Alphabet Inc. (NASDAQ:GOOG)

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 Alphabet Inc. common stock.

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

Rates of Return

Alphabet Inc., monthly rates of return

		Alphabet Inc. (GOOG)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_GOOG,t¹	Dividend_GOOG,t¹	R_GOOG,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$55.82			2,704.10
1.	Feb 28, 2019	$56.00		0.32%	2,784.49	2.97%
2.	Mar 31, 2019	$58.67		4.77%	2,834.40	1.79%
3.	Apr 30, 2019	$59.42		1.28%	2,945.83	3.93%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2023	$133.92		6.88%	4,567.80	8.92%
59.	Dec 31, 2023	$140.93		5.23%	4,769.83	4.42%
Average (R):				1.88%		1.11%
Standard deviation:				7.83%		5.31%

		Alphabet Inc. (GOOG)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_GOOG,t¹	Dividend_GOOG,t¹	R_GOOG,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$55.82			2,704.10
1.	Feb 28, 2019	$56.00		0.32%	2,784.49	2.97%
2.	Mar 31, 2019	$58.67		4.77%	2,834.40	1.79%
3.	Apr 30, 2019	$59.42		1.28%	2,945.83	3.93%
4.	May 31, 2019	$55.18		-7.14%	2,752.06	-6.58%
5.	Jun 30, 2019	$54.05		-2.05%	2,941.76	6.89%
6.	Jul 31, 2019	$60.83		12.54%	2,980.38	1.31%
7.	Aug 31, 2019	$59.41		-2.33%	2,926.46	-1.81%
8.	Sep 30, 2019	$60.95		2.59%	2,976.74	1.72%
9.	Oct 31, 2019	$63.01		3.38%	3,037.56	2.04%
10.	Nov 30, 2019	$65.25		3.55%	3,140.98	3.40%
11.	Dec 31, 2019	$66.85		2.45%	3,230.78	2.86%
12.	Jan 31, 2020	$71.71		7.27%	3,225.52	-0.16%
13.	Feb 29, 2020	$66.97		-6.61%	2,954.22	-8.41%
14.	Mar 31, 2020	$58.14		-13.19%	2,584.59	-12.51%
15.	Apr 30, 2020	$67.43		15.98%	2,912.43	12.68%
16.	May 31, 2020	$71.45		5.96%	3,044.31	4.53%
17.	Jun 30, 2020	$70.68		-1.08%	3,100.29	1.84%
18.	Jul 31, 2020	$74.15		4.91%	3,271.12	5.51%
19.	Aug 31, 2020	$81.71		10.20%	3,500.31	7.01%
20.	Sep 30, 2020	$73.48		-10.07%	3,363.00	-3.92%
21.	Oct 31, 2020	$81.05		10.30%	3,269.96	-2.77%
22.	Nov 30, 2020	$88.04		8.62%	3,621.63	10.75%
23.	Dec 31, 2020	$87.59		-0.51%	3,756.07	3.71%
24.	Jan 31, 2021	$91.79		4.80%	3,714.24	-1.11%
25.	Feb 28, 2021	$101.84		10.95%	3,811.15	2.61%
26.	Mar 31, 2021	$103.43		1.56%	3,972.89	4.24%
27.	Apr 30, 2021	$120.51		16.51%	4,181.17	5.24%
28.	May 31, 2021	$120.58		0.06%	4,204.11	0.55%
29.	Jun 30, 2021	$125.32		3.93%	4,297.50	2.22%
30.	Jul 31, 2021	$135.22		7.90%	4,395.26	2.27%
31.	Aug 31, 2021	$145.46		7.57%	4,522.68	2.90%
32.	Sep 30, 2021	$133.27		-8.38%	4,307.54	-4.76%
33.	Oct 31, 2021	$148.27		11.26%	4,605.38	6.91%
34.	Nov 30, 2021	$142.45		-3.93%	4,567.00	-0.83%
35.	Dec 31, 2021	$144.68		1.57%	4,766.18	4.36%
36.	Jan 31, 2022	$135.70		-6.21%	4,515.55	-5.26%
37.	Feb 28, 2022	$134.89		-0.60%	4,373.94	-3.14%
38.	Mar 31, 2022	$139.65		3.53%	4,530.41	3.58%
39.	Apr 30, 2022	$114.97		-17.67%	4,131.93	-8.80%
40.	May 31, 2022	$114.04		-0.81%	4,132.15	0.01%
41.	Jun 30, 2022	$109.37		-4.10%	3,785.38	-8.39%
42.	Jul 31, 2022	$116.64		6.65%	4,130.29	9.11%
43.	Aug 31, 2022	$109.15		-6.42%	3,955.00	-4.24%
44.	Sep 30, 2022	$96.15		-11.91%	3,585.62	-9.34%
45.	Oct 31, 2022	$94.66		-1.55%	3,871.98	7.99%
46.	Nov 30, 2022	$101.45		7.17%	4,080.11	5.38%
47.	Dec 31, 2022	$88.73		-12.54%	3,839.50	-5.90%
48.	Jan 31, 2023	$99.87		12.55%	4,076.60	6.18%
49.	Feb 28, 2023	$90.30		-9.58%	3,970.15	-2.61%
50.	Mar 31, 2023	$104.00		15.17%	4,109.31	3.51%
51.	Apr 30, 2023	$108.22		4.06%	4,169.48	1.46%
52.	May 31, 2023	$123.37		14.00%	4,179.83	0.25%
53.	Jun 30, 2023	$120.97		-1.95%	4,376.86	4.71%
54.	Jul 31, 2023	$133.11		10.04%	4,588.96	4.85%
55.	Aug 31, 2023	$137.35		3.19%	4,507.66	-1.77%
56.	Sep 30, 2023	$131.85		-4.00%	4,288.05	-4.87%
57.	Oct 31, 2023	$125.30		-4.97%	4,193.80	-2.20%
58.	Nov 30, 2023	$133.92		6.88%	4,567.80	8.92%
59.	Dec 31, 2023	$140.93		5.23%	4,769.83	4.42%
Average (R):				1.88%		1.11%
Standard deviation:				7.83%		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 GOOG during period t

