자본 자산 가격 책정 모델 (CAPM)

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

수익률
분산과 공분산
체계적인 위험 추정 (β)
기대 수익률

수익률

Kraft Heinz Co., 월별 수익률

		Kraft Heinz Co. (KHC)			Standard & Poor’s 500 (S&P 500)
t	날짜	값_KHC,t¹	피제수_KHC,t¹	R_KHC,t²	값_{S&P 500,t}	R_{S&P 500,t}³
	2015. 7. 31.	$79.47			2,103.84
1.	2015. 8. 31.	$72.66		-8.57%	1,972.18	-6.26%
2.	2015. 9. 30.	$70.58		-2.86%	1,920.03	-2.64%
3.	2015. 10. 31.	$77.97		10.47%	2,079.36	8.30%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
52.	2019. 11. 30.	$30.50	$0.40	-4.42%	3,140.98	3.40%
53.	2019. 12. 31.	$32.13		5.34%	3,230.78	2.86%
평균의 (R):				-1.00%		0.87%
표준 편차:				8.39%		3.54%

		Kraft Heinz Co. (KHC)			Standard & Poor’s 500 (S&P 500)
t	날짜	값_KHC,t¹	피제수_KHC,t¹	R_KHC,t²	값_{S&P 500,t}	R_{S&P 500,t}³
	2015. 7. 31.	$79.47			2,103.84
1.	2015. 8. 31.	$72.66		-8.57%	1,972.18	-6.26%
2.	2015. 9. 30.	$70.58		-2.86%	1,920.03	-2.64%
3.	2015. 10. 31.	$77.97		10.47%	2,079.36	8.30%
4.	2015. 11. 30.	$73.69	$0.575	-4.75%	2,080.41	0.05%
5.	2015. 12. 31.	$72.76	$0.575	-0.48%	2,043.94	-1.75%
6.	2016. 1. 31.	$78.06		7.28%	1,940.24	-5.07%
7.	2016. 2. 29.	$77.02		-1.33%	1,932.23	-0.41%
8.	2016. 3. 31.	$78.56	$0.575	2.75%	2,059.74	6.60%
9.	2016. 4. 30.	$78.07		-0.62%	2,065.30	0.27%
10.	2016. 5. 31.	$83.19	$0.575	7.29%	2,096.95	1.53%
11.	2016. 6. 30.	$88.48		6.36%	2,098.86	0.09%
12.	2016. 7. 31.	$86.39		-2.36%	2,173.60	3.56%
13.	2016. 8. 31.	$89.49	$0.60	4.28%	2,170.95	-0.12%
14.	2016. 9. 30.	$89.51		0.02%	2,168.27	-0.12%
15.	2016. 10. 31.	$88.95		-0.63%	2,126.15	-1.94%
16.	2016. 11. 30.	$81.65	$0.60	-7.53%	2,198.81	3.42%
17.	2016. 12. 31.	$87.32		6.94%	2,238.83	1.82%
18.	2017. 1. 31.	$89.29		2.26%	2,278.87	1.79%
19.	2017. 2. 28.	$91.51		2.49%	2,363.64	3.72%
20.	2017. 3. 31.	$90.81	$0.60	-0.11%	2,362.72	-0.04%
21.	2017. 4. 30.	$90.39		-0.46%	2,384.20	0.91%
22.	2017. 5. 31.	$92.20	$0.60	2.67%	2,411.80	1.16%
23.	2017. 6. 30.	$85.64		-7.11%	2,423.41	0.48%
24.	2017. 7. 31.	$87.46		2.13%	2,470.30	1.93%
25.	2017. 8. 31.	$80.75	$0.625	-6.96%	2,471.65	0.05%
26.	2017. 9. 30.	$77.55		-3.96%	2,519.36	1.93%
27.	2017. 10. 31.	$77.33		-0.28%	2,575.26	2.22%
28.	2017. 11. 30.	$81.37	$0.625	6.03%	2,647.58	2.81%
29.	2017. 12. 31.	$77.76		-4.44%	2,673.61	0.98%
30.	2018. 1. 31.	$78.39		0.81%	2,823.81	5.62%
31.	2018. 2. 28.	$67.05		-14.47%	2,713.83	-3.89%
32.	2018. 3. 31.	$62.29	$0.625	-6.17%	2,640.87	-2.69%
33.	2018. 4. 30.	$56.38		-9.49%	2,648.05	0.27%
34.	2018. 5. 31.	$57.48	$0.625	3.06%	2,705.27	2.16%
35.	2018. 6. 30.	$62.82		9.29%	2,718.37	0.48%
36.	2018. 7. 31.	$60.25		-4.09%	2,816.29	3.60%
37.	2018. 8. 31.	$58.27	$0.625	-2.25%	2,901.52	3.03%
38.	2018. 9. 30.	$55.11		-5.42%	2,913.98	0.43%
39.	2018. 10. 31.	$54.97		-0.25%	2,711.74	-6.94%
40.	2018. 11. 30.	$51.12	$0.625	-5.87%	2,760.17	1.79%
41.	2018. 12. 31.	$43.04		-15.81%	2,506.85	-9.18%
42.	2019. 1. 31.	$48.06		11.66%	2,704.10	7.87%
43.	2019. 2. 28.	$33.19		-30.94%	2,784.49	2.97%
44.	2019. 3. 31.	$32.65	$0.40	-0.42%	2,834.40	1.79%
45.	2019. 4. 30.	$33.24		1.81%	2,945.83	3.93%
46.	2019. 5. 31.	$27.65	$0.40	-15.61%	2,752.06	-6.58%
47.	2019. 6. 30.	$31.04		12.26%	2,941.76	6.89%
48.	2019. 7. 31.	$32.01		3.13%	2,980.38	1.31%
49.	2019. 8. 31.	$25.52	$0.40	-19.03%	2,926.46	-1.81%
50.	2019. 9. 30.	$27.93		9.44%	2,976.74	1.72%
51.	2019. 10. 31.	$32.33		15.75%	3,037.56	2.04%
52.	2019. 11. 30.	$30.50	$0.40	-4.42%	3,140.98	3.40%
53.	2019. 12. 31.	$32.13		5.34%	3,230.78	2.86%
평균의 (R):				-1.00%		0.87%
표준 편차:				8.39%		3.54%

