Eli Lilly & Co. (NYSE:LLY)

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 Eli Lilly & Co. common stock.

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

Rates of Return

Eli Lilly & Co., monthly rates of return

		Eli Lilly & Co. (LLY)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_LLY,t¹	Dividend_LLY,t¹	R_LLY,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$119.86			2,704.10
1.	Feb 28, 2019	$126.29	$0.645	5.90%	2,784.49	2.97%
2.	Mar 31, 2019	$129.76		2.75%	2,834.40	1.79%
3.	Apr 30, 2019	$117.04		-9.80%	2,945.83	3.93%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2023	$591.04	$1.13	6.90%	4,567.80	8.92%
59.	Dec 31, 2023	$582.92		-1.37%	4,769.83	4.42%
Average (R):				3.19%		1.11%
Standard deviation:				8.33%		5.31%

		Eli Lilly & Co. (LLY)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_LLY,t¹	Dividend_LLY,t¹	R_LLY,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$119.86			2,704.10
1.	Feb 28, 2019	$126.29	$0.645	5.90%	2,784.49	2.97%
2.	Mar 31, 2019	$129.76		2.75%	2,834.40	1.79%
3.	Apr 30, 2019	$117.04		-9.80%	2,945.83	3.93%
4.	May 31, 2019	$115.94	$0.645	-0.39%	2,752.06	-6.58%
5.	Jun 30, 2019	$110.79		-4.44%	2,941.76	6.89%
6.	Jul 31, 2019	$108.95		-1.66%	2,980.38	1.31%
7.	Aug 31, 2019	$112.97	$0.645	4.28%	2,926.46	-1.81%
8.	Sep 30, 2019	$111.83		-1.01%	2,976.74	1.72%
9.	Oct 31, 2019	$113.95		1.90%	3,037.56	2.04%
10.	Nov 30, 2019	$117.35	$0.645	3.55%	3,140.98	3.40%
11.	Dec 31, 2019	$131.43		12.00%	3,230.78	2.86%
12.	Jan 31, 2020	$139.64		6.25%	3,225.52	-0.16%
13.	Feb 29, 2020	$126.13	$0.74	-9.14%	2,954.22	-8.41%
14.	Mar 31, 2020	$138.72		9.98%	2,584.59	-12.51%
15.	Apr 30, 2020	$154.64		11.48%	2,912.43	12.68%
16.	May 31, 2020	$152.95	$0.74	-0.61%	3,044.31	4.53%
17.	Jun 30, 2020	$164.18		7.34%	3,100.29	1.84%
18.	Jul 31, 2020	$150.29		-8.46%	3,271.12	5.51%
19.	Aug 31, 2020	$148.39	$0.74	-0.77%	3,500.31	7.01%
20.	Sep 30, 2020	$148.02		-0.25%	3,363.00	-3.92%
21.	Oct 31, 2020	$130.46		-11.86%	3,269.96	-2.77%
22.	Nov 30, 2020	$145.65	$0.74	12.21%	3,621.63	10.75%
23.	Dec 31, 2020	$168.84		15.92%	3,756.07	3.71%
24.	Jan 31, 2021	$207.97		23.18%	3,714.24	-1.11%
25.	Feb 28, 2021	$204.89	$0.85	-1.07%	3,811.15	2.61%
26.	Mar 31, 2021	$186.82		-8.82%	3,972.89	4.24%
27.	Apr 30, 2021	$182.77		-2.17%	4,181.17	5.24%
28.	May 31, 2021	$199.74	$0.85	9.75%	4,204.11	0.55%
29.	Jun 30, 2021	$229.52		14.91%	4,297.50	2.22%
30.	Jul 31, 2021	$243.50		6.09%	4,395.26	2.27%
31.	Aug 31, 2021	$258.29	$0.85	6.42%	4,522.68	2.90%
32.	Sep 30, 2021	$231.05		-10.55%	4,307.54	-4.76%
33.	Oct 31, 2021	$254.76		10.26%	4,605.38	6.91%
34.	Nov 30, 2021	$248.04	$0.85	-2.30%	4,567.00	-0.83%
35.	Dec 31, 2021	$276.22		11.36%	4,766.18	4.36%
36.	Jan 31, 2022	$245.39		-11.16%	4,515.55	-5.26%
37.	Feb 28, 2022	$249.95	$0.98	2.26%	4,373.94	-3.14%
38.	Mar 31, 2022	$286.37		14.57%	4,530.41	3.58%
39.	Apr 30, 2022	$292.13		2.01%	4,131.93	-8.80%
40.	May 31, 2022	$313.44	$0.98	7.63%	4,132.15	0.01%
41.	Jun 30, 2022	$324.23		3.44%	3,785.38	-8.39%
42.	Jul 31, 2022	$329.69		1.68%	4,130.29	9.11%
43.	Aug 31, 2022	$301.23	$0.98	-8.34%	3,955.00	-4.24%
44.	Sep 30, 2022	$323.35		7.34%	3,585.62	-9.34%
45.	Oct 31, 2022	$362.09		11.98%	3,871.98	7.99%
46.	Nov 30, 2022	$371.08	$0.98	2.75%	4,080.11	5.38%
47.	Dec 31, 2022	$365.84		-1.41%	3,839.50	-5.90%
48.	Jan 31, 2023	$344.15		-5.93%	4,076.60	6.18%
49.	Feb 28, 2023	$311.22	$1.13	-9.24%	3,970.15	-2.61%
50.	Mar 31, 2023	$343.42		10.35%	4,109.31	3.51%
51.	Apr 30, 2023	$395.86		15.27%	4,169.48	1.46%
52.	May 31, 2023	$429.46	$1.13	8.77%	4,179.83	0.25%
53.	Jun 30, 2023	$468.98		9.20%	4,376.86	4.71%
54.	Jul 31, 2023	$454.55		-3.08%	4,588.96	4.85%
55.	Aug 31, 2023	$554.20	$1.13	22.17%	4,507.66	-1.77%
56.	Sep 30, 2023	$537.13		-3.08%	4,288.05	-4.87%
57.	Oct 31, 2023	$553.93		3.13%	4,193.80	-2.20%
58.	Nov 30, 2023	$591.04	$1.13	6.90%	4,567.80	8.92%
59.	Dec 31, 2023	$582.92		-1.37%	4,769.83	4.42%
Average (R):				3.19%		1.11%
Standard deviation:				8.33%		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 LLY during period t

