Stock Analysis on Net

Apple Inc. (NASDAQ:AAPL)

자본 자산 가격 책정 모델 (CAPM) 

Microsoft Excel

자본 자산 가격 책정 모델(CAPM)은 Apple보통주와 같은 위험 자산에 대한 예상 또는 필요한 수익률을 나타냅니다.


수익률

Apple Inc., 월별 수익률

Microsoft Excel
Apple Inc. (AAPL) Standard & Poor’s 500 (S&P 500)
t 날짜 AAPL,t1 피제수AAPL,t1 RAAPL,t2 S&P 500,t RS&P 500,t3
2017. 10. 31. $42.26 2,575.26
1. 2017. 11. 30. $42.96 $0.1575 2.03% 2,647.58 2.81%
2. 2017. 12. 31. $42.31 -1.51% 2,673.61 0.98%
3. 2018. 1. 31. $41.86 -1.06% 2,823.81 5.62%
. . . . . . .
. . . . . . .
. . . . . . .
70. 2023. 8. 31. $187.87 $0.24 -4.25% 4,507.66 -1.77%
71. 2023. 9. 30. $171.21 -8.87% 4,288.05 -4.87%
평균의 (R): 2.46% 0.85%
표준 편차: 8.90% 5.13%
Apple Inc. (AAPL) Standard & Poor’s 500 (S&P 500)
t 날짜 AAPL,t1 피제수AAPL,t1 RAAPL,t2 S&P 500,t RS&P 500,t3
2017. 10. 31. $42.26 2,575.26
1. 2017. 11. 30. $42.96 $0.1575 2.03% 2,647.58 2.81%
2. 2017. 12. 31. $42.31 -1.51% 2,673.61 0.98%
3. 2018. 1. 31. $41.86 -1.06% 2,823.81 5.62%
4. 2018. 2. 28. $44.53 $0.1575 6.75% 2,713.83 -3.89%
5. 2018. 3. 31. $41.95 -5.79% 2,640.87 -2.69%
6. 2018. 4. 30. $41.32 -1.50% 2,648.05 0.27%
7. 2018. 5. 31. $46.72 $0.1825 13.51% 2,705.27 2.16%
8. 2018. 6. 30. $46.28 -0.94% 2,718.37 0.48%
9. 2018. 7. 31. $47.57 2.79% 2,816.29 3.60%
10. 2018. 8. 31. $56.91 $0.1825 20.02% 2,901.52 3.03%
11. 2018. 9. 30. $56.44 -0.83% 2,913.98 0.43%
12. 2018. 10. 31. $54.72 -3.05% 2,711.74 -6.94%
13. 2018. 11. 30. $44.65 $0.1825 -18.07% 2,760.17 1.79%
14. 2018. 12. 31. $39.44 -11.67% 2,506.85 -9.18%
15. 2019. 1. 31. $41.61 5.50% 2,704.10 7.87%
16. 2019. 2. 28. $43.29 $0.1825 4.48% 2,784.49 2.97%
17. 2019. 3. 31. $47.49 9.70% 2,834.40 1.79%
18. 2019. 4. 30. $50.17 5.64% 2,945.83 3.93%
19. 2019. 5. 31. $43.77 $0.1925 -12.37% 2,752.06 -6.58%
20. 2019. 6. 30. $49.48 13.05% 2,941.76 6.89%
21. 2019. 7. 31. $53.26 7.64% 2,980.38 1.31%
22. 2019. 8. 31. $52.19 $0.1925 -1.65% 2,926.46 -1.81%
23. 2019. 9. 30. $55.99 7.28% 2,976.74 1.72%
24. 2019. 10. 31. $62.19 11.07% 3,037.56 2.04%
25. 2019. 11. 30. $66.81 $0.1925 7.74% 3,140.98 3.40%
26. 2019. 12. 31. $73.41 9.88% 3,230.78 2.86%
27. 2020. 1. 31. $77.38 5.41% 3,225.52 -0.16%
28. 2020. 2. 29. $68.34 $0.1925 -11.43% 2,954.22 -8.41%