모두 보기

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

² t기간 동안 KHC의 보통주 수익률

³ 기간 t 동안 S&P 500(시장 포트폴리오 프록시)의 수익률.

분산과 공분산

Kraft Heinz Co., 수익률의 분산 및 공분산 계산

t	날짜	R_KHC,t	R_{S&P 500,t}	(R_KHC,t–R_KHC)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_KHC,t–R_KHC)×(R_{S&P 500,t}–R_{S&P 500})
1.	2015. 8. 31.	-8.57%	-6.26%	57.24	50.87	53.96
2.	2015. 9. 30.	-2.86%	-2.64%	3.46	12.38	6.54
3.	2015. 10. 31.	10.47%	8.30%	131.65	55.11	85.18
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
52.	2019. 11. 30.	-4.42%	3.40%	11.70	6.40	-8.65
53.	2019. 12. 31.	5.34%	2.86%	40.29	3.94	12.60
합계 (Σ):				3,657.69	650.55	667.22

t	날짜	R_KHC,t	R_{S&P 500,t}	(R_KHC,t–R_KHC)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_KHC,t–R_KHC)×(R_{S&P 500,t}–R_{S&P 500})
1.	2015. 8. 31.	-8.57%	-6.26%	57.24	50.87	53.96
2.	2015. 9. 30.	-2.86%	-2.64%	3.46	12.38	6.54
3.	2015. 10. 31.	10.47%	8.30%	131.65	55.11	85.18
4.	2015. 11. 30.	-4.75%	0.05%	14.05	0.68	3.09
5.	2015. 12. 31.	-0.48%	-1.75%	0.27	6.90	-1.37
6.	2016. 1. 31.	7.28%	-5.07%	68.68	35.38	-49.29
7.	2016. 2. 29.	-1.33%	-0.41%	0.11	1.66	0.42
8.	2016. 3. 31.	2.75%	6.60%	14.06	32.77	21.46
9.	2016. 4. 30.	-0.62%	0.27%	0.14	0.37	-0.23
10.	2016. 5. 31.	7.29%	1.53%	68.86	0.43	5.46
11.	2016. 6. 30.	6.36%	0.09%	54.20	0.61	-5.77
12.	2016. 7. 31.	-2.36%	3.56%	1.85	7.22	-3.65
13.	2016. 8. 31.	4.28%	-0.12%	27.94	0.99	-5.27
14.	2016. 9. 30.	0.02%	-0.12%	1.05	1.00	-1.02
15.	2016. 10. 31.	-0.63%	-1.94%	0.14	7.94	-1.06
16.	2016. 11. 30.	-7.53%	3.42%	42.63	6.47	-16.60
17.	2016. 12. 31.	6.94%	1.82%	63.16	0.89	7.52
18.	2017. 1. 31.	2.26%	1.79%	10.62	0.84	2.98
19.	2017. 2. 28.	2.49%	3.72%	12.18	8.10	9.93
20.	2017. 3. 31.	-0.11%	-0.04%	0.80	0.83	-0.82
21.	2017. 4. 30.	-0.46%	0.91%	0.29	0.00	0.02
22.	2017. 5. 31.	2.67%	1.16%	13.47	0.08	1.04
23.	2017. 6. 30.	-7.11%	0.48%	37.35	0.15	2.40
24.	2017. 7. 31.	2.13%	1.93%	9.79	1.12	3.32
25.	2017. 8. 31.	-6.96%	0.05%	35.45	0.67	4.88
26.	2017. 9. 30.	-3.96%	1.93%	8.76	1.11	-3.12
27.	2017. 10. 31.	-0.28%	2.22%	0.52	1.81	0.97
28.	2017. 11. 30.	6.03%	2.81%	49.50	3.74	13.61
29.	2017. 12. 31.	-4.44%	0.98%	11.79	0.01	-0.37
30.	2018. 1. 31.	0.81%	5.62%	3.29	22.50	8.60
