Occidental Petroleum Corp. (NYSE:OXY)

Capital Asset Pricing Model (CAPM)

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Occidental Petroleum Corp. common stock.

Rates of Return
Variance and Covariance
Systematic Risk (β) Estimation
Expected Rate of Return

Rates of Return

Occidental Petroleum Corp., monthly rates of return

		Occidental Petroleum Corp. (OXY)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_OXY,t¹	Dividend_OXY,t¹	R_OXY,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$66.78			2,704.10
1.	Feb 28, 2019	$66.15		-0.94%	2,784.49	2.97%
2.	Mar 31, 2019	$66.20	$0.78	1.25%	2,834.40	1.79%
3.	Apr 30, 2019	$58.88		-11.06%	2,945.83	3.93%
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58.	Nov 30, 2023	$59.15		-4.30%	4,567.80	8.92%
59.	Dec 31, 2023	$59.71	$0.18	1.25%	4,769.83	4.42%
Average (R):				1.99%		1.11%
Standard deviation:				19.46%		5.31%

		Occidental Petroleum Corp. (OXY)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_OXY,t¹	Dividend_OXY,t¹	R_OXY,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$66.78			2,704.10
1.	Feb 28, 2019	$66.15		-0.94%	2,784.49	2.97%
2.	Mar 31, 2019	$66.20	$0.78	1.25%	2,834.40	1.79%
3.	Apr 30, 2019	$58.88		-11.06%	2,945.83	3.93%
4.	May 31, 2019	$49.77		-15.47%	2,752.06	-6.58%
5.	Jun 30, 2019	$50.28	$0.78	2.59%	2,941.76	6.89%
6.	Jul 31, 2019	$51.36		2.15%	2,980.38	1.31%
7.	Aug 31, 2019	$43.48		-15.34%	2,926.46	-1.81%
8.	Sep 30, 2019	$44.47	$0.79	4.09%	2,976.74	1.72%
9.	Oct 31, 2019	$40.50		-8.93%	3,037.56	2.04%
10.	Nov 30, 2019	$38.57		-4.77%	3,140.98	3.40%
11.	Dec 31, 2019	$41.21	$0.79	8.89%	3,230.78	2.86%
12.	Jan 31, 2020	$39.72		-3.62%	3,225.52	-0.16%
13.	Feb 29, 2020	$32.74		-17.57%	2,954.22	-8.41%
14.	Mar 31, 2020	$11.58	$0.79	-62.22%	2,584.59	-12.51%
15.	Apr 30, 2020	$16.60		43.35%	2,912.43	12.68%
16.	May 31, 2020	$12.95		-21.99%	3,044.31	4.53%
17.	Jun 30, 2020	$18.30	$0.01	41.39%	3,100.29	1.84%
18.	Jul 31, 2020	$15.74		-13.99%	3,271.12	5.51%
19.	Aug 31, 2020	$12.74		-19.06%	3,500.31	7.01%
20.	Sep 30, 2020	$10.01	$0.01	-21.35%	3,363.00	-3.92%
21.	Oct 31, 2020	$9.13		-8.79%	3,269.96	-2.77%
22.	Nov 30, 2020	$15.76		72.62%	3,621.63	10.75%
23.	Dec 31, 2020	$17.31	$0.01	9.90%	3,756.07	3.71%
24.	Jan 31, 2021	$20.06		15.89%	3,714.24	-1.11%
25.	Feb 28, 2021	$26.61		32.65%	3,811.15	2.61%
26.	Mar 31, 2021	$26.62	$0.01	0.08%	3,972.89	4.24%
27.	Apr 30, 2021	$25.36		-4.73%	4,181.17	5.24%
28.	May 31, 2021	$25.96		2.37%	4,204.11	0.55%
29.	Jun 30, 2021	$31.27	$0.01	20.49%	4,297.50	2.22%
30.	Jul 31, 2021	$26.10		-16.53%	4,395.26	2.27%
31.	Aug 31, 2021	$25.69		-1.57%	4,522.68	2.90%
32.	Sep 30, 2021	$29.58	$0.01	15.18%	4,307.54	-4.76%
33.	Oct 31, 2021	$33.53		13.35%	4,605.38	6.91%
34.	Nov 30, 2021	$29.65		-11.57%	4,567.00	-0.83%
35.	Dec 31, 2021	$28.99	$0.01	-2.19%	4,766.18	4.36%
36.	Jan 31, 2022	$37.67		29.94%	4,515.55	-5.26%
37.	Feb 28, 2022	$43.73		16.09%	4,373.94	-3.14%
38.	Mar 31, 2022	$56.74	$0.13	30.05%	4,530.41	3.58%
39.	Apr 30, 2022	$55.09		-2.91%	4,131.93	-8.80%
40.	May 31, 2022	$69.31		25.81%	4,132.15	0.01%
41.	Jun 30, 2022	$58.88	$0.13	-14.86%	3,785.38	-8.39%
42.	Jul 31, 2022	$65.75		11.67%	4,130.29	9.11%
43.	Aug 31, 2022	$71.00		7.98%	3,955.00	-4.24%
44.	Sep 30, 2022	$61.45	$0.13	-13.27%	3,585.62	-9.34%
45.	Oct 31, 2022	$72.60		18.14%	3,871.98	7.99%
46.	Nov 30, 2022	$69.49		-4.28%	4,080.11	5.38%
47.	Dec 31, 2022	$62.99	$0.13	-9.17%	3,839.50	-5.90%
48.	Jan 31, 2023	$64.79		2.86%	4,076.60	6.18%
49.	Feb 28, 2023	$58.56		-9.62%	3,970.15	-2.61%
50.	Mar 31, 2023	$62.43	$0.18	6.92%	4,109.31	3.51%
51.	Apr 30, 2023	$61.53		-1.44%	4,169.48	1.46%
52.	May 31, 2023	$57.66		-6.29%	4,179.83	0.25%
53.	Jun 30, 2023	$58.80	$0.18	2.29%	4,376.86	4.71%
54.	Jul 31, 2023	$63.13		7.36%	4,588.96	4.85%
55.	Aug 31, 2023	$62.79		-0.54%	4,507.66	-1.77%
56.	Sep 30, 2023	$64.88	$0.18	3.62%	4,288.05	-4.87%
57.	Oct 31, 2023	$61.81		-4.73%	4,193.80	-2.20%
58.	Nov 30, 2023	$59.15		-4.30%	4,567.80	8.92%
59.	Dec 31, 2023	$59.71	$0.18	1.25%	4,769.83	4.42%
Average (R):				1.99%		1.11%
Standard deviation:				19.46%		5.31%

