Intuitive Surgical Inc. (NASDAQ:ISRG)

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 Intuitive Surgical Inc. common stock.

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

Rates of Return

Intuitive Surgical Inc., monthly rates of return

		Intuitive Surgical Inc. (ISRG)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_ISRG,t¹	Dividend_ISRG,t¹	R_ISRG,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2020	$186.59			3,225.52
1.	Feb 29, 2020	$177.99		-4.61%	2,954.22	-8.41%
2.	Mar 31, 2020	$165.07		-7.26%	2,584.59	-12.51%
3.	Apr 30, 2020	$170.29		3.16%	2,912.43	12.68%
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58.	Nov 30, 2024	$542.00		7.57%	6,032.38	5.73%
59.	Dec 31, 2024	$521.96		-3.70%	5,881.63	-2.50%
Average (R):				2.26%		1.16%
Standard deviation:				10.19%		5.28%

		Intuitive Surgical Inc. (ISRG)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_ISRG,t¹	Dividend_ISRG,t¹	R_ISRG,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2020	$186.59			3,225.52
1.	Feb 29, 2020	$177.99		-4.61%	2,954.22	-8.41%
2.	Mar 31, 2020	$165.07		-7.26%	2,584.59	-12.51%
3.	Apr 30, 2020	$170.29		3.16%	2,912.43	12.68%
4.	May 31, 2020	$193.34		13.54%	3,044.31	4.53%
5.	Jun 30, 2020	$189.94		-1.76%	3,100.29	1.84%
6.	Jul 31, 2020	$228.48		20.29%	3,271.12	5.51%
7.	Aug 31, 2020	$243.61		6.62%	3,500.31	7.01%
8.	Sep 30, 2020	$236.51		-2.91%	3,363.00	-3.92%
9.	Oct 31, 2020	$222.36		-5.98%	3,269.96	-2.77%
10.	Nov 30, 2020	$242.02		8.84%	3,621.63	10.75%
11.	Dec 31, 2020	$272.70		12.68%	3,756.07	3.71%
12.	Jan 31, 2021	$249.21		-8.61%	3,714.24	-1.11%
13.	Feb 28, 2021	$245.60		-1.45%	3,811.15	2.61%
14.	Mar 31, 2021	$246.31		0.29%	3,972.89	4.24%
15.	Apr 30, 2021	$288.33		17.06%	4,181.17	5.24%
16.	May 31, 2021	$280.73		-2.64%	4,204.11	0.55%
17.	Jun 30, 2021	$306.55		9.20%	4,297.50	2.22%
18.	Jul 31, 2021	$330.49		7.81%	4,395.26	2.27%
19.	Aug 31, 2021	$351.19		6.26%	4,522.68	2.90%
20.	Sep 30, 2021	$331.38		-5.64%	4,307.54	-4.76%
21.	Oct 31, 2021	$361.13		8.98%	4,605.38	6.91%
22.	Nov 30, 2021	$324.34		-10.19%	4,567.00	-0.83%
23.	Dec 31, 2021	$359.30		10.78%	4,766.18	4.36%
24.	Jan 31, 2022	$284.18		-20.91%	4,515.55	-5.26%
25.	Feb 28, 2022	$290.33		2.16%	4,373.94	-3.14%
26.	Mar 31, 2022	$301.68		3.91%	4,530.41	3.58%
27.	Apr 30, 2022	$239.30		-20.68%	4,131.93	-8.80%
28.	May 31, 2022	$227.64		-4.87%	4,132.15	0.01%
29.	Jun 30, 2022	$200.71		-11.83%	3,785.38	-8.39%
30.	Jul 31, 2022	$230.17		14.68%	4,130.29	9.11%
31.	Aug 31, 2022	$205.74		-10.61%	3,955.00	-4.24%
32.	Sep 30, 2022	$187.44		-8.89%	3,585.62	-9.34%
33.	Oct 31, 2022	$246.47		31.49%	3,871.98	7.99%
34.	Nov 30, 2022	$270.39		9.71%	4,080.11	5.38%
35.	Dec 31, 2022	$265.35		-1.86%	3,839.50	-5.90%
36.	Jan 31, 2023	$245.69		-7.41%	4,076.60	6.18%
37.	Feb 28, 2023	$229.39		-6.63%	3,970.15	-2.61%
38.	Mar 31, 2023	$255.47		11.37%	4,109.31	3.51%
39.	Apr 30, 2023	$301.22		17.91%	4,169.48	1.46%
40.	May 31, 2023	$307.84		2.20%	4,179.83	0.25%
41.	Jun 30, 2023	$341.94		11.08%	4,376.86	4.71%
42.	Jul 31, 2023	$324.40		-5.13%	4,588.96	4.85%
43.	Aug 31, 2023	$312.68		-3.61%	4,507.66	-1.77%
44.	Sep 30, 2023	$292.29		-6.52%	4,288.05	-4.87%
45.	Oct 31, 2023	$262.22		-10.29%	4,193.80	-2.20%
46.	Nov 30, 2023	$310.84		18.54%	4,567.80	8.92%
47.	Dec 31, 2023	$337.36		8.53%	4,769.83	4.42%
48.	Jan 31, 2024	$378.22		12.11%	4,845.65	1.59%
49.	Feb 29, 2024	$385.60		1.95%	5,096.27	5.17%
50.	Mar 31, 2024	$399.09		3.50%	5,254.35	3.10%
51.	Apr 30, 2024	$370.62		-7.13%	5,035.69	-4.16%
52.	May 31, 2024	$402.12		8.50%	5,277.51	4.80%
53.	Jun 30, 2024	$444.85		10.63%	5,460.48	3.47%
54.	Jul 31, 2024	$444.61		-0.05%	5,522.30	1.13%
55.	Aug 31, 2024	$492.63		10.80%	5,648.40	2.28%
56.	Sep 30, 2024	$491.27		-0.28%	5,762.48	2.02%
57.	Oct 31, 2024	$503.84		2.56%	5,705.45	-0.99%
58.	Nov 30, 2024	$542.00		7.57%	6,032.38	5.73%
59.	Dec 31, 2024	$521.96		-3.70%	5,881.63	-2.50%
Average (R):				2.26%		1.16%
Standard deviation:				10.19%		5.28%