31.	2018. 2. 28.	-14.47%	-3.89%	181.25	22.74	64.21
32.	2018. 3. 31.	-6.17%	-2.69%	26.66	12.69	18.40
33.	2018. 4. 30.	-9.49%	0.27%	71.99	0.36	5.11
34.	2018. 5. 31.	3.06%	2.16%	16.51	1.65	5.23
35.	2018. 6. 30.	9.29%	0.48%	105.96	0.15	-4.02
36.	2018. 7. 31.	-4.09%	3.60%	9.53	7.44	-8.42
37.	2018. 8. 31.	-2.25%	3.03%	1.55	4.63	-2.68
38.	2018. 9. 30.	-5.42%	0.43%	19.53	0.20	1.97
39.	2018. 10. 31.	-0.25%	-6.94%	0.56	61.07	-5.86
40.	2018. 11. 30.	-5.87%	1.79%	23.65	0.83	-4.43
41.	2018. 12. 31.	-15.81%	-9.18%	219.12	101.04	148.80
42.	2019. 1. 31.	11.66%	7.87%	160.45	48.92	88.59
43.	2019. 2. 28.	-30.94%	2.97%	896.23	4.40	-62.82
44.	2019. 3. 31.	-0.42%	1.79%	0.34	0.84	0.53
45.	2019. 4. 30.	1.81%	3.93%	7.90	9.34	8.59
46.	2019. 5. 31.	-15.61%	-6.58%	213.46	55.54	108.88
47.	2019. 6. 30.	12.26%	6.89%	175.93	36.22	79.83
48.	2019. 7. 31.	3.13%	1.31%	17.04	0.19	1.81
49.	2019. 8. 31.	-19.03%	-1.81%	324.79	7.20	48.36
50.	2019. 9. 30.	9.44%	1.72%	109.14	0.71	8.81
51.	2019. 10. 31.	15.75%	2.04%	280.80	1.37	19.58
52.	2019. 11. 30.	-4.42%	3.40%	11.70	6.40	-8.65
53.	2019. 12. 31.	5.34%	2.86%	40.29	3.94	12.60
합계 (Σ):				3,657.69	650.55	667.22

모두 보기

분산_KHC = Σ(R_KHC,t–R_KHC)² ÷ (53 – 1)
= 3,657.69 ÷ (53 – 1)
= 70.34

분산_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (53 – 1)
= 650.55 ÷ (53 – 1)
= 12.51

공분산_{KHC, S&P 500} = Σ(R_KHC,t–R_KHC)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (53 – 1)
= 667.22 ÷ (53 – 1)
= 12.83

체계적인 위험 추정 (β)

분산_KHC	70.34
분산_{S&P 500}	12.51
공분산_{KHC, S&P 500}	12.83
상관 계수_{KHC, S&P 500}¹	0.43
β_KHC²	1.03
α_KHC³	-1.90%

계산

¹ 상관 계수_{KHC, S&P 500}
= 공분산_{KHC, S&P 500} ÷ (표준 편차_KHC × 표준 편차_{S&P 500})
= 12.83 ÷ (8.39% × 3.54%)
= 0.43

² β_KHC
= 공분산_{KHC, S&P 500} ÷ 분산_{S&P 500}
= 12.83 ÷ 12.51
= 1.03

³ α_KHC
= 평균의_KHC – β_KHC × 평균의_{S&P 500}
= -1.00% – 1.03 × 0.87%
= -1.90%

기대 수익률

가정
LT Treasury Composite의 수익률¹	R_F	4.67%
시장 포트폴리오에 대한 예상 수익률²	E(R_M)	14.91%
보통주의 체계적 위험Kraft Heinz	β_KHC	1.03

Kraft Heinz 보통주의 예상 수익률³	E(R_KHC)	15.17%

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_KHC) = R_F + β_KHC [E(R_M) – R_F]
= 4.67% + 1.03 [14.91% – 4.67%]
= 15.17%

Kraft Heinz Co. (NASDAQ:KHC)

자본 자산 가격 책정 모델 (CAPM)

수익률

분산과 공분산

체계적인 위험 추정 (β)

기대 수익률