29. 2020. 3. 31. $63.57 -6.98% 2,584.59 -12.51%
30. 2020. 4. 30. $73.45 15.54% 2,912.43 12.68%
31. 2020. 5. 31. $79.49 $0.205 8.50% 3,044.31 4.53%
32. 2020. 6. 30. $91.20 14.73% 3,100.29 1.84%
33. 2020. 7. 31. $106.26 16.51% 3,271.12 5.51%
34. 2020. 8. 31. $129.04 $0.205 21.63% 3,500.31 7.01%
35. 2020. 9. 30. $115.81 -10.25% 3,363.00 -3.92%
36. 2020. 10. 31. $108.86 -6.00% 3,269.96 -2.77%
37. 2020. 11. 30. $119.05 $0.205 9.55% 3,621.63 10.75%
38. 2020. 12. 31. $132.69 11.46% 3,756.07 3.71%
39. 2021. 1. 31. $131.96 -0.55% 3,714.24 -1.11%
40. 2021. 2. 28. $121.26 $0.205 -7.95% 3,811.15 2.61%
41. 2021. 3. 31. $122.15 0.73% 3,972.89 4.24%
42. 2021. 4. 30. $131.46 7.62% 4,181.17 5.24%
43. 2021. 5. 31. $124.61 $0.22 -5.04% 4,204.11 0.55%
44. 2021. 6. 30. $136.96 9.91% 4,297.50 2.22%
45. 2021. 7. 31. $145.86 6.50% 4,395.26 2.27%
46. 2021. 8. 31. $151.83 $0.22 4.24% 4,522.68 2.90%
47. 2021. 9. 30. $141.50 -6.80% 4,307.54 -4.76%
48. 2021. 10. 31. $149.80 5.87% 4,605.38 6.91%
49. 2021. 11. 30. $165.30 $0.22 10.49% 4,567.00 -0.83%
50. 2021. 12. 31. $177.57 7.42% 4,766.18 4.36%
51. 2022. 1. 31. $174.78 -1.57% 4,515.55 -5.26%
52. 2022. 2. 28. $165.12 $0.22 -5.40% 4,373.94 -3.14%
53. 2022. 3. 31. $174.61 5.75% 4,530.41 3.58%
54. 2022. 4. 30. $157.65 -9.71% 4,131.93 -8.80%
55. 2022. 5. 31. $148.84 $0.23 -5.44% 4,132.15 0.01%
56. 2022. 6. 30. $136.72 -8.14% 3,785.38 -8.39%
57. 2022. 7. 31. $162.51 18.86% 4,130.29 9.11%
58. 2022. 8. 31. $157.22 $0.23 -3.11% 3,955.00 -4.24%
59. 2022. 9. 30. $138.20 -12.10% 3,585.62 -9.34%
60. 2022. 10. 31. $153.34 10.96% 3,871.98 7.99%
61. 2022. 11. 30. $148.03 $0.23 -3.31% 4,080.11 5.38%
62. 2022. 12. 31. $129.93 -12.23% 3,839.50 -5.90%
63. 2023. 1. 31. $144.29 11.05% 4,076.60 6.18%
64. 2023. 2. 28. $147.41 $0.23 2.32% 3,970.15 -2.61%
65. 2023. 3. 31. $164.90 11.86% 4,109.31 3.51%
66. 2023. 4. 30. $169.68 2.90% 4,169.48 1.46%
67. 2023. 5. 31. $177.25 $0.24 4.60% 4,179.83 0.25%
68. 2023. 6. 30. $193.97 9.43% 4,376.86 4.71%
69. 2023. 7. 31. $196.45 1.28% 4,588.96 4.85%
70. 2023. 8. 31. $187.87 $0.24 -4.25% 4,507.66 -1.77%
71. 2023. 9. 30. $171.21 -8.87% 4,288.05 -4.87%
평균의 (R): 2.46% 0.85%
표준 편차: 8.90% 5.13%