Show all

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

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

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

Variance and Covariance

Intuitive Surgical Inc., calculation of variance and covariance of returns

t	Date	R_ISRG,t	R_{S&P 500,t}	(R_ISRG,t–R_ISRG)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ISRG,t–R_ISRG)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2020	-4.61%	-8.41%	47.16	91.63	65.74
2.	Mar 31, 2020	-7.26%	-12.51%	90.57	186.96	130.13
3.	Apr 30, 2020	3.16%	12.68%	0.82	132.78	10.42
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58.	Nov 30, 2024	7.57%	5.73%	28.26	20.87	24.29
59.	Dec 31, 2024	-3.70%	-2.50%	35.47	13.40	21.80
Total (Σ):				6,018.47	1,618.62	2,223.06

t	Date	R_ISRG,t	R_{S&P 500,t}	(R_ISRG,t–R_ISRG)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ISRG,t–R_ISRG)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2020	-4.61%	-8.41%	47.16	91.63	65.74
2.	Mar 31, 2020	-7.26%	-12.51%	90.57	186.96	130.13
3.	Apr 30, 2020	3.16%	12.68%	0.82	132.78	10.42
4.	May 31, 2020	13.54%	4.53%	127.18	11.34	37.97
5.	Jun 30, 2020	-1.76%	1.84%	16.13	0.46	-2.72
6.	Jul 31, 2020	20.29%	5.51%	325.17	18.91	78.42
7.	Aug 31, 2020	6.62%	7.01%	19.04	34.17	25.51
8.	Sep 30, 2020	-2.91%	-3.92%	26.76	25.85	26.30
9.	Oct 31, 2020	-5.98%	-2.77%	67.91	15.43	32.37
10.	Nov 30, 2020	8.84%	10.75%	43.34	92.03	63.16
11.	Dec 31, 2020	12.68%	3.71%	108.54	6.51	26.58
12.	Jan 31, 2021	-8.61%	-1.11%	118.20	5.18	24.73
13.	Feb 28, 2021	-1.45%	2.61%	13.74	2.10	-5.37
14.	Mar 31, 2021	0.29%	4.24%	3.88	9.50	-6.07
15.	Apr 30, 2021	17.06%	5.24%	219.09	16.66	60.41
16.	May 31, 2021	-2.64%	0.55%	23.95	0.38	3.00
17.	Jun 30, 2021	9.20%	2.22%	48.15	1.12	7.36
18.	Jul 31, 2021	7.81%	2.27%	30.82	1.24	6.18
19.	Aug 31, 2021	6.26%	2.90%	16.04	3.02	6.96
20.	Sep 30, 2021	-5.64%	-4.76%	62.39	35.02	46.75
21.	Oct 31, 2021	8.98%	6.91%	45.15	33.10	38.66
22.	Nov 30, 2021	-10.19%	-0.83%	154.89	3.98	24.82
23.	Dec 31, 2021	10.78%	4.36%	72.60	10.24	27.27
24.	Jan 31, 2022	-20.91%	-5.26%	536.64	41.21	148.72
25.	Feb 28, 2022	2.16%	-3.14%	0.01	18.47	0.40
26.	Mar 31, 2022	3.91%	3.58%	2.73	5.84	3.99
27.	Apr 30, 2022	-20.68%	-8.80%	526.05	99.14	228.37
28.	May 31, 2022	-4.87%	0.01%	50.85	1.34	8.24
29.	Jun 30, 2022	-11.83%	-8.39%	198.48	91.26	134.59
30.	Jul 31, 2022	14.68%	9.11%	154.25	63.21	98.74
31.	Aug 31, 2022	-10.61%	-4.24%	165.69	29.22	69.58
32.	Sep 30, 2022	-8.89%	-9.34%	124.39	110.27	117.11
33.	Oct 31, 2022	31.49%	7.99%	854.66	46.58	199.53
