Schlumberger Ltd. (NYSE:SLB)

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 Schlumberger Ltd. common stock.

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

Rates of Return

Schlumberger Ltd., monthly rates of return

		Schlumberger Ltd. (SLB)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_SLB,t¹	Dividend_SLB,t¹	R_SLB,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$44.21			2,704.10
1.	Feb 28, 2019	$44.06	$0.50	0.79%	2,784.49	2.97%
2.	Mar 31, 2019	$43.57		-1.11%	2,834.40	1.79%
3.	Apr 30, 2019	$42.68		-2.04%	2,945.83	3.93%
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58.	Nov 30, 2023	$52.04		-6.50%	4,567.80	8.92%
59.	Dec 31, 2023	$52.04	$0.25	0.48%	4,769.83	4.42%
Average (R):				1.67%		1.11%
Standard deviation:				14.99%		5.31%

		Schlumberger Ltd. (SLB)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_SLB,t¹	Dividend_SLB,t¹	R_SLB,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$44.21			2,704.10
1.	Feb 28, 2019	$44.06	$0.50	0.79%	2,784.49	2.97%
2.	Mar 31, 2019	$43.57		-1.11%	2,834.40	1.79%
3.	Apr 30, 2019	$42.68		-2.04%	2,945.83	3.93%
4.	May 31, 2019	$34.69		-18.72%	2,752.06	-6.58%
5.	Jun 30, 2019	$39.74	$0.50	16.00%	2,941.76	6.89%
6.	Jul 31, 2019	$39.97		0.58%	2,980.38	1.31%
7.	Aug 31, 2019	$32.43		-18.86%	2,926.46	-1.81%
8.	Sep 30, 2019	$34.17	$0.50	6.91%	2,976.74	1.72%
9.	Oct 31, 2019	$32.69		-4.33%	3,037.56	2.04%
10.	Nov 30, 2019	$36.20		10.74%	3,140.98	3.40%
11.	Dec 31, 2019	$40.20	$0.50	12.43%	3,230.78	2.86%
12.	Jan 31, 2020	$33.51		-16.64%	3,225.52	-0.16%
13.	Feb 29, 2020	$27.09	$0.50	-17.67%	2,954.22	-8.41%
14.	Mar 31, 2020	$13.49		-50.20%	2,584.59	-12.51%
15.	Apr 30, 2020	$16.82		24.68%	2,912.43	12.68%
16.	May 31, 2020	$18.47		9.81%	3,044.31	4.53%
17.	Jun 30, 2020	$18.39	$0.125	0.24%	3,100.29	1.84%
18.	Jul 31, 2020	$18.14		-1.36%	3,271.12	5.51%
19.	Aug 31, 2020	$19.01		4.80%	3,500.31	7.01%
20.	Sep 30, 2020	$15.56	$0.125	-17.49%	3,363.00	-3.92%
21.	Oct 31, 2020	$14.94		-3.98%	3,269.96	-2.77%
22.	Nov 30, 2020	$20.79		39.16%	3,621.63	10.75%
23.	Dec 31, 2020	$21.83	$0.125	5.60%	3,756.07	3.71%
24.	Jan 31, 2021	$22.21		1.74%	3,714.24	-1.11%
25.	Feb 28, 2021	$27.91	$0.125	26.23%	3,811.15	2.61%
26.	Mar 31, 2021	$27.19		-2.58%	3,972.89	4.24%
27.	Apr 30, 2021	$27.05		-0.51%	4,181.17	5.24%
28.	May 31, 2021	$31.33		15.82%	4,204.11	0.55%
29.	Jun 30, 2021	$32.01	$0.125	2.57%	4,297.50	2.22%
30.	Jul 31, 2021	$28.83		-9.93%	4,395.26	2.27%
31.	Aug 31, 2021	$28.04	$0.125	-2.31%	4,522.68	2.90%
32.	Sep 30, 2021	$29.64		5.71%	4,307.54	-4.76%
33.	Oct 31, 2021	$32.26		8.84%	4,605.38	6.91%
34.	Nov 30, 2021	$28.68	$0.125	-10.71%	4,567.00	-0.83%
35.	Dec 31, 2021	$29.95		4.43%	4,766.18	4.36%
36.	Jan 31, 2022	$39.07		30.45%	4,515.55	-5.26%
37.	Feb 28, 2022	$39.24	$0.125	0.76%	4,373.94	-3.14%
38.	Mar 31, 2022	$41.31		5.28%	4,530.41	3.58%
39.	Apr 30, 2022	$39.01		-5.57%	4,131.93	-8.80%
40.	May 31, 2022	$45.96	$0.175	18.26%	4,132.15	0.01%
41.	Jun 30, 2022	$35.76		-22.19%	3,785.38	-8.39%
42.	Jul 31, 2022	$37.03		3.55%	4,130.29	9.11%
43.	Aug 31, 2022	$38.15		3.02%	3,955.00	-4.24%
44.	Sep 30, 2022	$35.90	$0.175	-5.44%	3,585.62	-9.34%
45.	Oct 31, 2022	$52.03		44.93%	3,871.98	7.99%
46.	Nov 30, 2022	$51.55		-0.92%	4,080.11	5.38%
47.	Dec 31, 2022	$53.46	$0.175	4.04%	3,839.50	-5.90%
48.	Jan 31, 2023	$56.98		6.58%	4,076.60	6.18%
49.	Feb 28, 2023	$53.21	$0.25	-6.18%	3,970.15	-2.61%
50.	Mar 31, 2023	$49.10		-7.72%	4,109.31	3.51%
51.	Apr 30, 2023	$49.35		0.51%	4,169.48	1.46%
52.	May 31, 2023	$42.83		-13.21%	4,179.83	0.25%
53.	Jun 30, 2023	$49.12	$0.25	15.27%	4,376.86	4.71%
54.	Jul 31, 2023	$58.34		18.77%	4,588.96	4.85%
55.	Aug 31, 2023	$58.96		1.06%	4,507.66	-1.77%
56.	Sep 30, 2023	$58.30	$0.25	-0.70%	4,288.05	-4.87%
57.	Oct 31, 2023	$55.66		-4.53%	4,193.80	-2.20%
58.	Nov 30, 2023	$52.04		-6.50%	4,567.80	8.92%
59.	Dec 31, 2023	$52.04	$0.25	0.48%	4,769.83	4.42%
Average (R):				1.67%		1.11%
Standard deviation:				14.99%		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 SLB during period t

