $0.50 | -0.44% | 2,705.27 | 2.16% |
| 6. | Jun 30, 2018 | $57.31 | -7.98% | 2,718.37 | 0.48% | |
| 7. | Jul 31, 2018 | $59.24 | 3.37% | 2,816.29 | 3.60% | |
| 8. | Aug 31, 2018 | $61.49 | $0.50 | 4.64% | 2,901.52 | 3.03% |
| 9. | Sep 30, 2018 | $63.77 | 3.71% | 2,913.98 | 0.43% | |
| 10. | Oct 31, 2018 | $56.04 | -12.12% | 2,711.74 | -6.94% | |
| 11. | Nov 30, 2018 | $60.29 | $0.50 | 8.48% | 2,760.17 | 1.79% |
| 12. | Dec 31, 2018 | $49.30 | -18.23% | 2,506.85 | -9.18% | |
| 13. | Jan 31, 2019 | $57.58 | 16.80% | 2,704.10 | 7.87% | |
| 14. | Feb 28, 2019 | $57.76 | $0.50 | 1.18% | 2,784.49 | 2.97% |
| 15. | Mar 31, 2019 | $50.72 | -12.19% | 2,834.40 | 1.79% | |
| 16. | Apr 30, 2019 | $54.86 | 8.16% | 2,945.83 | 3.93% | |
| 17. | May 31, 2019 | $51.19 | $0.50 | -5.78% | 2,752.06 | -6.58% |
| 18. | Jun 30, 2019 | $46.55 | -9.06% | 2,941.76 | 6.89% | |
| 19. | Jul 31, 2019 | $47.23 | 1.46% | 2,980.38 | 1.31% | |
| 20. | Aug 31, 2019 | $44.08 | $0.50 | -5.61% | 2,926.46 | -1.81% |
| 21. | Sep 30, 2019 | $43.71 | -0.84% | 2,976.74 | 1.72% | |
| 22. | Oct 31, 2019 | $42.89 | -1.88% | 3,037.56 | 2.04% | |
| 23. | Nov 30, 2019 | $45.08 | $0.50 | 6.27% | 3,140.98 | 3.40% |
| 24. | Dec 31, 2019 | $50.83 | 12.76% | 3,230.78 | 2.86% | |
| 25. | Jan 31, 2020 | $43.53 | -14.36% | 3,225.52 | -0.16% | |
| 26. | Feb 29, 2020 | $33.46 | $0.50 | -21.98% | 2,954.22 | -8.41% |
| 27. | Mar 31, 2020 | $13.17 | -60.64% | 2,584.59 | -12.51% | |
| 28. | Apr 30, 2020 | $15.90 | 20.73% | 2,912.43 | 12.68% | |
| 29. | May 31, 2020 | $15.74 | -1.01% | 3,044.31 | 4.53% | |
| 30. | Jun 30, 2020 | $16.42 | 4.32% | 3,100.29 | 1.84% | |
| 31. | Jul 31, 2020 | $13.88 | -15.47% | 3,271.12 | 5.51% | |
| 32. | Aug 31, 2020 | $16.48 | 18.73% | 3,500.31 | 7.01% | |
| 33. | Sep 30, 2020 | $15.18 | -7.89% | 3,363.00 | -3.92% | |
| 34. | Oct 31, 2020 | $13.71 | -9.68% | 3,269.96 | -2.77% | |
| 35. | Nov 30, 2020 | $19.98 | 45.73% | 3,621.63 | 10.75% | |
| 36. | Dec 31, 2020 | $21.66 | 8.41% | 3,756.07 | 3.71% | |
| 37. | Jan 31, 2021 | $18.67 | -13.80% | 3,714.24 | -1.11% | |
| 38. | Feb 28, 2021 | $26.75 | 43.28% | 3,811.15 | 2.61% | |
| 39. | Mar 31, 2021 | $26.54 | -0.79% | 3,972.89 | 4.24% | |
| 40. | Apr 30, 2021 | $27.96 | 5.35% | 4,181.17 | 5.24% | |
| 41. | May 31, 2021 | $29.56 | 5.72% | 4,204.11 | 0.55% | |
| 42. | Jun 30, 2021 | $26.36 | -10.83% | 4,297.50 | 2.22% | |
| 43. | Jul 31, 2021 | $21.65 | -17.87% | 4,395.26 | 2.27% | |
| 44. | Aug 31, 2021 | $24.14 | 11.50% | 4,522.68 | 2.90% | |
| 45. | Sep 30, 2021 | $25.01 | 3.60% | 4,307.54 | -4.76% | |
| 46. | Oct 31, 2021 | $22.16 | -11.40% | 4,605.38 | 6.91% | |
| 47. | Nov 30, 2021 | $17.62 | -20.49% | 4,567.00 | -0.83% | |
