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

수익률
분산과 공분산
체계적인 위험 추정 (β)
기대 수익률

Carrier Global Corp., 월별 수익률

		Carrier Global Corp. (CARR)			Standard & Poor’s 500 (S&P 500)
t	날짜	값_CARR,t¹	피제수_CARR,t¹	R_CARR,t²	값_{S&P 500,t}	R_{S&P 500,t}³
	2020. 3. 31.	$17.25			2,584.59
1.	2020. 4. 30.	$17.71		2.67%	2,912.43	12.68%
2.	2020. 5. 31.	$20.47		15.58%	3,044.31	4.53%
3.	2020. 6. 30.	$22.22	$0.08	8.94%	3,100.29	1.84%
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32.	2022. 11. 30.	$44.32		11.47%	4,080.11	5.38%
33.	2022. 12. 31.	$41.25	$0.185	-6.51%	3,839.50	-5.90%
평균의 (R):				3.19%		1.36%
표준 편차:				9.19%		5.68%

		Carrier Global Corp. (CARR)			Standard & Poor’s 500 (S&P 500)
t	날짜	값_CARR,t¹	피제수_CARR,t¹	R_CARR,t²	값_{S&P 500,t}	R_{S&P 500,t}³
	2020. 3. 31.	$17.25			2,584.59
1.	2020. 4. 30.	$17.71		2.67%	2,912.43	12.68%
2.	2020. 5. 31.	$20.47		15.58%	3,044.31	4.53%
3.	2020. 6. 30.	$22.22	$0.08	8.94%	3,100.29	1.84%
4.	2020. 7. 31.	$27.24		22.59%	3,271.12	5.51%
5.	2020. 8. 31.	$29.85		9.58%	3,500.31	7.01%
6.	2020. 9. 30.	$30.54		2.31%	3,363.00	-3.92%
7.	2020. 10. 31.	$33.39	$0.08	9.59%	3,269.96	-2.77%
8.	2020. 11. 30.	$38.07		14.02%	3,621.63	10.75%
9.	2020. 12. 31.	$37.72	$0.12	-0.60%	3,756.07	3.71%
10.	2021. 1. 31.	$38.50		2.07%	3,714.24	-1.11%
11.	2021. 2. 28.	$36.53		-5.12%	3,811.15	2.61%
12.	2021. 3. 31.	$42.22		15.58%	3,972.89	4.24%
13.	2021. 4. 30.	$43.58	$0.12	3.51%	4,181.17	5.24%
14.	2021. 5. 31.	$45.93		5.39%	4,204.11	0.55%
15.	2021. 6. 30.	$48.60	$0.12	6.07%	4,297.50	2.22%
16.	2021. 7. 31.	$55.25		13.68%	4,395.26	2.27%
17.	2021. 8. 31.	$57.60		4.25%	4,522.68	2.90%
18.	2021. 9. 30.	$51.76		-10.14%	4,307.54	-4.76%
19.	2021. 10. 31.	$52.23	$0.12	1.14%	4,605.38	6.91%
20.	2021. 11. 30.	$54.12		3.62%	4,567.00	-0.83%
21.	2021. 12. 31.	$54.24	$0.15	0.50%	4,766.18	4.36%
22.	2022. 1. 31.	$47.68		-12.09%	4,515.55	-5.26%
23.	2022. 2. 28.	$44.88		-5.87%	4,373.94	-3.14%
24.	2022. 3. 31.	$45.87		2.21%	4,530.41	3.58%
25.	2022. 4. 30.	$38.27	$0.15	-16.24%	4,131.93	-8.80%
26.	2022. 5. 31.	$39.31		2.72%	4,132.15	0.01%
27.	2022. 6. 30.	$35.66	$0.15	-8.90%	3,785.38	-8.39%
28.	2022. 7. 31.	$40.53		13.66%	4,130.29	9.11%
29.	2022. 8. 31.	$39.12		-3.48%	3,955.00	-4.24%
30.	2022. 9. 30.	$35.56		-9.10%	3,585.62	-9.34%
31.	2022. 10. 31.	$39.76	$0.15	12.23%	3,871.98	7.99%
32.	2022. 11. 30.	$44.32		11.47%	4,080.11	5.38%
33.	2022. 12. 31.	$41.25	$0.185	-6.51%	3,839.50	-5.90%
평균의 (R):				3.19%		1.36%
표준 편차:				9.19%		5.68%

모두 보기

¹ 보통주 주당 미화 달러(USD)로 표시되며, 분할 및 주식 배당금에 대해 조정되었습니다.

² 기간 t 동안 CARR의 보통주 수익률.

³ 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.