34.	Nov 30, 2022	9.71%	5.38%	55.46	17.76	31.38
35.	Dec 31, 2022	-1.86%	-5.90%	16.99	49.82	29.10
36.	Jan 31, 2023	-7.41%	6.18%	93.46	25.14	-48.47
37.	Feb 28, 2023	-6.63%	-2.61%	79.08	14.23	33.55
38.	Mar 31, 2023	11.37%	3.51%	83.01	5.49	21.36
39.	Apr 30, 2023	17.91%	1.46%	244.92	0.09	4.74
40.	May 31, 2023	2.20%	0.25%	0.00	0.83	0.06
41.	Jun 30, 2023	11.08%	4.71%	77.77	12.62	31.33
42.	Jul 31, 2023	-5.13%	4.85%	54.58	13.58	-27.22
43.	Aug 31, 2023	-3.61%	-1.77%	34.47	8.60	17.22
44.	Sep 30, 2023	-6.52%	-4.87%	77.07	36.40	52.97
45.	Oct 31, 2023	-10.29%	-2.20%	157.40	11.28	42.14
46.	Nov 30, 2023	18.54%	8.92%	265.15	60.17	126.31
47.	Dec 31, 2023	8.53%	4.42%	39.36	10.64	20.46
48.	Jan 31, 2024	12.11%	1.59%	97.09	0.18	4.22
49.	Feb 29, 2024	1.95%	5.17%	0.09	16.09	-1.23
50.	Mar 31, 2024	3.50%	3.10%	1.54	3.77	2.41
51.	Apr 30, 2024	-7.13%	-4.16%	88.21	28.33	49.99
52.	May 31, 2024	8.50%	4.80%	38.95	13.26	22.72
53.	Jun 30, 2024	10.63%	3.47%	70.02	5.32	19.29
54.	Jul 31, 2024	-0.05%	1.13%	5.35	0.00	0.07
55.	Aug 31, 2024	10.80%	2.28%	72.97	1.26	9.59
56.	Sep 30, 2024	-0.28%	2.02%	6.42	0.74	-2.18
57.	Oct 31, 2024	2.56%	-0.99%	0.09	4.63	-0.65
58.	Nov 30, 2024	7.57%	5.73%	28.26	20.87	24.29
59.	Dec 31, 2024	-3.70%	-2.50%	35.47	13.40	21.80
Total (Σ):				6,018.47	1,618.62	2,223.06

Show all

Variance_ISRG = Σ(R_ISRG,t–R_ISRG)² ÷ (59 – 1)
= 6,018.47 ÷ (59 – 1)
= 103.77

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91

Covariance_{ISRG, S&P 500} = Σ(R_ISRG,t–R_ISRG)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 2,223.06 ÷ (59 – 1)
= 38.33

Systematic Risk (β) Estimation

Variance_ISRG	103.77
Variance_{S&P 500}	27.91
Covariance_{ISRG, S&P 500}	38.33
Correlation coefficient_{ISRG, S&P 500}¹	0.71
β_ISRG²	1.37
α_ISRG³	0.66%

Calculations

¹ Correlation coefficient_{ISRG, S&P 500}
= Covariance_{ISRG, S&P 500} ÷ (Standard deviation_ISRG × Standard deviation_{S&P 500})
= 38.33 ÷ (10.19% × 5.28%)
= 0.71

² β_ISRG
= Covariance_{ISRG, S&P 500} ÷ Variance_{S&P 500}
= 38.33 ÷ 27.91
= 1.37

³ α_ISRG
= Average_ISRG – β_ISRG × Average_{S&P 500}
= 2.26% – 1.37 × 1.16%
= 0.66%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.78%
Expected rate of return on market portfolio²	E(R_M)	14.95%
Systematic risk (β) of Intuitive Surgical Inc. common stock	β_ISRG	1.37

Expected rate of return on Intuitive Surgical Inc. common stock³	E(R_ISRG)	18.75%

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_ISRG) = R_F + β_ISRG [E(R_M) – R_F]
= 4.78% + 1.37 [14.95% – 4.78%]
= 18.75%