| 48. | Dec 31, 2021 | $20.12 | 14.19% | 4,766.18 | 4.36% | |
| 49. | Jan 31, 2022 | $19.81 | -1.54% | 4,515.55 | -5.26% | |
| 50. | Feb 28, 2022 | $20.33 | 2.62% | 4,373.94 | -3.14% | |
| 51. | Mar 31, 2022 | $20.22 | -0.54% | 4,530.41 | 3.58% | |
| 52. | Apr 30, 2022 | $17.30 | -14.44% | 4,131.93 | -8.80% | |
| 53. | May 31, 2022 | $13.88 | -19.77% | 4,132.15 | 0.01% | |
| 54. | Jun 30, 2022 | $8.65 | -37.68% | 3,785.38 | -8.39% | |
| 55. | Jul 31, 2022 | $9.06 | 4.74% | 4,130.29 | 9.11% | |
| 56. | Aug 31, 2022 | $9.46 | 4.42% | 3,955.00 | -4.24% | |
| 57. | Sep 30, 2022 | $7.03 | -25.69% | 3,585.62 | -9.34% | |
| 58. | Oct 31, 2022 | $9.06 | 28.88% | 3,871.98 | 7.99% | |
| 59. | Nov 30, 2022 | $9.93 | 9.60% | 4,080.11 | 5.38% | |
| 60. | Dec 31, 2022 | $8.06 | -18.83% | 3,839.50 | -5.90% | |
| 61. | Jan 31, 2023 | $10.82 | 34.24% | 4,076.60 | 6.18% | |
| 62. | Feb 28, 2023 | $10.62 | -1.85% | 3,970.15 | -2.61% | |
| 63. | Mar 31, 2023 | $10.15 | -4.43% | 4,109.31 | 3.51% | |
| 64. | Apr 30, 2023 | $9.21 | -9.26% | 4,169.48 | 1.46% | |
| 65. | May 31, 2023 | $11.23 | 21.93% | 4,179.83 | 0.25% | |
| 66. | Jun 30, 2023 | $18.83 | 67.68% | 4,376.86 | 4.71% | |
| 67. | Jul 31, 2023 | $18.84 | 0.05% | 4,588.96 | 4.85% | |
| 68. | Aug 31, 2023 | $15.82 | -16.03% | 4,507.66 | -1.77% | |
| 69. | Sep 30, 2023 | $13.72 | -13.27% | 4,288.05 | -4.87% | |
| 70. | Oct 31, 2023 | $11.46 | -16.47% | 4,193.80 | -2.20% | |
| 71. | Nov 30, 2023 | $15.06 | 31.41% | 4,567.80 | 8.92% | |
| Average (R): | -0.14% | 0.89% | ||||
| Standard deviation: | 18.84% | 5.22% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of CCL during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Carnival Corp. & plc, calculation of variance and covariance of returns
| t | Date | RCCL,t | RS&P 500,t | (RCCL,t–RCCL)2 | (RS&P 500,t–RS&P 500)2 | (RCCL,t–RCCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Jan 31, 2018 | 7.90% | 5.62% | 64.59 | 22.33 | 37.98 |
| 2. | Feb 28, 2018 | -5.93% | -3.89% | 33.57 | 22.92 | 27.74 |
| 3. | Mar 31, 2018 | -1.99% | -2.69% | 3.41 | 12.82 | 6.61 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Oct 31, 2023 | -16.47% | -2.20% | 266.70 | 9.55 | 50.47 |
| 71. | Nov 30, 2023 | 31.41% | 8.92% | 995.72 | 64.41 | 253.24 |
| Total (Σ): | 24,858.07 | 1,909.09 | 4,523.25 | |||
| t | Date | RCCL,t | RS&P 500,t | (RCCL,t–RCCL)2 | (RS&P 500,t–RS&P 500)2 | (RCCL,t–RCCL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Jan 31, 2018 | 7.90% | 5.62% | 64.59 | 22.33 | 37.98 |
| 2. | Feb 28, 2018 | -5.93% | -3.89% | 33.57 | 22.92 | 27.74 |
| 3. | Mar 31, 2018 | -1.99% | -2.69% | 3.41 | 12.82 | 6.61 |
| 4. | Apr 30, 2018 | -3.84% | 0.27% | 13.70 | 0.39 | 2.30 |
| 5. | May 31, 2018 | -0.44% | 2.16% | 0.09 | 1.61 | -0.38 |