Carrier Global Corp., 수익률의 분산 및 공분산 계산

t	날짜	R_CARR,t	R_{S&P 500,t}	(R_CARR,t–R_CARR)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_CARR,t–R_CARR)×(R_{S&P 500,t}–R_{S&P 500})
1.	2020. 4. 30.	2.67%	12.68%	0.28	128.19	-5.94
2.	2020. 5. 31.	15.58%	4.53%	153.59	10.02	39.24
3.	2020. 6. 30.	8.94%	1.84%	33.04	0.23	2.74
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32.	2022. 11. 30.	11.47%	5.38%	68.51	16.11	33.22
33.	2022. 12. 31.	-6.51%	-5.90%	94.11	52.70	70.42
합계 (Σ):				2,705.36	1,031.79	1,195.31

t	날짜	R_CARR,t	R_{S&P 500,t}	(R_CARR,t–R_CARR)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_CARR,t–R_CARR)×(R_{S&P 500,t}–R_{S&P 500})
1.	2020. 4. 30.	2.67%	12.68%	0.28	128.19	-5.94
2.	2020. 5. 31.	15.58%	4.53%	153.59	10.02	39.24
3.	2020. 6. 30.	8.94%	1.84%	33.04	0.23	2.74
4.	2020. 7. 31.	22.59%	5.51%	376.39	17.21	80.48
5.	2020. 8. 31.	9.58%	7.01%	40.83	31.86	36.07
6.	2020. 9. 30.	2.31%	-3.92%	0.77	27.93	4.65
7.	2020. 10. 31.	9.59%	-2.77%	40.99	17.05	-26.43
8.	2020. 11. 30.	14.02%	10.75%	117.17	88.22	101.67
9.	2020. 12. 31.	-0.60%	3.71%	14.41	5.52	-8.92
10.	2021. 1. 31.	2.07%	-1.11%	1.26	6.13	2.78
11.	2021. 2. 28.	-5.12%	2.61%	69.03	1.56	-10.36
12.	2021. 3. 31.	15.58%	4.24%	153.38	8.30	35.69
13.	2021. 4. 30.	3.51%	5.24%	0.10	15.06	1.22
14.	2021. 5. 31.	5.39%	0.55%	4.84	0.66	-1.79
15.	2021. 6. 30.	6.07%	2.22%	8.31	0.74	2.48
16.	2021. 7. 31.	13.68%	2.27%	110.08	0.83	9.58
17.	2021. 8. 31.	4.25%	2.90%	1.13	2.36	1.63
18.	2021. 9. 30.	-10.14%	-4.76%	177.70	37.44	81.57
19.	2021. 10. 31.	1.14%	6.91%	4.21	30.83	-11.39
20.	2021. 11. 30.	3.62%	-0.83%	0.18	4.82	-0.94
21.	2021. 12. 31.	0.50%	4.36%	7.25	9.00	-8.08
22.	2022. 1. 31.	-12.09%	-5.26%	233.66	43.83	101.20
23.	2022. 2. 28.	-5.87%	-3.14%	82.16	20.23	40.77
24.	2022. 3. 31.	2.21%	3.58%	0.97	4.91	-2.18
25.	2022. 4. 30.	-16.24%	-8.80%	377.64	103.18	197.40
26.	2022. 5. 31.	2.72%	0.01%	0.22	1.84	0.64
27.	2022. 6. 30.	-8.90%	-8.39%	146.29	95.14	117.98
28.	2022. 7. 31.	13.66%	9.11%	109.52	60.06	81.10
29.	2022. 8. 31.	-3.48%	-4.24%	44.49	31.43	37.39
30.	2022. 9. 30.	-9.10%	-9.34%	151.08	114.53	131.54
31.	2022. 10. 31.	12.23%	7.99%	81.75	43.88	59.89
32.	2022. 11. 30.	11.47%	5.38%	68.51	16.11	33.22
33.	2022. 12. 31.	-6.51%	-5.90%	94.11	52.70	70.42
합계 (Σ):				2,705.36	1,031.79	1,195.31

모두 보기

분산_CARR = Σ(R_CARR,t–R_CARR)² ÷ (33 – 1)
= 2,705.36 ÷ (33 – 1)
= 84.54

분산_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (33 – 1)
= 1,031.79 ÷ (33 – 1)
= 32.24

공분산_{CARR, S&P 500} = Σ(R_CARR,t–R_CARR)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (33 – 1)
= 1,195.31 ÷ (33 – 1)
= 37.35

분산_CARR	84.54
분산_{S&P 500}	32.24
공분산_{CARR, S&P 500}	37.35
상관 계수_{CARR, S&P 500}¹	0.72
β_CARR²	1.16
α_CARR³	1.61%

계산

¹ 상관 계수_{CARR, S&P 500}
= 공분산_{CARR, S&P 500} ÷ (표준 편차_CARR × 표준 편차_{S&P 500})
= 37.35 ÷ (9.19% × 5.68%)
= 0.72

² β_CARR
= 공분산_{CARR, S&P 500} ÷ 분산_{S&P 500}
= 37.35 ÷ 32.24
= 1.16

³ α_CARR
= 평균의_CARR – β_CARR × 평균의_{S&P 500}
= 3.19% – 1.16 × 1.36%
= 1.61%

가정
LT Treasury Composite의 수익률¹	R_F	4.69%
시장 포트폴리오에 대한 예상 수익률²	E(R_M)	14.90%
보통주의 체계적 위험Carrier	β_CARR	1.16

항공사 보통주에 대한 예상 수익률³	E(R_CARR)	16.52%

¹ 10년 이내에 만기가 도래하거나 콜링할 수 없는 모든 미결제 고정 쿠폰 미국 국채에 대한 입찰 수익률의 비가중 평균(무위험 수익률 대리).

² 자세히 보기 »

³ E(R_CARR) = R_F + β_CARR [E(R_M) – R_F]
= 4.69% + 1.16 [14.90% – 4.69%]
= 16.52%

Carrier Global Corp. (NYSE:CARR)

자본 자산 가격 책정 모델 (CAPM)

수익률

분산과 공분산

체계적인 위험 추정 (β)

기대 수익률