Moderna Inc. (NASDAQ:MRNA)

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 Moderna Inc. common stock.

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

Rates of Return

Moderna Inc., monthly rates of return

		Moderna Inc. (MRNA)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_MRNA,t¹	Dividend_MRNA,t¹	R_MRNA,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Dec 31, 2018	$15.27			2,506.85
1.	Jan 31, 2019	$16.60		8.71%	2,704.10	7.87%
2.	Feb 28, 2019	$22.60		36.14%	2,784.49	2.97%
3.	Mar 31, 2019	$20.35		-9.96%	2,834.40	1.79%
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47.	Nov 30, 2022	$175.91		17.02%	4,080.11	5.38%
48.	Dec 31, 2022	$179.62		2.11%	3,839.50	-5.90%
Average (R):				8.38%		1.05%
Standard deviation:				28.25%		5.61%

		Moderna Inc. (MRNA)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_MRNA,t¹	Dividend_MRNA,t¹	R_MRNA,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Dec 31, 2018	$15.27			2,506.85
1.	Jan 31, 2019	$16.60		8.71%	2,704.10	7.87%
2.	Feb 28, 2019	$22.60		36.14%	2,784.49	2.97%
3.	Mar 31, 2019	$20.35		-9.96%	2,834.40	1.79%
4.	Apr 30, 2019	$26.03		27.91%	2,945.83	3.93%
5.	May 31, 2019	$20.78		-20.17%	2,752.06	-6.58%
6.	Jun 30, 2019	$14.64		-29.55%	2,941.76	6.89%
7.	Jul 31, 2019	$13.10		-10.52%	2,980.38	1.31%
8.	Aug 31, 2019	$15.73		20.08%	2,926.46	-1.81%
9.	Sep 30, 2019	$15.92		1.21%	2,976.74	1.72%
10.	Oct 31, 2019	$16.75		5.21%	3,037.56	2.04%
11.	Nov 30, 2019	$20.36		21.55%	3,140.98	3.40%
12.	Dec 31, 2019	$19.56		-3.93%	3,230.78	2.86%
13.	Jan 31, 2020	$20.51		4.86%	3,225.52	-0.16%
14.	Feb 29, 2020	$25.93		26.43%	2,954.22	-8.41%
15.	Mar 31, 2020	$29.95		15.50%	2,584.59	-12.51%
16.	Apr 30, 2020	$45.99		53.56%	2,912.43	12.68%
17.	May 31, 2020	$61.50		33.72%	3,044.31	4.53%
18.	Jun 30, 2020	$64.21		4.41%	3,100.29	1.84%
19.	Jul 31, 2020	$74.10		15.40%	3,271.12	5.51%
20.	Aug 31, 2020	$64.89		-12.43%	3,500.31	7.01%
21.	Sep 30, 2020	$70.75		9.03%	3,363.00	-3.92%
22.	Oct 31, 2020	$67.47		-4.64%	3,269.96	-2.77%
23.	Nov 30, 2020	$152.74		126.38%	3,621.63	10.75%
24.	Dec 31, 2020	$104.47		-31.60%	3,756.07	3.71%
25.	Jan 31, 2021	$173.16		65.75%	3,714.24	-1.11%
26.	Feb 28, 2021	$154.81		-10.60%	3,811.15	2.61%
27.	Mar 31, 2021	$130.95		-15.41%	3,972.89	4.24%
28.	Apr 30, 2021	$178.82		36.56%	4,181.17	5.24%
29.	May 31, 2021	$185.01		3.46%	4,204.11	0.55%
30.	Jun 30, 2021	$234.98		27.01%	4,297.50	2.22%
31.	Jul 31, 2021	$353.60		50.48%	4,395.26	2.27%
32.	Aug 31, 2021	$376.69		6.53%	4,522.68	2.90%
33.	Sep 30, 2021	$384.86		2.17%	4,307.54	-4.76%
34.	Oct 31, 2021	$345.21		-10.30%	4,605.38	6.91%
35.	Nov 30, 2021	$352.43		2.09%	4,567.00	-0.83%
36.	Dec 31, 2021	$253.98		-27.93%	4,766.18	4.36%
37.	Jan 31, 2022	$169.33		-33.33%	4,515.55	-5.26%
38.	Feb 28, 2022	$153.60		-9.29%	4,373.94	-3.14%
39.	Mar 31, 2022	$172.26		12.15%	4,530.41	3.58%
40.	Apr 30, 2022	$134.41		-21.97%	4,131.93	-8.80%
41.	May 31, 2022	$145.33		8.12%	4,132.15	0.01%
42.	Jun 30, 2022	$142.85		-1.71%	3,785.38	-8.39%
43.	Jul 31, 2022	$164.09		14.87%	4,130.29	9.11%
44.	Aug 31, 2022	$132.27		-19.39%	3,955.00	-4.24%
45.	Sep 30, 2022	$118.25		-10.60%	3,585.62	-9.34%
46.	Oct 31, 2022	$150.33		27.13%	3,871.98	7.99%
47.	Nov 30, 2022	$175.91		17.02%	4,080.11	5.38%
48.	Dec 31, 2022	$179.62		2.11%	3,839.50	-5.90%
Average (R):				8.38%		1.05%
Standard deviation:				28.25%		5.61%