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

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

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

Variance and Covariance

Occidental Petroleum Corp., calculation of variance and covariance of returns

t	Date	R_OXY,t	R_{S&P 500,t}	(R_OXY,t–R_OXY)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_OXY,t–R_OXY)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	-0.94%	2.97%	8.58	3.49	-5.47
2.	Mar 31, 2019	1.25%	1.79%	0.53	0.47	-0.50
3.	Apr 30, 2019	-11.06%	3.93%	170.11	7.98	-36.85
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58.	Nov 30, 2023	-4.30%	8.92%	39.55	61.03	-49.13
59.	Dec 31, 2023	1.25%	4.42%	0.54	11.00	-2.44
Total (Σ):				21,965.27	1,634.30	2,703.97

t	Date	R_OXY,t	R_{S&P 500,t}	(R_OXY,t–R_OXY)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_OXY,t–R_OXY)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	-0.94%	2.97%	8.58	3.49	-5.47
2.	Mar 31, 2019	1.25%	1.79%	0.53	0.47	-0.50
3.	Apr 30, 2019	-11.06%	3.93%	170.11	7.98	-36.85
4.	May 31, 2019	-15.47%	-6.58%	304.76	59.04	134.14
5.	Jun 30, 2019	2.59%	6.89%	0.37	33.49	3.51
6.	Jul 31, 2019	2.15%	1.31%	0.03	0.04	0.03
7.	Aug 31, 2019	-15.34%	-1.81%	300.25	8.50	50.51
8.	Sep 30, 2019	4.09%	1.72%	4.45	0.37	1.29
9.	Oct 31, 2019	-8.93%	2.04%	119.08	0.88	-10.23
10.	Nov 30, 2019	-4.77%	3.40%	45.57	5.28	-15.52
11.	Dec 31, 2019	8.89%	2.86%	47.72	3.07	12.11
12.	Jan 31, 2020	-3.62%	-0.16%	31.37	1.61	7.11
13.	Feb 29, 2020	-17.57%	-8.41%	382.52	90.57	186.13
14.	Mar 31, 2020	-62.22%	-12.51%	4,121.98	185.44	874.30
15.	Apr 30, 2020	43.35%	12.68%	1,711.10	134.06	478.95
16.	May 31, 2020	-21.99%	4.53%	574.71	11.71	-82.04
17.	Jun 30, 2020	41.39%	1.84%	1,552.74	0.54	28.88
18.	Jul 31, 2020	-13.99%	5.51%	255.18	19.40	-70.35
19.	Aug 31, 2020	-19.06%	7.01%	442.89	34.82	-124.18
20.	Sep 30, 2020	-21.35%	-3.92%	544.53	25.29	117.34
21.	Oct 31, 2020	-8.79%	-2.77%	116.13	15.00	41.73
22.	Nov 30, 2020	72.62%	10.75%	4,988.96	93.10	681.51
23.	Dec 31, 2020	9.90%	3.71%	62.62	6.79	20.62
24.	Jan 31, 2021	15.89%	-1.11%	193.26	4.93	-30.85
25.	Feb 28, 2021	32.65%	2.61%	940.46	2.26	46.10
26.	Mar 31, 2021	0.08%	4.24%	3.65	9.85	-5.99
27.	Apr 30, 2021	-4.73%	5.24%	45.14	17.11	-27.79
28.	May 31, 2021	2.37%	0.55%	0.15	0.31	-0.21
29.	Jun 30, 2021	20.49%	2.22%	342.54	1.24	20.65
30.	Jul 31, 2021	-16.53%	2.27%	342.94	1.37	-21.65
31.	Aug 31, 2021	-1.57%	2.90%	12.65	3.22	-6.38
32.	Sep 30, 2021	15.18%	-4.76%	174.13	34.37	-77.36
33.	Oct 31, 2021	13.35%	6.91%	129.24	33.74	66.03