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

Variance and Covariance

Alphabet Inc., calculation of variance and covariance of returns

t	Date	R_GOOG,t	R_{S&P 500,t}	(R_GOOG,t–R_GOOG)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_GOOG,t–R_GOOG)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	0.32%	2.97%	2.44	3.49	-2.91
2.	Mar 31, 2019	4.77%	1.79%	8.32	0.47	1.98
3.	Apr 30, 2019	1.28%	3.93%	0.37	7.98	-1.71
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2023	6.88%	8.92%	24.96	61.03	39.03
59.	Dec 31, 2023	5.23%	4.42%	11.23	11.00	11.12
Total (Σ):				3,552.13	1,634.30	1,765.97

t	Date	R_GOOG,t	R_{S&P 500,t}	(R_GOOG,t–R_GOOG)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_GOOG,t–R_GOOG)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	0.32%	2.97%	2.44	3.49	-2.91
2.	Mar 31, 2019	4.77%	1.79%	8.32	0.47	1.98
3.	Apr 30, 2019	1.28%	3.93%	0.37	7.98	-1.71
4.	May 31, 2019	-7.14%	-6.58%	81.34	59.04	69.30
5.	Jun 30, 2019	-2.05%	6.89%	15.45	33.49	-22.75
6.	Jul 31, 2019	12.54%	1.31%	113.65	0.04	2.21
7.	Aug 31, 2019	-2.33%	-1.81%	17.79	8.50	12.29
8.	Sep 30, 2019	2.59%	1.72%	0.50	0.37	0.43
9.	Oct 31, 2019	3.38%	2.04%	2.24	0.88	1.40
10.	Nov 30, 2019	3.55%	3.40%	2.79	5.28	3.84
11.	Dec 31, 2019	2.45%	2.86%	0.32	3.07	1.00
12.	Jan 31, 2020	7.27%	-0.16%	29.02	1.61	-6.83
13.	Feb 29, 2020	-6.61%	-8.41%	72.14	90.57	80.83
14.	Mar 31, 2020	-13.19%	-12.51%	227.06	185.44	205.20
15.	Apr 30, 2020	15.98%	12.68%	198.68	134.06	163.20
16.	May 31, 2020	5.96%	4.53%	16.63	11.71	13.96
17.	Jun 30, 2020	-1.08%	1.84%	8.77	0.54	-2.17
18.	Jul 31, 2020	4.91%	5.51%	9.16	19.40	13.33
19.	Aug 31, 2020	10.20%	7.01%	69.09	34.82	49.05
20.	Sep 30, 2020	-10.07%	-3.92%	142.94	25.29	60.12
21.	Oct 31, 2020	10.30%	-2.77%	70.87	15.00	-32.60
22.	Nov 30, 2020	8.62%	10.75%	45.44	93.10	65.04
23.	Dec 31, 2020	-0.51%	3.71%	5.73	6.79	-6.24
24.	Jan 31, 2021	4.80%	-1.11%	8.48	4.93	-6.46
25.	Feb 28, 2021	10.95%	2.61%	82.18	2.26	13.63
26.	Mar 31, 2021	1.56%	4.24%	0.10	9.85	-1.01
27.	Apr 30, 2021	16.51%	5.24%	214.04	17.11	60.52
28.	May 31, 2021	0.06%	0.55%	3.33	0.31	1.02
29.	Jun 30, 2021	3.93%	2.22%	4.19	1.24	2.28
30.	Jul 31, 2021	7.90%	2.27%	36.20	1.37	7.03
31.	Aug 31, 2021	7.57%	2.90%	32.37	3.22	10.20
32.	Sep 30, 2021	-8.38%	-4.76%	105.34	34.37	60.17
33.	Oct 31, 2021	11.26%	6.91%	87.83	33.74	54.44
34.	Nov 30, 2021	-3.93%	-0.83%	33.74	3.76	11.26
35.	Dec 31, 2021	1.57%	4.36%	0.10	10.60	-1.04
