Texas Instruments Inc. (NASDAQ:TXN)

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 Texas Instruments Inc. common stock.

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

Rates of Return

Texas Instruments Inc., monthly rates of return

		Texas Instruments Inc. (TXN)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_TXN,t¹	Dividend_TXN,t¹	R_TXN,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$100.68			2,704.10
1.	Feb 28, 2019	$105.78		5.07%	2,784.49	2.97%
2.	Mar 31, 2019	$106.07		0.27%	2,834.40	1.79%
3.	Apr 30, 2019	$117.83		11.09%	2,945.83	3.93%
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58.	Nov 30, 2023	$152.71		7.53%	4,567.80	8.92%
59.	Dec 31, 2023	$170.46		11.62%	4,769.83	4.42%
Average (R):				1.38%		1.11%
Standard deviation:				7.30%		5.31%

		Texas Instruments Inc. (TXN)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_TXN,t¹	Dividend_TXN,t¹	R_TXN,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$100.68			2,704.10
1.	Feb 28, 2019	$105.78		5.07%	2,784.49	2.97%
2.	Mar 31, 2019	$106.07		0.27%	2,834.40	1.79%
3.	Apr 30, 2019	$117.83		11.09%	2,945.83	3.93%
4.	May 31, 2019	$104.31	$0.77	-10.82%	2,752.06	-6.58%
5.	Jun 30, 2019	$114.76		10.02%	2,941.76	6.89%
6.	Jul 31, 2019	$125.01	$0.77	9.60%	2,980.38	1.31%
7.	Aug 31, 2019	$123.75		-1.01%	2,926.46	-1.81%
8.	Sep 30, 2019	$129.24		4.44%	2,976.74	1.72%
9.	Oct 31, 2019	$117.99	$0.90	-8.01%	3,037.56	2.04%
10.	Nov 30, 2019	$120.21		1.88%	3,140.98	3.40%
11.	Dec 31, 2019	$128.29		6.72%	3,230.78	2.86%
12.	Jan 31, 2020	$120.65	$0.90	-5.25%	3,225.52	-0.16%
13.	Feb 29, 2020	$114.14		-5.40%	2,954.22	-8.41%
14.	Mar 31, 2020	$99.93		-12.45%	2,584.59	-12.51%
15.	Apr 30, 2020	$116.07		16.15%	2,912.43	12.68%
16.	May 31, 2020	$118.74	$0.90	3.08%	3,044.31	4.53%
17.	Jun 30, 2020	$126.97		6.93%	3,100.29	1.84%
18.	Jul 31, 2020	$127.55	$0.90	1.17%	3,271.12	5.51%
19.	Aug 31, 2020	$142.15		11.45%	3,500.31	7.01%
20.	Sep 30, 2020	$142.79		0.45%	3,363.00	-3.92%
21.	Oct 31, 2020	$144.59	$1.02	1.97%	3,269.96	-2.77%
22.	Nov 30, 2020	$161.25		11.52%	3,621.63	10.75%
23.	Dec 31, 2020	$164.13		1.79%	3,756.07	3.71%
24.	Jan 31, 2021	$165.69	$1.02	1.57%	3,714.24	-1.11%
25.	Feb 28, 2021	$172.27		3.97%	3,811.15	2.61%
26.	Mar 31, 2021	$188.99		9.71%	3,972.89	4.24%
27.	Apr 30, 2021	$180.51	$1.02	-3.95%	4,181.17	5.24%
28.	May 31, 2021	$189.82		5.16%	4,204.11	0.55%
29.	Jun 30, 2021	$192.30		1.31%	4,297.50	2.22%
30.	Jul 31, 2021	$190.62	$1.02	-0.34%	4,395.26	2.27%
31.	Aug 31, 2021	$190.91		0.15%	4,522.68	2.90%
32.	Sep 30, 2021	$192.21		0.68%	4,307.54	-4.76%
33.	Oct 31, 2021	$187.48	$1.15	-1.86%	4,605.38	6.91%
34.	Nov 30, 2021	$192.37		2.61%	4,567.00	-0.83%
35.	Dec 31, 2021	$188.47		-2.03%	4,766.18	4.36%
36.	Jan 31, 2022	$179.49	$1.15	-4.15%	4,515.55	-5.26%
37.	Feb 28, 2022	$169.99		-5.29%	4,373.94	-3.14%
38.	Mar 31, 2022	$183.48		7.94%	4,530.41	3.58%
39.	Apr 30, 2022	$170.25		-7.21%	4,131.93	-8.80%
40.	May 31, 2022	$176.76	$1.15	4.50%	4,132.15	0.01%
41.	Jun 30, 2022	$153.65		-13.07%	3,785.38	-8.39%
42.	Jul 31, 2022	$178.89	$1.15	17.18%	4,130.29	9.11%
43.	Aug 31, 2022	$165.21		-7.65%	3,955.00	-4.24%
44.	Sep 30, 2022	$154.78		-6.31%	3,585.62	-9.34%
45.	Oct 31, 2022	$160.63	$1.24	4.58%	3,871.98	7.99%
46.	Nov 30, 2022	$180.46		12.35%	4,080.11	5.38%
47.	Dec 31, 2022	$165.22		-8.45%	3,839.50	-5.90%
48.	Jan 31, 2023	$177.21	$1.24	8.01%	4,076.60	6.18%
49.	Feb 28, 2023	$171.45		-3.25%	3,970.15	-2.61%
50.	Mar 31, 2023	$186.01		8.49%	4,109.31	3.51%
51.	Apr 30, 2023	$167.20		-10.11%	4,169.48	1.46%
52.	May 31, 2023	$173.88	$1.24	4.74%	4,179.83	0.25%
53.	Jun 30, 2023	$180.02		3.53%	4,376.86	4.71%
54.	Jul 31, 2023	$180.00	$1.24	0.68%	4,588.96	4.85%
55.	Aug 31, 2023	$168.06		-6.63%	4,507.66	-1.77%
56.	Sep 30, 2023	$159.01		-5.38%	4,288.05	-4.87%
57.	Oct 31, 2023	$142.01	$1.30	-9.87%	4,193.80	-2.20%
58.	Nov 30, 2023	$152.71		7.53%	4,567.80	8.92%
59.	Dec 31, 2023	$170.46		11.62%	4,769.83	4.42%
Average (R):				1.38%		1.11%
Standard deviation:				7.30%		5.31%