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

Variance and Covariance

Eli Lilly & Co., calculation of variance and covariance of returns

t	Date	R_LLY,t	R_{S&P 500,t}	(R_LLY,t–R_LLY)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_LLY,t–R_LLY)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	5.90%	2.97%	7.37	3.49	5.07
2.	Mar 31, 2019	2.75%	1.79%	0.19	0.47	-0.30
3.	Apr 30, 2019	-9.80%	3.93%	168.75	7.98	-36.70
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2023	6.90%	8.92%	13.81	61.03	29.03
59.	Dec 31, 2023	-1.37%	4.42%	20.81	11.00	-15.13
Total (Σ):				4,020.05	1,634.30	491.40

t	Date	R_LLY,t	R_{S&P 500,t}	(R_LLY,t–R_LLY)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_LLY,t–R_LLY)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	5.90%	2.97%	7.37	3.49	5.07
2.	Mar 31, 2019	2.75%	1.79%	0.19	0.47	-0.30
3.	Apr 30, 2019	-9.80%	3.93%	168.75	7.98	-36.70
4.	May 31, 2019	-0.39%	-6.58%	12.79	59.04	27.48
5.	Jun 30, 2019	-4.44%	6.89%	58.21	33.49	-44.15
6.	Jul 31, 2019	-1.66%	1.31%	23.51	0.04	-1.00
7.	Aug 31, 2019	4.28%	-1.81%	1.20	8.50	-3.19
8.	Sep 30, 2019	-1.01%	1.72%	17.61	0.37	-2.57
9.	Oct 31, 2019	1.90%	2.04%	1.67	0.88	-1.21
10.	Nov 30, 2019	3.55%	3.40%	0.13	5.28	0.83
11.	Dec 31, 2019	12.00%	2.86%	77.63	3.07	15.45
12.	Jan 31, 2020	6.25%	-0.16%	9.36	1.61	-3.88
13.	Feb 29, 2020	-9.14%	-8.41%	152.09	90.57	117.37
14.	Mar 31, 2020	9.98%	-12.51%	46.16	185.44	-92.52
15.	Apr 30, 2020	11.48%	12.68%	68.70	134.06	95.97
16.	May 31, 2020	-0.61%	4.53%	14.45	11.71	-13.01
17.	Jun 30, 2020	7.34%	1.84%	17.26	0.54	3.05
18.	Jul 31, 2020	-8.46%	5.51%	135.67	19.40	-51.30
19.	Aug 31, 2020	-0.77%	7.01%	15.68	34.82	-23.36
20.	Sep 30, 2020	-0.25%	-3.92%	11.81	25.29	17.28
21.	Oct 31, 2020	-11.86%	-2.77%	226.53	15.00	58.28
22.	Nov 30, 2020	12.21%	10.75%	81.41	93.10	87.06
23.	Dec 31, 2020	15.92%	3.71%	162.16	6.79	33.19
24.	Jan 31, 2021	23.18%	-1.11%	399.53	4.93	-44.36
25.	Feb 28, 2021	-1.07%	2.61%	18.15	2.26	-6.40
26.	Mar 31, 2021	-8.82%	4.24%	144.17	9.85	-37.68
27.	Apr 30, 2021	-2.17%	5.24%	28.68	17.11	-22.15
28.	May 31, 2021	9.75%	0.55%	43.06	0.31	-3.66
29.	Jun 30, 2021	14.91%	2.22%	137.40	1.24	13.08
30.	Jul 31, 2021	6.09%	2.27%	8.43	1.37	3.39
31.	Aug 31, 2021	6.42%	2.90%	10.47	3.22	5.80
32.	Sep 30, 2021	-10.55%	-4.76%	188.62	34.37	80.52
33.	Oct 31, 2021	10.26%	6.91%	50.04	33.74	41.09
34.	Nov 30, 2021	-2.30%	-0.83%	30.16	3.76	10.65