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

Variance and Covariance

Schlumberger Ltd., calculation of variance and covariance of returns

t	Date	R_SLB,t	R_{S&P 500,t}	(R_SLB,t–R_SLB)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_SLB,t–R_SLB)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	0.79%	2.97%	0.77	3.49	-1.64
2.	Mar 31, 2019	-1.11%	1.79%	7.75	0.47	-1.91
3.	Apr 30, 2019	-2.04%	3.93%	13.80	7.98	-10.49
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58.	Nov 30, 2023	-6.50%	8.92%	66.84	61.03	-63.87
59.	Dec 31, 2023	0.48%	4.42%	1.42	11.00	-3.95
Total (Σ):				13,036.39	1,634.30	2,649.68

t	Date	R_SLB,t	R_{S&P 500,t}	(R_SLB,t–R_SLB)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_SLB,t–R_SLB)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	0.79%	2.97%	0.77	3.49	-1.64
2.	Mar 31, 2019	-1.11%	1.79%	7.75	0.47	-1.91
3.	Apr 30, 2019	-2.04%	3.93%	13.80	7.98	-10.49
4.	May 31, 2019	-18.72%	-6.58%	415.84	59.04	156.69
5.	Jun 30, 2019	16.00%	6.89%	205.27	33.49	82.91
6.	Jul 31, 2019	0.58%	1.31%	1.19	0.04	-0.23
7.	Aug 31, 2019	-18.86%	-1.81%	421.71	8.50	59.86
8.	Sep 30, 2019	6.91%	1.72%	27.41	0.37	3.21
9.	Oct 31, 2019	-4.33%	2.04%	36.03	0.88	-5.63
10.	Nov 30, 2019	10.74%	3.40%	82.19	5.28	20.84
11.	Dec 31, 2019	12.43%	2.86%	115.76	3.07	18.86
12.	Jan 31, 2020	-16.64%	-0.16%	335.38	1.61	23.23
13.	Feb 29, 2020	-17.67%	-8.41%	373.95	90.57	184.04
14.	Mar 31, 2020	-50.20%	-12.51%	2,690.97	185.44	706.42
15.	Apr 30, 2020	24.68%	12.68%	529.62	134.06	266.46
16.	May 31, 2020	9.81%	4.53%	66.23	11.71	27.85
17.	Jun 30, 2020	0.24%	1.84%	2.04	0.54	-1.05
18.	Jul 31, 2020	-1.36%	5.51%	9.19	19.40	-13.35
19.	Aug 31, 2020	4.80%	7.01%	9.76	34.82	18.44
20.	Sep 30, 2020	-17.49%	-3.92%	367.19	25.29	96.36
21.	Oct 31, 2020	-3.98%	-2.77%	31.99	15.00	21.90
22.	Nov 30, 2020	39.16%	10.75%	1,405.13	93.10	361.68
23.	Dec 31, 2020	5.60%	3.71%	15.46	6.79	10.25
24.	Jan 31, 2021	1.74%	-1.11%	0.00	4.93	-0.15
25.	Feb 28, 2021	26.23%	2.61%	602.97	2.26	36.91
26.	Mar 31, 2021	-2.58%	4.24%	18.07	9.85	-13.34
27.	Apr 30, 2021	-0.51%	5.24%	4.78	17.11	-9.04
28.	May 31, 2021	15.82%	0.55%	200.25	0.31	-7.88
29.	Jun 30, 2021	2.57%	2.22%	0.81	1.24	1.00
30.	Jul 31, 2021	-9.93%	2.27%	134.70	1.37	-13.57
31.	Aug 31, 2021	-2.31%	2.90%	15.83	3.22	-7.13
32.	Sep 30, 2021	5.71%	-4.76%	16.28	34.37	-23.65
33.	Oct 31, 2021	8.84%	6.91%	51.38	33.74	41.63
34.	Nov 30, 2021	-10.71%	-0.83%	153.30	3.76	24.01