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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 MRNA during period t

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

Variance and Covariance

Moderna Inc., calculation of variance and covariance of returns

t	Date	R_MRNA,t	R_{S&P 500,t}	(R_MRNA,t–R_MRNA)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_MRNA,t–R_MRNA)×(R_{S&P 500,t}–R_{S&P 500})
1.	Jan 31, 2019	8.71%	7.87%	0.11	46.53	2.25
2.	Feb 28, 2019	36.14%	2.97%	770.89	3.71	53.46
3.	Mar 31, 2019	-9.96%	1.79%	336.19	0.56	-13.66
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47.	Nov 30, 2022	17.02%	5.38%	74.58	18.73	37.38
48.	Dec 31, 2022	2.11%	-5.90%	39.32	48.23	43.55
Total (Σ):				37,518.58	1,479.77	2,524.34

t	Date	R_MRNA,t	R_{S&P 500,t}	(R_MRNA,t–R_MRNA)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_MRNA,t–R_MRNA)×(R_{S&P 500,t}–R_{S&P 500})
1.	Jan 31, 2019	8.71%	7.87%	0.11	46.53	2.25
2.	Feb 28, 2019	36.14%	2.97%	770.89	3.71	53.46
3.	Mar 31, 2019	-9.96%	1.79%	336.19	0.56	-13.66
4.	Apr 30, 2019	27.91%	3.93%	381.49	8.32	56.33
5.	May 31, 2019	-20.17%	-6.58%	815.03	58.14	217.69
6.	Jun 30, 2019	-29.55%	6.89%	1,438.48	34.17	-221.71
7.	Jul 31, 2019	-10.52%	1.31%	357.16	0.07	-5.02
8.	Aug 31, 2019	20.08%	-1.81%	136.81	8.16	-33.41
9.	Sep 30, 2019	1.21%	1.72%	51.43	0.45	-4.81
10.	Oct 31, 2019	5.21%	2.04%	10.02	0.99	-3.15
11.	Nov 30, 2019	21.55%	3.40%	173.52	5.56	31.05
12.	Dec 31, 2019	-3.93%	2.86%	151.51	3.28	-22.30
13.	Jan 31, 2020	4.86%	-0.16%	12.41	1.46	4.26
14.	Feb 29, 2020	26.43%	-8.41%	325.67	89.46	-170.69
15.	Mar 31, 2020	15.50%	-12.51%	50.75	183.85	-96.59
16.	Apr 30, 2020	53.56%	12.68%	2,040.89	135.42	525.72
17.	May 31, 2020	33.72%	4.53%	642.37	12.12	88.22
18.	Jun 30, 2020	4.41%	1.84%	15.79	0.63	-3.14
19.	Jul 31, 2020	15.40%	5.51%	49.32	19.92	31.34
20.	Aug 31, 2020	-12.43%	7.01%	433.01	35.51	-124.00
21.	Sep 30, 2020	9.03%	-3.92%	0.42	24.70	-3.24
22.	Oct 31, 2020	-4.64%	-2.77%	169.41	14.55	49.64
23.	Nov 30, 2020	126.38%	10.75%	13,924.57	94.23	1,145.48
24.	Dec 31, 2020	-31.60%	3.71%	1,598.59	7.10	-106.54
25.	Jan 31, 2021	65.75%	-1.11%	3,291.46	4.67	-123.98
26.	Feb 28, 2021	-10.60%	2.61%	360.12	2.44	-29.64
27.	Mar 31, 2021	-15.41%	4.24%	566.06	10.22	-76.05
28.	Apr 30, 2021	36.56%	5.24%	793.90	17.60	118.20