모두 표시

1 보통주 주당 US$ 단위의 데이터로, 분할 및 주식 배당금에 맞게 조정됩니다.

2 기간 t 동안 AAPL의 보통주에 대한 수익률.

3 기간 t 동안 S&P 500(시장 포트폴리오 프록시)에 대한 수익률.


분산과 공분산

Apple Inc., 수익률의 분산 및 공분산 계산

Microsoft Excel
t 날짜 RAAPL,t RS&P 500,t (RAAPL,tRAAPL)2 (RS&P 500,tRS&P 500)2 (RAAPL,tRAAPL)×(RS&P 500,tRS&P 500)
1. 2017. 11. 30. 2.03% 2.81% 0.19 3.83 -0.84
2. 2017. 12. 31. -1.51% 0.98% 15.78 0.02 -0.52
3. 2018. 1. 31. -1.06% 5.62% 12.41 22.72 -16.79
. . . . . . .
. . . . . . .
. . . . . . .
70. 2023. 8. 31. -4.25% -1.77% 44.95 6.88 17.59
71. 2023. 9. 30. -8.87% -4.87% 128.31 32.75 64.83
합계 (Σ): 5,545.99 1,838.69 2,309.32
t 날짜 RAAPL,t RS&P 500,t (RAAPL,tRAAPL)2 (RS&P 500,tRS&P 500)2 (RAAPL,tRAAPL)×(RS&P 500,tRS&P 500)
1. 2017. 11. 30. 2.03% 2.81% 0.19 3.83 -0.84
2. 2017. 12. 31. -1.51% 0.98% 15.78 0.02 -0.52
3. 2018. 1. 31. -1.06% 5.62% 12.41 22.72 -16.79
4. 2018. 2. 28. 6.75% -3.89% 18.45 22.52 -20.38
5. 2018. 3. 31. -5.79% -2.69% 68.12 12.53 29.21
6. 2018. 4. 30. -1.50% 0.27% 15.69 0.34 2.30
7. 2018. 5. 31. 13.51% 2.16% 122.12 1.71 14.47
8. 2018. 6. 30. -0.94% 0.48% 11.57 0.13 1.25
9. 2018. 7. 31. 2.79% 3.60% 0.11 7.57 0.90
10. 2018. 8. 31. 20.02% 3.03% 308.30 4.73 38.19
11. 2018. 9. 30. -0.83% 0.43% 10.79 0.18 1.39
12. 2018. 10. 31. -3.05% -6.94% 30.33 60.71 42.91
13. 2018. 11. 30. -18.07% 1.79% 421.43 0.87 -19.19
14. 2018. 12. 31. -11.67% -9.18% 199.60 100.58 141.69
15. 2019. 1. 31. 5.50% 7.87% 9.26 49.24 21.35
16. 2019. 2. 28. 4.48% 2.97% 4.07 4.50 4.28
17. 2019. 3. 31. 9.70% 1.79% 52.45 0.89 6.82
18. 2019. 4. 30. 5.64% 3.93% 10.14 9.49 9.81
19. 2019. 5. 31. -12.37% -6.58% 220.00 55.19 110.19
20. 2019. 6. 30. 13.05% 6.89% 112.06 36.50 63.96
21. 2019. 7. 31. 7.64% 1.31% 26.83 0.21 2.39
22. 2019. 8. 31. -1.65% -1.81% 16.87 7.08 10.93
23. 2019. 9. 30. 7.28% 1.72% 23.25 0.75 4.18
24. 2019. 10. 31. 11.07% 2.04% 74.20 1.42 10.27
25. 2019. 11. 30. 7.74% 3.40% 27.87 6.52 13.48
26. 2019. 12. 31. 9.88% 2.86% 55.05 4.03 14.90
27. 2020. 1. 31. 5.41% -0.16% 8.69 1.03 -2.99
28. 2020. 2. 29. -11.43% -8.41% 193.02 85.79 128.68
29. 2020. 3. 31. -6.98% -12.51% 89.10 178.57 126.14
30. 2020. 4. 30. 15.54% 12.68% 171.15 140.02 154.81
31. 2020. 5. 31. 8.50% 4.53% 36.52 13.52 22.22
32. 2020. 6. 30. 14.73% 1.84% 150.60 0.98 12.12
33. 2020. 7. 31. 16.51% 5.51% 197.51 21.71 65.47
34. 2020. 8. 31. 21.63% 7.01% 367.54 37.89 118.00
35. 2020. 9. 30. -10.25% -3.92% 161.60 22.79 60.69
36. 2020. 10. 31. -6.00% -2.77% 71.58 13.09 30.61
37. 2020. 11. 30. 9.55% 10.75% 50.26 98.08 70.21
38. 2020. 12. 31. 11.46% 3.71% 80.96 8.18 25.74
39. 2021. 1. 31. -0.55% -1.11% 9.06 3.86 5.91
40. 2021. 2. 28. -7.95% 2.61% 108.42 3.09 -18.30
41. 2021. 3. 31. 0.73% 4.24% 2.98 11.51 -5.85
42. 2021. 4. 30. 7.62% 5.24% 26.65 19.28 22.67
43. 2021. 5. 31. -5.04% 0.55% 56.29 0.09 2.27
44. 2021. 6. 30. 9.91% 2.22% 55.52 1.88 10.21
45. 2021. 7. 31. 6.50% 2.27% 16.31 2.03 5.75
46. 2021. 8. 31. 4.24% 2.90% 3.18 4.19 3.65
47. 2021. 9. 30. -6.80% -4.76% 85.81 31.45 51.95
48. 2021. 10. 31. 5.87% 6.91% 11.60 36.76 20.65
49. 2021. 11. 30. 10.49% -0.83% 64.55 2.84 -13.54
50. 2021. 12. 31. 7.42% 4.36% 24.64 12.32 17.42
51. 2022. 1. 31. -1.57% -5.26% 16.25 37.33 24.63
52. 2022. 2. 28. -5.40% -3.14% 61.79 15.90 31.34
53. 2022. 3. 31. 5.75% 3.58% 10.81 7.43 8.96
54. 2022. 4. 30. -9.71% -8.80% 148.17 93.06 117.43
55. 2022. 5. 31. -5.44% 0.01% 62.44 0.72 6.68
56. 2022. 6. 30. -8.14% -8.39% 112.41 85.44 98.00
57. 2022. 7. 31. 18.86% 9.11% 269.09 68.23 135.50
58. 2022. 8. 31. -3.11% -4.24% 31.06 25.96 28.40
59. 2022. 9. 30. -12.10% -9.34% 211.91 103.85 148.35
60. 2022. 10. 31. 10.96% 7.99% 72.18 50.91 60.62
61. 2022. 11. 30. -3.31% 5.38% 33.32 20.47 -26.11
62. 2022. 12. 31. -12.23% -5.90% 215.70 45.54 99.11
63. 2023. 1. 31. 11.05% 6.18% 73.83 28.35 45.75
64. 2023. 2. 28. 2.32% -2.61% 0.02 11.99 0.48
65. 2023. 3. 31. 11.86% 3.51% 88.46 7.04 24.96
66. 2023. 4. 30. 2.90% 1.46% 0.19 0.38 0.27
67. 2023. 5. 31. 4.60% 0.25% 4.59 0.36 -1.29
68. 2023. 6. 30. 9.43% 4.71% 48.63 14.92 26.94
69. 2023. 7. 31. 1.28% 4.85% 1.39 15.96 -4.72
70. 2023. 8. 31. -4.25% -1.77% 44.95 6.88 17.59
71. 2023. 9. 30. -8.87% -4.87% 128.31 32.75 64.83
합계 (Σ): 5,545.99 1,838.69 2,309.32