| 6. | Jun 30, 2018 | -7.98% | 0.48% | 61.45 | 0.17 | 3.20 |
| 7. | Jul 31, 2018 | 3.37% | 3.60% | 12.31 | 7.34 | 9.51 |
| 8. | Aug 31, 2018 | 4.64% | 3.03% | 22.88 | 4.55 | 10.21 |
| 9. | Sep 30, 2018 | 3.71% | 0.43% | 14.82 | 0.21 | -1.78 |
| 10. | Oct 31, 2018 | -12.12% | -6.94% | 143.53 | 61.35 | 93.84 |
| 11. | Nov 30, 2018 | 8.48% | 1.79% | 74.26 | 0.80 | 7.70 |
| 12. | Dec 31, 2018 | -18.23% | -9.18% | 327.15 | 101.41 | 182.14 |
| 13. | Jan 31, 2019 | 16.80% | 7.87% | 286.85 | 48.66 | 118.15 |
| 14. | Feb 28, 2019 | 1.18% | 2.97% | 1.75 | 4.33 | 2.75 |
| 15. | Mar 31, 2019 | -12.19% | 1.79% | 145.13 | 0.81 | -10.84 |
| 16. | Apr 30, 2019 | 8.16% | 3.93% | 68.95 | 9.23 | 25.23 |
| 17. | May 31, 2019 | -5.78% | -6.58% | 31.78 | 55.81 | 42.11 |
| 18. | Jun 30, 2019 | -9.06% | 6.89% | 79.62 | 36.01 | -53.54 |
| 19. | Jul 31, 2019 | 1.46% | 1.31% | 2.57 | 0.18 | 0.67 |
| 20. | Aug 31, 2019 | -5.61% | -1.81% | 29.91 | 7.30 | 14.78 |
| 21. | Sep 30, 2019 | -0.84% | 1.72% | 0.49 | 0.68 | -0.58 |
| 22. | Oct 31, 2019 | -1.88% | 2.04% | 3.01 | 1.32 | -2.00 |
| 23. | Nov 30, 2019 | 6.27% | 3.40% | 41.13 | 6.31 | 16.11 |
| 24. | Dec 31, 2019 | 12.76% | 2.86% | 166.32 | 3.87 | 25.36 |
| 25. | Jan 31, 2020 | -14.36% | -0.16% | 202.21 | 1.11 | 15.01 |
| 26. | Feb 29, 2020 | -21.98% | -8.41% | 477.14 | 86.56 | 203.22 |
| 27. | Mar 31, 2020 | -60.64% | -12.51% | 3,660.03 | 179.68 | 810.94 |
| 28. | Apr 30, 2020 | 20.73% | 12.68% | 435.57 | 139.05 | 246.10 |
| 29. | May 31, 2020 | -1.01% | 4.53% | 0.75 | 13.22 | -3.14 |
| 30. | Jun 30, 2020 | 4.32% | 1.84% | 19.91 | 0.90 | 4.22 |
| 31. | Jul 31, 2020 | -15.47% | 5.51% | 234.93 | 21.32 | -70.78 |
| 32. | Aug 31, 2020 | 18.73% | 7.01% | 356.20 | 37.38 | 115.39 |
| 33. | Sep 30, 2020 | -7.89% | -3.92% | 60.02 | 23.19 | 37.30 |
| 34. | Oct 31, 2020 | -9.68% | -2.77% | 91.06 | 13.39 | 34.92 |
| 35. | Nov 30, 2020 | 45.73% | 10.75% | 2,104.46 | 97.26 | 452.42 |
| 36. | Dec 31, 2020 | 8.41% | 3.71% | 73.10 | 7.95 | 24.11 |
| 37. | Jan 31, 2021 | -13.80% | -1.11% | 186.67 | 4.02 | 27.41 |
| 38. | Feb 28, 2021 | 43.28% | 2.61% | 1,885.24 | 2.95 | 74.54 |
| 39. | Mar 31, 2021 | -0.79% | 4.24% | 0.41 | 11.23 | -2.16 |
| 40. | Apr 30, 2021 | 5.35% | 5.24% | 30.16 | 18.92 | 23.89 |
| 41. | May 31, 2021 | 5.72% | 0.55% | 34.38 | 0.12 | -2.02 |
| 42. | Jun 30, 2021 | -10.83% | 2.22% | 114.15 | 1.77 | -14.20 |
| 43. | Jul 31, 2021 | -17.87% | 2.27% | 314.23 | 1.91 | -24.50 |
| 44. | Aug 31, 2021 | 11.50% | 2.90% | 135.55 | 4.03 | 23.36 |
| 45. | Sep 30, 2021 | 3.60% | -4.76% | 14.03 | 31.92 | -21.16 |
| 46. | Oct 31, 2021 | -11.40% | 6.91% | 126.65 | 36.26 | -67.77 |
| 47. | Nov 30, 2021 | -20.49% | -0.83% | 413.96 | 2.98 | 35.11 |
