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 Delta's common stock.


Rates of Return

Delta Air Lines Inc., monthly rates of return

 
Delta Air Lines Inc. (DAL) Standard & Poor's 500 (S&P 500)
t Date PriceDAL,t1 DividendDAL,t1 RDAL,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2013 13.89 1,498.11
1. Feb 28, 2013 14.27 2.74% 1,514.68 1.11%
2. Mar 31, 2013 16.51 15.70% 1,569.19 3.60%
3. Apr 30, 2013 17.14 3.82% 1,597.57 1.81%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2017 52.92 0.305 6.39% 2,647.58 2.81%
59. Dec 31, 2017 56.00 5.82% 2,673.61 0.98%
Average: 2.80% 1.02%
Standard Deviation: 7.97% 2.71%
Delta Air Lines Inc. (DAL) Standard & Poor's 500 (S&P 500)
t Date PriceDAL,t1 DividendDAL,t1 RDAL,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2013 13.89 1,498.11
1. Feb 28, 2013 14.27 2.74% 1,514.68 1.11%
2. Mar 31, 2013 16.51 15.70% 1,569.19 3.60%
3. Apr 30, 2013 17.14 3.82% 1,597.57 1.81%
4. May 31, 2013 18.01 5.08% 1,630.74 2.08%
5. Jun 30, 2013 18.71 3.89% 1,606.28 -1.50%
6. Jul 31, 2013 21.23 13.47% 1,685.73 4.95%
7. Aug 31, 2013 19.73 0.06 -6.78% 1,632.97 -3.13%
8. Sep 30, 2013 23.59 19.56% 1,681.55 2.97%
9. Oct 31, 2013 26.38 11.83% 1,756.54 4.46%
10. Nov 30, 2013 28.98 0.06 10.08% 1,805.81 2.80%
11. Dec 31, 2013 27.47 -5.21% 1,848.36 2.36%
12. Jan 31, 2014 30.61 11.43% 1,782.59 -3.56%
13. Feb 28, 2014 33.21 0.06 8.69% 1,859.45 4.31%
14. Mar 31, 2014 34.65 4.34% 1,872.34 0.69%
15. Apr 30, 2014 36.83 6.29% 1,883.95 0.62%
16. May 31, 2014 39.91 0.06 8.53% 1,923.57 2.10%
17. Jun 30, 2014 38.72 -2.98% 1,960.23 1.91%
18. Jul 31, 2014 37.46 -3.25% 1,930.67 -1.51%
19. Aug 31, 2014 39.58 0.09 5.90% 2,003.37 3.77%
20. Sep 30, 2014 36.15 -8.67% 1,972.29 -1.55%
21. Oct 31, 2014 40.23 11.29% 2,018.05 2.32%
22. Nov 30, 2014 46.67 0.09 16.23% 2,067.56 2.45%
23. Dec 31, 2014 49.19 5.40% 2,058.90 -0.42%
24. Jan 31, 2015 47.31 -3.82% 1,994.99 -3.10%
25. Feb 28, 2015 44.52 0.09 -5.71% 2,104.50 5.49%
26. Mar 31, 2015 44.96 0.99% 2,067.89 -1.74%
27. Apr 30, 2015 44.64 -0.71% 2,085.51 0.85%
28. May 31, 2015 42.92 0.09 -3.65% 2,107.39 1.05%
29. Jun 30, 2015 41.08 -4.29% 2,063.11 -2.10%
30. Jul 31, 2015 44.34 7.94% 2,103.84 1.97%
31. Aug 31, 2015 43.78 0.135 -0.96% 1,972.18 -6.26%
32. Sep 30, 2015 44.87 2.49% 1,920.03 -2.64%
33. Oct 31, 2015 50.84 13.31% 2,079.36 8.30%
34. Nov 30, 2015 46.46 0.135 -8.35% 2,080.41 0.05%
35. Dec 31, 2015 50.69 9.10% 2,043.94 -1.75%
36. Jan 31, 2016 44.29 -12.63% 1,940.24 -5.07%
37. Feb 29, 2016 48.24 0.135 9.22% 1,932.23 -0.41%
38. Mar 31, 2016 48.68 0.91% 2,059.74 6.60%
39. Apr 30, 2016 41.67 -14.40% 2,065.30 0.27%
40. May 31, 2016 43.46 0.135 4.62% 2,096.95 1.53%
41. Jun 30, 2016 36.43 -16.18% 2,098.86 0.09%
42. Jul 31, 2016 38.75 6.37% 2,173.60 3.56%
43. Aug 31, 2016 36.75 0.2025 -4.64% 2,170.95 -0.12%
44. Sep 30, 2016 39.36 7.10% 2,168.27 -0.12%
45. Oct 31, 2016 41.77 6.12% 2,126.15 -1.94%
46. Nov 30, 2016 48.18 0.2025 15.83% 2,198.81 3.42%
47. Dec 31, 2016 49.19 2.10% 2,238.83 1.82%
48. Jan 31, 2017 47.24 -3.96% 2,278.87 1.79%
49. Feb 28, 2017 49.93 0.2025 6.12% 2,363.64 3.72%
50. Mar 31, 2017 45.96 -7.95% 2,362.72 -0.04%
51. Apr 30, 2017 45.44 -1.13% 2,384.20 0.91%
52. May 31, 2017 49.13 0.2025 8.57% 2,411.80 1.16%
53. Jun 30, 2017 53.74 9.38% 2,423.41 0.48%
54. Jul 31, 2017 49.36 -8.15% 2,470.30 1.93%
55. Aug 31, 2017 47.19 0.305 -3.78% 2,471.65 0.05%
56. Sep 30, 2017 48.22 2.18% 2,519.36 1.93%
57. Oct 31, 2017 50.03 3.75% 2,575.26 2.22%
58. Nov 30, 2017 52.92 0.305 6.39% 2,647.58 2.81%
59. Dec 31, 2017 56.00 5.82% 2,673.61 0.98%
Average: 2.80% 1.02%
Standard Deviation: 7.97% 2.71%

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

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

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

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Systematic Risk (β) Estimation

 
VarianceDAL 63.54
VarianceS&P 500 7.32
CovarianceDAL, S&P 500 8.89
Correlation CoefficientDAL, S&P 5001 0.41
βDAL2 1.21
αDAL3 1.56

Calculations

1 CovarianceDAL, S&P 500 ÷ (Standard DeviationDAL × Standard DeviationS&P 500)
= 8.89 ÷ (7.97 × 2.71)

2 CovarianceDAL, S&P 500 ÷ VarianceS&P 500
= 8.89 ÷ 7.32

3 AverageDAL – βDAL × AverageS&P 500
= 2.80 – 1.21 × 1.02

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Expected Rate of Return

 
Assumptions
Rate of return on LT Treasury Composite1 RF 3.17%
Expected rate of return on market portfolio2 E(RM) 12.48%
Systematic risk (β) of Delta's common stock βDAL 1.21
Expected rate of return on Delta's common stock3 E(RDAL) 14.48%

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(RDAL) = RF + βDAL [E(RM) – RF]
= 3.17% + 1.21 [12.48% – 3.17%]
= 14.48%

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