35.	Dec 31, 2021	4.43%	4.36%	7.60	10.60	8.97
36.	Jan 31, 2022	30.45%	-5.26%	828.24	40.51	-183.16
37.	Feb 28, 2022	0.76%	-3.14%	0.84	17.99	3.89
38.	Mar 31, 2022	5.28%	3.58%	12.99	6.11	8.91
39.	Apr 30, 2022	-5.57%	-8.80%	52.41	98.04	71.68
40.	May 31, 2022	18.26%	0.01%	275.33	1.21	-18.26
41.	Jun 30, 2022	-22.19%	-8.39%	569.53	90.21	226.66
42.	Jul 31, 2022	3.55%	9.11%	3.53	64.09	15.05
43.	Aug 31, 2022	3.02%	-4.24%	1.83	28.62	-7.24
44.	Sep 30, 2022	-5.44%	-9.34%	50.56	109.11	74.27
45.	Oct 31, 2022	44.93%	7.99%	1,871.33	47.34	297.64
46.	Nov 30, 2022	-0.92%	5.38%	6.73	18.23	-11.08
47.	Dec 31, 2022	4.04%	-5.90%	5.63	49.04	-16.62
48.	Jan 31, 2023	6.58%	6.18%	24.14	25.70	24.91
49.	Feb 28, 2023	-6.18%	-2.61%	61.61	13.82	29.18
50.	Mar 31, 2023	-7.72%	3.51%	88.28	5.76	-22.54
51.	Apr 30, 2023	0.51%	1.46%	1.35	0.13	-0.42
52.	May 31, 2023	-13.21%	0.25%	221.51	0.74	12.76
53.	Jun 30, 2023	15.27%	4.71%	184.91	13.02	49.06
54.	Jul 31, 2023	18.77%	4.85%	292.37	13.99	63.95
55.	Aug 31, 2023	1.06%	-1.77%	0.37	8.28	1.75
56.	Sep 30, 2023	-0.70%	-4.87%	5.60	35.73	14.15
57.	Oct 31, 2023	-4.53%	-2.20%	38.44	10.92	20.48
58.	Nov 30, 2023	-6.50%	8.92%	66.84	61.03	-63.87
59.	Dec 31, 2023	0.48%	4.42%	1.42	11.00	-3.95
Total (Σ):				13,036.39	1,634.30	2,649.68

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Variance_SLB = Σ(R_SLB,t–R_SLB)² ÷ (59 – 1)
= 13,036.39 ÷ (59 – 1)
= 224.77

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_{SLB, S&P 500} = Σ(R_SLB,t–R_SLB)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 2,649.68 ÷ (59 – 1)
= 45.68

Systematic Risk (β) Estimation

Variance_SLB	224.77
Variance_{S&P 500}	28.18
Covariance_{SLB, S&P 500}	45.68
Correlation coefficient_{SLB, S&P 500}¹	0.57
β_SLB²	1.62
α_SLB³	-0.12%

Calculations

¹ Correlation coefficient_{SLB, S&P 500}
= Covariance_{SLB, S&P 500} ÷ (Standard deviation_SLB × Standard deviation_{S&P 500})
= 45.68 ÷ (14.99% × 5.31%)
= 0.57

² β_SLB
= Covariance_{SLB, S&P 500} ÷ Variance_{S&P 500}
= 45.68 ÷ 28.18
= 1.62

³ α_SLB
= Average_SLB – β_SLB × Average_{S&P 500}
= 1.67% – 1.62 × 1.11%
= -0.12%

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)	13.86%
Systematic risk (β) of Schlumberger Ltd. common stock	β_SLB	1.62

Expected rate of return on Schlumberger Ltd. common stock³	E(R_SLB)	19.43%

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_SLB) = R_F + β_SLB [E(R_M) – R_F]
= 4.90% + 1.62 [13.86% – 4.90%]
= 19.43%