| 48. | Dec 31, 2021 | 14.19% | 4.36% | 205.34 | 12.03 | 49.71 |
| 49. | Jan 31, 2022 | -1.54% | -5.26% | 1.96 | 37.83 | 8.61 |
| 50. | Feb 28, 2022 | 2.62% | -3.14% | 7.65 | 16.23 | -11.14 |
| 51. | Mar 31, 2022 | -0.54% | 3.58% | 0.16 | 7.21 | -1.07 |
| 52. | Apr 30, 2022 | -14.44% | -8.80% | 204.48 | 93.86 | 138.54 |
| 53. | May 31, 2022 | -19.77% | 0.01% | 385.23 | 0.79 | 17.41 |
| 54. | Jun 30, 2022 | -37.68% | -8.39% | 1,409.16 | 86.20 | 348.53 |
| 55. | Jul 31, 2022 | 4.74% | 9.11% | 23.83 | 67.55 | 40.12 |
| 56. | Aug 31, 2022 | 4.42% | -4.24% | 20.76 | 26.38 | -23.40 |
| 57. | Sep 30, 2022 | -25.69% | -9.34% | 652.58 | 104.70 | 261.39 |
| 58. | Oct 31, 2022 | 28.88% | 7.99% | 842.02 | 50.32 | 205.85 |
| 59. | Nov 30, 2022 | 9.60% | 5.38% | 94.95 | 20.10 | 43.68 |
| 60. | Dec 31, 2022 | -18.83% | -5.90% | 349.33 | 46.10 | 126.90 |
| 61. | Jan 31, 2023 | 34.24% | 6.18% | 1,182.30 | 27.91 | 181.65 |
| 62. | Feb 28, 2023 | -1.85% | -2.61% | 2.91 | 12.28 | 5.98 |
| 63. | Mar 31, 2023 | -4.43% | 3.51% | 18.35 | 6.83 | -11.19 |
| 64. | Apr 30, 2023 | -9.26% | 1.46% | 83.17 | 0.33 | -5.21 |
| 65. | May 31, 2023 | 21.93% | 0.25% | 487.26 | 0.42 | -14.22 |
| 66. | Jun 30, 2023 | 67.68% | 4.71% | 4,599.18 | 14.60 | 259.15 |
| 67. | Jul 31, 2023 | 0.05% | 4.85% | 0.04 | 15.63 | 0.77 |
| 68. | Aug 31, 2023 | -16.03% | -1.77% | 252.44 | 7.10 | 42.33 |
| 69. | Sep 30, 2023 | -13.27% | -4.87% | 172.47 | 33.23 | 75.70 |
| 70. | Oct 31, 2023 | -16.47% | -2.20% | 266.70 | 9.55 | 50.47 |
| 71. | Nov 30, 2023 | 31.41% | 8.92% | 995.72 | 64.41 | 253.24 |
| Total (Σ): | 24,858.07 | 1,909.09 | 4,523.25 | |||
Show all
VarianceCCL = Σ(RCCL,t–RCCL)2 ÷ (71 – 1)
= 24,858.07 ÷ (71 – 1)
= 355.12
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,909.09 ÷ (71 – 1)
= 27.27
CovarianceCCL, S&P 500 = Σ(RCCL,t–RCCL)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 4,523.25 ÷ (71 – 1)
= 64.62
Systematic Risk (β) Estimation
| VarianceCCL | 355.12 |
| VarianceS&P 500 | 27.27 |
| CovarianceCCL, S&P 500 | 64.62 |
| Correlation coefficientCCL, S&P 5001 | 0.66 |
| βCCL2 | 2.37 |
| αCCL3 | -2.26% |
Calculations
1 Correlation coefficientCCL, S&P 500
= CovarianceCCL, S&P 500 ÷ (Standard deviationCCL × Standard deviationS&P 500)
= 64.62 ÷ (18.84% × 5.22%)
= 0.66
2 βCCL
= CovarianceCCL, S&P 500 ÷ VarianceS&P 500
= 64.62 ÷ 27.27
= 2.37
3 αCCL
= AverageCCL – βCCL × AverageS&P 500
= -0.14% – 2.37 × 0.89%
= -2.26%
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 Carnival Corp. & plc common stock | βCCL | 2.37 |
| Expected rate of return on Carnival Corp. & plc common stock3 | E(RCCL) | 25.32% |
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(RCCL) = RF + βCCL [E(RM) – RF]
= 4.83% + 2.37 [13.48% – 4.83%]
= 25.32%