36.	Jan 31, 2022	-6.21%	-5.26%	65.45	40.51	51.49
37.	Feb 28, 2022	-0.60%	-3.14%	6.15	17.99	10.52
38.	Mar 31, 2022	3.53%	3.58%	2.71	6.11	4.07
39.	Apr 30, 2022	-17.67%	-8.80%	382.44	98.04	193.64
40.	May 31, 2022	-0.81%	0.01%	7.25	1.21	2.96
41.	Jun 30, 2022	-4.10%	-8.39%	35.74	90.21	56.78
42.	Jul 31, 2022	6.65%	9.11%	22.69	64.09	38.14
43.	Aug 31, 2022	-6.42%	-4.24%	68.97	28.62	44.43
44.	Sep 30, 2022	-11.91%	-9.34%	190.26	109.11	144.08
45.	Oct 31, 2022	-1.55%	7.99%	11.79	47.34	-23.62
46.	Nov 30, 2022	7.17%	5.38%	27.98	18.23	22.58
47.	Dec 31, 2022	-12.54%	-5.90%	207.98	49.04	100.99
48.	Jan 31, 2023	12.55%	6.18%	113.88	25.70	54.10
49.	Feb 28, 2023	-9.58%	-2.61%	131.47	13.82	42.62
50.	Mar 31, 2023	15.17%	3.51%	176.58	5.76	31.88
51.	Apr 30, 2023	4.06%	1.46%	4.73	0.13	0.78
52.	May 31, 2023	14.00%	0.25%	146.79	0.74	-10.39
53.	Jun 30, 2023	-1.95%	4.71%	14.66	13.02	-13.81
54.	Jul 31, 2023	10.04%	4.85%	66.46	13.99	30.49
55.	Aug 31, 2023	3.19%	-1.77%	1.69	8.28	-3.75
56.	Sep 30, 2023	-4.00%	-4.87%	34.67	35.73	35.20
57.	Oct 31, 2023	-4.97%	-2.20%	46.94	10.92	22.64
58.	Nov 30, 2023	6.88%	8.92%	24.96	61.03	39.03
59.	Dec 31, 2023	5.23%	4.42%	11.23	11.00	11.12
Total (Σ):				3,552.13	1,634.30	1,765.97

Show all

Variance_GOOG = Σ(R_GOOG,t–R_GOOG)² ÷ (59 – 1)
= 3,552.13 ÷ (59 – 1)
= 61.24

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_{GOOG, S&P 500} = Σ(R_GOOG,t–R_GOOG)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 1,765.97 ÷ (59 – 1)
= 30.45

Systematic Risk (β) Estimation

Variance_GOOG	61.24
Variance_{S&P 500}	28.18
Covariance_{GOOG, S&P 500}	30.45
Correlation coefficient_{GOOG, S&P 500}¹	0.73
β_GOOG²	1.08
α_GOOG³	0.69%

Calculations

¹ Correlation coefficient_{GOOG, S&P 500}
= Covariance_{GOOG, S&P 500} ÷ (Standard deviation_GOOG × Standard deviation_{S&P 500})
= 30.45 ÷ (7.83% × 5.31%)
= 0.73

² β_GOOG
= Covariance_{GOOG, S&P 500} ÷ Variance_{S&P 500}
= 30.45 ÷ 28.18
= 1.08

³ α_GOOG
= Average_GOOG – β_GOOG × Average_{S&P 500}
= 1.88% – 1.08 × 1.11%
= 0.69%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.81%
Expected rate of return on market portfolio²	E(R_M)	13.54%
Systematic risk (β) of Alphabet Inc. common stock	β_GOOG	1.08

Expected rate of return on Alphabet Inc. common stock³	E(R_GOOG)	14.24%

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_GOOG) = R_F + β_GOOG [E(R_M) – R_F]
= 4.81% + 1.08 [13.54% – 4.81%]
= 14.24%