34.	Nov 30, 2021	-11.57%	-0.83%	183.79	3.76	26.29
35.	Dec 31, 2021	-2.19%	4.36%	17.45	10.60	-13.60
36.	Jan 31, 2022	29.94%	-5.26%	781.55	40.51	-177.92
37.	Feb 28, 2022	16.09%	-3.14%	198.86	17.99	-59.82
38.	Mar 31, 2022	30.05%	3.58%	787.53	6.11	69.36
39.	Apr 30, 2022	-2.91%	-8.80%	23.94	98.04	48.45
40.	May 31, 2022	25.81%	0.01%	567.73	1.21	-26.22
41.	Jun 30, 2022	-14.86%	-8.39%	283.78	90.21	160.00
42.	Jul 31, 2022	11.67%	9.11%	93.75	64.09	77.52
43.	Aug 31, 2022	7.98%	-4.24%	36.00	28.62	-32.10
44.	Sep 30, 2022	-13.27%	-9.34%	232.65	109.11	159.32
45.	Oct 31, 2022	18.14%	7.99%	261.14	47.34	111.19
46.	Nov 30, 2022	-4.28%	5.38%	39.30	18.23	-26.76
47.	Dec 31, 2022	-9.17%	-5.90%	124.37	49.04	78.10
48.	Jan 31, 2023	2.86%	6.18%	0.76	25.70	4.42
49.	Feb 28, 2023	-9.62%	-2.61%	134.58	13.82	43.12
50.	Mar 31, 2023	6.92%	3.51%	24.31	5.76	11.83
51.	Apr 30, 2023	-1.44%	1.46%	11.74	0.13	-1.23
52.	May 31, 2023	-6.29%	0.25%	68.47	0.74	7.10
53.	Jun 30, 2023	2.29%	4.71%	0.09	13.02	1.10
54.	Jul 31, 2023	7.36%	4.85%	28.93	13.99	20.12
55.	Aug 31, 2023	-0.54%	-1.77%	6.37	8.28	7.26
56.	Sep 30, 2023	3.62%	-4.87%	2.66	35.73	-9.74
57.	Oct 31, 2023	-4.73%	-2.20%	45.12	10.92	22.19
58.	Nov 30, 2023	-4.30%	8.92%	39.55	61.03	-49.13
59.	Dec 31, 2023	1.25%	4.42%	0.54	11.00	-2.44
Total (Σ):				21,965.27	1,634.30	2,703.97

Show all

Variance_OXY = Σ(R_OXY,t–R_OXY)² ÷ (59 – 1)
= 21,965.27 ÷ (59 – 1)
= 378.71

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18

Covariance_{OXY, S&P 500} = Σ(R_OXY,t–R_OXY)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 2,703.97 ÷ (59 – 1)
= 46.62

Systematic Risk (β) Estimation

Variance_OXY	378.71
Variance_{S&P 500}	28.18
Covariance_{OXY, S&P 500}	46.62
Correlation coefficient_{OXY, S&P 500}¹	0.45
β_OXY²	1.65
α_OXY³	0.16%

Calculations

¹ Correlation coefficient_{OXY, S&P 500}
= Covariance_{OXY, S&P 500} ÷ (Standard deviation_OXY × Standard deviation_{S&P 500})
= 46.62 ÷ (19.46% × 5.31%)
= 0.45

² β_OXY
= Covariance_{OXY, S&P 500} ÷ Variance_{S&P 500}
= 46.62 ÷ 28.18
= 1.65

³ α_OXY
= Average_OXY – β_OXY × Average_{S&P 500}
= 1.99% – 1.65 × 1.11%
= 0.16%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.90%
Expected rate of return on market portfolio²	E(R_M)	13.55%
Systematic risk (β) of Occidental Petroleum Corp. common stock	β_OXY	1.65

Expected rate of return on Occidental Petroleum Corp. common stock³	E(R_OXY)	19.21%

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).

² See details »

³ E(R_OXY) = R_F + β_OXY [E(R_M) – R_F]
= 4.90% + 1.65 [13.55% – 4.90%]
= 19.21%