35.	Dec 31, 2021	11.36%	4.36%	66.81	10.60	26.61
36.	Jan 31, 2022	-11.16%	-5.26%	205.89	40.51	91.32
37.	Feb 28, 2022	2.26%	-3.14%	0.86	17.99	3.94
38.	Mar 31, 2022	14.57%	3.58%	129.58	6.11	28.13
39.	Apr 30, 2022	2.01%	-8.80%	1.38	98.04	11.65
40.	May 31, 2022	7.63%	0.01%	19.74	1.21	-4.89
41.	Jun 30, 2022	3.44%	-8.39%	0.06	90.21	-2.42
42.	Jul 31, 2022	1.68%	9.11%	2.26	64.09	-12.04
43.	Aug 31, 2022	-8.34%	-4.24%	132.77	28.62	61.64
44.	Sep 30, 2022	7.34%	-9.34%	17.27	109.11	-43.41
45.	Oct 31, 2022	11.98%	7.99%	77.32	47.34	60.50
46.	Nov 30, 2022	2.75%	5.38%	0.19	18.23	-1.85
47.	Dec 31, 2022	-1.41%	-5.90%	21.16	49.04	32.21
48.	Jan 31, 2023	-5.93%	6.18%	83.11	25.70	-46.22
49.	Feb 28, 2023	-9.24%	-2.61%	154.45	13.82	46.20
50.	Mar 31, 2023	10.35%	3.51%	51.25	5.76	17.18
51.	Apr 30, 2023	15.27%	1.46%	145.98	0.13	4.33
52.	May 31, 2023	8.77%	0.25%	31.20	0.74	-4.79
53.	Jun 30, 2023	9.20%	4.71%	36.18	13.02	21.70
54.	Jul 31, 2023	-3.08%	4.85%	39.24	13.99	-23.43
55.	Aug 31, 2023	22.17%	-1.77%	360.38	8.28	-54.63
56.	Sep 30, 2023	-3.08%	-4.87%	39.28	35.73	37.47
57.	Oct 31, 2023	3.13%	-2.20%	0.00	10.92	0.20
58.	Nov 30, 2023	6.90%	8.92%	13.81	61.03	29.03
59.	Dec 31, 2023	-1.37%	4.42%	20.81	11.00	-15.13
Total (Σ):				4,020.05	1,634.30	491.40

Show all

Variance_LLY = Σ(R_LLY,t–R_LLY)² ÷ (59 – 1)
= 4,020.05 ÷ (59 – 1)
= 69.31

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_{LLY, S&P 500} = Σ(R_LLY,t–R_LLY)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 491.40 ÷ (59 – 1)
= 8.47

Systematic Risk (β) Estimation

Variance_LLY	69.31
Variance_{S&P 500}	28.18
Covariance_{LLY, S&P 500}	8.47
Correlation coefficient_{LLY, S&P 500}¹	0.19
β_LLY²	0.30
α_LLY³	2.86%

Calculations

¹ Correlation coefficient_{LLY, S&P 500}
= Covariance_{LLY, S&P 500} ÷ (Standard deviation_LLY × Standard deviation_{S&P 500})
= 8.47 ÷ (8.33% × 5.31%)
= 0.19

² β_LLY
= Covariance_{LLY, S&P 500} ÷ Variance_{S&P 500}
= 8.47 ÷ 28.18
= 0.30

³ α_LLY
= Average_LLY – β_LLY × Average_{S&P 500}
= 3.19% – 0.30 × 1.11%
= 2.86%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.65%
Expected rate of return on market portfolio²	E(R_M)	13.79%
Systematic risk (β) of Eli Lilly & Co. common stock	β_LLY	0.30

Expected rate of return on Eli Lilly & Co. common stock³	E(R_LLY)	7.40%

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_LLY) = R_F + β_LLY [E(R_M) – R_F]
= 4.65% + 0.30 [13.79% – 4.65%]
= 7.40%