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 TXN during period t

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

Variance and Covariance

Texas Instruments Inc., calculation of variance and covariance of returns

t	Date	R_TXN,t	R_{S&P 500,t}	(R_TXN,t–R_TXN)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_TXN,t–R_TXN)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	5.07%	2.97%	13.59	3.49	6.88
2.	Mar 31, 2019	0.27%	1.79%	1.22	0.47	-0.76
3.	Apr 30, 2019	11.09%	3.93%	94.24	7.98	27.43
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58.	Nov 30, 2023	7.53%	8.92%	37.89	61.03	48.09
59.	Dec 31, 2023	11.62%	4.42%	104.94	11.00	33.98
Total (Σ):				3,089.71	1,634.30	1,704.50

t	Date	R_TXN,t	R_{S&P 500,t}	(R_TXN,t–R_TXN)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_TXN,t–R_TXN)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	5.07%	2.97%	13.59	3.49	6.88
2.	Mar 31, 2019	0.27%	1.79%	1.22	0.47	-0.76
3.	Apr 30, 2019	11.09%	3.93%	94.24	7.98	27.43
4.	May 31, 2019	-10.82%	-6.58%	148.84	59.04	93.74
5.	Jun 30, 2019	10.02%	6.89%	74.63	33.49	50.00
6.	Jul 31, 2019	9.60%	1.31%	67.62	0.04	1.70
7.	Aug 31, 2019	-1.01%	-1.81%	5.70	8.50	6.96
8.	Sep 30, 2019	4.44%	1.72%	9.35	0.37	1.87
9.	Oct 31, 2019	-8.01%	2.04%	88.13	0.88	-8.80
10.	Nov 30, 2019	1.88%	3.40%	0.25	5.28	1.15
11.	Dec 31, 2019	6.72%	2.86%	28.54	3.07	9.37
12.	Jan 31, 2020	-5.25%	-0.16%	44.00	1.61	8.41
13.	Feb 29, 2020	-5.40%	-8.41%	45.90	90.57	64.48
14.	Mar 31, 2020	-12.45%	-12.51%	191.24	185.44	188.32
15.	Apr 30, 2020	16.15%	12.68%	218.21	134.06	171.04
16.	May 31, 2020	3.08%	4.53%	2.88	11.71	5.81
17.	Jun 30, 2020	6.93%	1.84%	30.82	0.54	4.07
18.	Jul 31, 2020	1.17%	5.51%	0.05	19.40	-0.94
19.	Aug 31, 2020	11.45%	7.01%	101.35	34.82	59.40
20.	Sep 30, 2020	0.45%	-3.92%	0.86	25.29	4.67
21.	Oct 31, 2020	1.97%	-2.77%	0.35	15.00	-2.31
22.	Nov 30, 2020	11.52%	10.75%	102.88	93.10	97.87
23.	Dec 31, 2020	1.79%	3.71%	0.17	6.79	1.06
24.	Jan 31, 2021	1.57%	-1.11%	0.04	4.93	-0.43
25.	Feb 28, 2021	3.97%	2.61%	6.72	2.26	3.90
26.	Mar 31, 2021	9.71%	4.24%	69.33	9.85	26.13
27.	Apr 30, 2021	-3.95%	5.24%	28.37	17.11	-22.03
28.	May 31, 2021	5.16%	0.55%	14.28	0.31	-2.11
29.	Jun 30, 2021	1.31%	2.22%	0.01	1.24	-0.08
30.	Jul 31, 2021	-0.34%	2.27%	2.97	1.37	-2.01
31.	Aug 31, 2021	0.15%	2.90%	1.51	3.22	-2.20
32.	Sep 30, 2021	0.68%	-4.76%	0.49	34.37	4.09
33.	Oct 31, 2021	-1.86%	6.91%	10.51	33.74	-18.83