모두 표시

분산AAPL = Σ(RAAPL,tRAAPL)2 ÷ (71 – 1)
= 5,545.99 ÷ (71 – 1)
= 79.23

분산S&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (71 – 1)
= 1,838.69 ÷ (71 – 1)
= 26.27

공분산AAPL, S&P 500 = Σ(RAAPL,tRAAPL)×(RS&P 500,tRS&P 500) ÷ (71 – 1)
= 2,309.32 ÷ (71 – 1)
= 32.99


체계적인 위험 추정 (β)

Microsoft Excel
분산AAPL 79.23
분산S&P 500 26.27
공분산AAPL, S&P 500 32.99
상관 계수AAPL, S&P 5001 0.72
βAAPL2 1.26
αAAPL3 1.39%

계산

1 상관 계수AAPL, S&P 500
= 공분산AAPL, S&P 500 ÷ (표준 편차AAPL × 표준 편차S&P 500)
= 32.99 ÷ (8.90% × 5.13%)
= 0.72

2 βAAPL
= 공분산AAPL, S&P 500 ÷ 분산S&P 500
= 32.99 ÷ 26.27
= 1.26

3 αAAPL
= 평균의AAPL – βAAPL × 평균의S&P 500
= 2.46%1.26 × 0.85%
= 1.39%


예상 수익률

Microsoft Excel
가정
LT Treasury Composite의 수익률1 RF 4.43%
시장 포트폴리오에 대한 예상 수익률2 E(RM) 13.83%
보통주의 체계적 위험Apple βAAPL 1.26
 
Apple 보통주 예상 수익률3 E(RAAPL) 16.24%

1 10년 이내에 만기가 되지 않거나 콜 가능하지 않은 모든 미결제 고정 쿠폰 미국 재무부 채권에 대한 입찰 수익률의 가중 평균(무위험 수익률 프록시).

2 자세히 보기 »

3 E(RAAPL) = RF + βAAPL [E(RM) – RF]
= 4.43% + 1.26 [13.83%4.43%]
= 16.24%