Microsoft Excel LibreOffice Calc

Marriott International Inc. (MAR)


Capital Asset Pricing Model (CAPM)

Difficulty: Intermediate

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Marriott International Inc.’s common stock.


Rates of Return

Marriott International Inc., monthly rates of return

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Marriott International Inc. (MAR) Standard & Poor’s 500 (S&P 500)
t Date PriceMAR,t1 DividendMAR,t1 RMAR,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 49.30 1,782.59
1. Feb 28, 2014 54.23 0.17 10.34% 1,859.45 4.31%
2. Mar 31, 2014 56.02 3.30% 1,872.34 0.69%
3. Apr 30, 2014 57.93 3.41% 1,883.95 0.62%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2018 115.03 0.41 -1.24% 2,760.17 1.79%
59. Dec 31, 2018 108.56 -5.62% 2,506.85 -9.18%
Average: 1.64% 0.63%
Standard Deviation: 6.07% 3.13%
Marriott International Inc. (MAR) Standard & Poor’s 500 (S&P 500)
t Date PriceMAR,t1 DividendMAR,t1 RMAR,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 49.30 1,782.59
1. Feb 28, 2014 54.23 0.17 10.34% 1,859.45 4.31%
2. Mar 31, 2014 56.02 3.30% 1,872.34 0.69%
3. Apr 30, 2014 57.93 3.41% 1,883.95 0.62%
4. May 31, 2014 61.62 0.20 6.72% 1,923.57 2.10%
5. Jun 30, 2014 64.10 4.02% 1,960.23 1.91%
6. Jul 31, 2014 64.71 0.95% 1,930.67 -1.51%
7. Aug 31, 2014 69.40 0.20 7.56% 2,003.37 3.77%
8. Sep 30, 2014 69.90 0.72% 1,972.29 -1.55%
9. Oct 31, 2014 75.75 8.37% 2,018.05 2.32%
10. Nov 30, 2014 78.79 0.20 4.28% 2,067.56 2.45%
11. Dec 31, 2014 78.03 -0.96% 2,058.90 -0.42%
12. Jan 31, 2015 74.50 -4.52% 1,994.99 -3.10%
13. Feb 28, 2015 83.10 0.20 11.81% 2,104.50 5.49%
14. Mar 31, 2015 80.32 -3.35% 2,067.89 -1.74%
15. Apr 30, 2015 80.05 -0.34% 2,085.51 0.85%
16. May 31, 2015 77.99 0.25 -2.26% 2,107.39 1.05%
17. Jun 30, 2015 74.39 -4.62% 2,063.11 -2.10%
18. Jul 31, 2015 72.61 -2.39% 2,103.84 1.97%
19. Aug 31, 2015 70.66 0.25 -2.34% 1,972.18 -6.26%
20. Sep 30, 2015 68.20 -3.48% 1,920.03 -2.64%
21. Oct 31, 2015 76.78 12.58% 2,079.36 8.30%
22. Nov 30, 2015 70.91 0.25 -7.32% 2,080.41 0.05%
23. Dec 31, 2015 67.04 -5.46% 2,043.94 -1.75%
24. Jan 31, 2016 61.28 -8.59% 1,940.24 -5.07%
25. Feb 29, 2016 68.15 0.25 11.62% 1,932.23 -0.41%
26. Mar 31, 2016 71.18 4.45% 2,059.74 6.60%
27. Apr 30, 2016 70.09 -1.53% 2,065.30 0.27%
28. May 31, 2016 66.04 0.30 -5.35% 2,096.95 1.53%
29. Jun 30, 2016 66.46 0.64% 2,098.86 0.09%
30. Jul 31, 2016 71.70 7.88% 2,173.60 3.56%
31. Aug 31, 2016 71.33 -0.52% 2,170.95 -0.12%
32. Sep 30, 2016 67.33 0.30 -5.19% 2,168.27 -0.12%
33. Oct 31, 2016 68.70 2.03% 2,126.15 -1.94%
34. Nov 30, 2016 78.78 0.30 15.11% 2,198.81 3.42%
35. Dec 31, 2016 82.68 4.95% 2,238.83 1.82%
36. Jan 31, 2017 84.60 2.32% 2,278.87 1.79%
37. Feb 28, 2017 86.99 0.30 3.18% 2,363.64 3.72%
38. Mar 31, 2017 94.18 8.27% 2,362.72 -0.04%
39. Apr 30, 2017 94.42 0.25% 2,384.20 0.91%
40. May 31, 2017 107.65 0.33 14.36% 2,411.80 1.16%
41. Jun 30, 2017 100.31 -6.82% 2,423.41 0.48%
42. Jul 31, 2017 104.19 3.87% 2,470.30 1.93%
43. Aug 31, 2017 103.58 0.33 -0.27% 2,471.65 0.05%
44. Sep 30, 2017 110.26 6.45% 2,519.36 1.93%
45. Oct 31, 2017 119.48 8.36% 2,575.26 2.22%
46. Nov 30, 2017 127.00 0.33 6.57% 2,647.58 2.81%
47. Dec 31, 2017 135.73 6.87% 2,673.61 0.98%
48. Jan 31, 2018 147.34 8.55% 2,823.81 5.62%
49. Feb 28, 2018 141.21 0.33 -3.94% 2,713.83 -3.89%
50. Mar 31, 2018 135.98 -3.70% 2,640.87 -2.69%
51. Apr 30, 2018 136.68 0.51% 2,648.05 0.27%
52. May 31, 2018 135.36 0.41 -0.67% 2,705.27 2.16%
53. Jun 30, 2018 126.60 -6.47% 2,718.37 0.48%
54. Jul 31, 2018 127.84 0.98% 2,816.29 3.60%
55. Aug 31, 2018 126.47 0.41 -0.75% 2,901.52 3.03%
56. Sep 30, 2018 132.03 4.40% 2,913.98 0.43%
57. Oct 31, 2018 116.89 -11.47% 2,711.74 -6.94%
58. Nov 30, 2018 115.03 0.41 -1.24% 2,760.17 1.79%
59. Dec 31, 2018 108.56 -5.62% 2,506.85 -9.18%
Average: 1.64% 0.63%
Standard Deviation: 6.07% 3.13%

Show All

1 Data in USD $ per share of common stock, adjusted for splits and stock dividends.

2 Rate of return on common stock of MAR during period t

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


Systematic Risk (β) Estimation

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VarianceMAR 36.79
VarianceS&P 500 9.77
CovarianceMAR, S&P 500 12.58
Correlation CoefficientMAR, S&P 5001 0.66
βMAR2 1.29
αMAR3 0.83

Calculations

1 CovarianceMAR, S&P 500 ÷ (Standard DeviationMAR × Standard DeviationS&P 500)
= 12.58 ÷ (6.07 × 3.13)

2 CovarianceMAR, S&P 500 ÷ VarianceS&P 500
= 12.58 ÷ 9.77

3 AverageMAR – βMAR × AverageS&P 500
= 1.641.29 × 0.63


Expected Rate of Return

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Assumptions
Rate of return on LT Treasury Composite1 RF 2.72%
Expected rate of return on market portfolio2 E(RM) 11.99%
Systematic risk (β) of Marriott International Inc.’s common stock βMAR 1.29
Expected rate of return on Marriott International Inc.’s common stock3 E(RMAR) 14.67%

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).

Calculations

2 See Details »

3 E(RMAR) = RF + βMAR [E(RM) – RF]
= 2.72% + 1.29 [11.99%2.72%]
= 14.67%