34.	Nov 30, 2021	2.61%	-0.83%	1.51	3.76	-2.38
35.	Dec 31, 2021	-2.03%	4.36%	11.60	10.60	-11.09
36.	Jan 31, 2022	-4.15%	-5.26%	30.62	40.51	35.22
37.	Feb 28, 2022	-5.29%	-3.14%	44.52	17.99	28.30
38.	Mar 31, 2022	7.94%	3.58%	42.99	6.11	16.20
39.	Apr 30, 2022	-7.21%	-8.80%	73.79	98.04	85.05
40.	May 31, 2022	4.50%	0.01%	9.73	1.21	-3.43
41.	Jun 30, 2022	-13.07%	-8.39%	208.90	90.21	137.28
42.	Jul 31, 2022	17.18%	9.11%	249.52	64.09	126.46
43.	Aug 31, 2022	-7.65%	-4.24%	81.48	28.62	48.29
44.	Sep 30, 2022	-6.31%	-9.34%	59.17	109.11	80.35
45.	Oct 31, 2022	4.58%	7.99%	10.25	47.34	22.03
46.	Nov 30, 2022	12.35%	5.38%	120.25	18.23	46.82
47.	Dec 31, 2022	-8.45%	-5.90%	96.52	49.04	68.80
48.	Jan 31, 2023	8.01%	6.18%	43.93	25.70	33.60
49.	Feb 28, 2023	-3.25%	-2.61%	21.43	13.82	17.21
50.	Mar 31, 2023	8.49%	3.51%	50.59	5.76	17.07
51.	Apr 30, 2023	-10.11%	1.46%	132.06	0.13	-4.12
52.	May 31, 2023	4.74%	0.25%	11.27	0.74	-2.88
53.	Jun 30, 2023	3.53%	4.71%	4.63	13.02	7.76
54.	Jul 31, 2023	0.68%	4.85%	0.49	13.99	-2.62
55.	Aug 31, 2023	-6.63%	-1.77%	64.20	8.28	23.06
56.	Sep 30, 2023	-5.38%	-4.87%	45.75	35.73	40.44
57.	Oct 31, 2023	-9.87%	-2.20%	126.63	10.92	37.18
58.	Nov 30, 2023	7.53%	8.92%	37.89	61.03	48.09
59.	Dec 31, 2023	11.62%	4.42%	104.94	11.00	33.98
Total (Σ):				3,089.71	1,634.30	1,704.50

Show all

Variance_TXN = Σ(R_TXN,t–R_TXN)² ÷ (59 – 1)
= 3,089.71 ÷ (59 – 1)
= 53.27

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_{TXN, S&P 500} = Σ(R_TXN,t–R_TXN)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 1,704.50 ÷ (59 – 1)
= 29.39

Systematic Risk (β) Estimation

Variance_TXN	53.27
Variance_{S&P 500}	28.18
Covariance_{TXN, S&P 500}	29.39
Correlation coefficient_{TXN, S&P 500}¹	0.76
β_TXN²	1.04
α_TXN³	0.23%

Calculations

¹ Correlation coefficient_{TXN, S&P 500}
= Covariance_{TXN, S&P 500} ÷ (Standard deviation_TXN × Standard deviation_{S&P 500})
= 29.39 ÷ (7.30% × 5.31%)
= 0.76

² β_TXN
= Covariance_{TXN, S&P 500} ÷ Variance_{S&P 500}
= 29.39 ÷ 28.18
= 1.04

³ α_TXN
= Average_TXN – β_TXN × Average_{S&P 500}
= 1.38% – 1.04 × 1.11%
= 0.23%

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)	13.54%
Systematic risk (β) of Texas Instruments Inc. common stock	β_TXN	1.04

Expected rate of return on Texas Instruments Inc. common stock³	E(R_TXN)	13.92%

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_TXN) = R_F + β_TXN [E(R_M) – R_F]
= 4.90% + 1.04 [13.54% – 4.90%]
= 13.92%