29.	May 31, 2021	3.46%	0.55%	24.19	0.25	2.45
30.	Jun 30, 2021	27.01%	2.22%	347.06	1.38	21.87
31.	Jul 31, 2021	50.48%	2.27%	1,772.51	1.51	51.68
32.	Aug 31, 2021	6.53%	2.90%	3.42	3.43	-3.43
33.	Sep 30, 2021	2.17%	-4.76%	38.57	33.69	36.05
34.	Oct 31, 2021	-10.30%	6.91%	349.02	34.42	-109.61
35.	Nov 30, 2021	2.09%	-0.83%	39.54	3.54	11.83
36.	Dec 31, 2021	-27.93%	4.36%	1,318.73	10.98	-120.34
37.	Jan 31, 2022	-33.33%	-5.26%	1,739.65	39.76	263.01
38.	Feb 28, 2022	-9.29%	-3.14%	312.20	17.50	73.92
39.	Mar 31, 2022	12.15%	3.58%	14.20	6.40	9.53
40.	Apr 30, 2022	-21.97%	-8.80%	921.26	96.89	298.76
41.	May 31, 2022	8.12%	0.01%	0.07	1.09	0.27
42.	Jun 30, 2022	-1.71%	-8.39%	101.73	89.10	95.21
43.	Jul 31, 2022	14.87%	9.11%	42.11	65.03	52.33
44.	Aug 31, 2022	-19.39%	-4.24%	771.25	28.00	146.95
45.	Sep 30, 2022	-10.60%	-9.34%	360.21	107.89	197.14
46.	Oct 31, 2022	27.13%	7.99%	351.54	48.15	130.10
47.	Nov 30, 2022	17.02%	5.38%	74.58	18.73	37.38
48.	Dec 31, 2022	2.11%	-5.90%	39.32	48.23	43.55
Total (Σ):				37,518.58	1,479.77	2,524.34

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Variance_MRNA = Σ(R_MRNA,t–R_MRNA)² ÷ (48 – 1)
= 37,518.58 ÷ (48 – 1)
= 798.27

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (48 – 1)
= 1,479.77 ÷ (48 – 1)
= 31.48

Covariance_{MRNA, S&P 500} = Σ(R_MRNA,t–R_MRNA)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (48 – 1)
= 2,524.34 ÷ (48 – 1)
= 53.71

Systematic Risk (β) Estimation

Variance_MRNA	798.27
Variance_{S&P 500}	31.48
Covariance_{MRNA, S&P 500}	53.71
Correlation coefficient_{MRNA, S&P 500}¹	0.34
β_MRNA²	1.71
α_MRNA³	6.59%

Calculations

¹ Correlation coefficient_{MRNA, S&P 500}
= Covariance_{MRNA, S&P 500} ÷ (Standard deviation_MRNA × Standard deviation_{S&P 500})
= 53.71 ÷ (28.25% × 5.61%)
= 0.34

² β_MRNA
= Covariance_{MRNA, S&P 500} ÷ Variance_{S&P 500}
= 53.71 ÷ 31.48
= 1.71

³ α_MRNA
= Average_MRNA – β_MRNA × Average_{S&P 500}
= 8.38% – 1.71 × 1.05%
= 6.59%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.86%
Expected rate of return on market portfolio²	E(R_M)	13.54%
Systematic risk (β) of Moderna Inc. common stock	β_MRNA	1.71

Expected rate of return on Moderna Inc. common stock³	E(R_MRNA)	19.66%

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_MRNA) = R_F + β_MRNA [E(R_M) – R_F]
= 4.86% + 1.71 [13.54% – 4.86%]
= 19.66%