Trade Desk Inc. (NASDAQ:TTD)

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 Trade Desk Inc. common stock.

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

Rates of Return

Trade Desk Inc., monthly rates of return

		Trade Desk Inc. (TTD)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_TTD,t¹	Dividend_TTD,t¹	R_TTD,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2020	$26.92			3,225.52
1.	Feb 29, 2020	$28.73		6.72%	2,954.22	-8.41%
2.	Mar 31, 2020	$19.30		-32.82%	2,584.59	-12.51%
3.	Apr 30, 2020	$29.26		51.61%	2,912.43	12.68%
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58.	Nov 30, 2024	$128.55		6.94%	6,032.38	5.73%
59.	Dec 31, 2024	$117.53		-8.57%	5,881.63	-2.50%
Average (R):				3.94%		1.16%
Standard deviation:				17.71%		5.28%

		Trade Desk Inc. (TTD)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_TTD,t¹	Dividend_TTD,t¹	R_TTD,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2020	$26.92			3,225.52
1.	Feb 29, 2020	$28.73		6.72%	2,954.22	-8.41%
2.	Mar 31, 2020	$19.30		-32.82%	2,584.59	-12.51%
3.	Apr 30, 2020	$29.26		51.61%	2,912.43	12.68%
4.	May 31, 2020	$31.16		6.49%	3,044.31	4.53%
5.	Jun 30, 2020	$40.65		30.46%	3,100.29	1.84%
6.	Jul 31, 2020	$45.13		11.02%	3,271.12	5.51%
7.	Aug 31, 2020	$48.13		6.65%	3,500.31	7.01%
8.	Sep 30, 2020	$51.88		7.79%	3,363.00	-3.92%
9.	Oct 31, 2020	$56.65		9.19%	3,269.96	-2.77%
10.	Nov 30, 2020	$90.11		59.06%	3,621.63	10.75%
11.	Dec 31, 2020	$80.10		-11.11%	3,756.07	3.71%
12.	Jan 31, 2021	$76.60		-4.37%	3,714.24	-1.11%
13.	Feb 28, 2021	$80.54		5.14%	3,811.15	2.61%
14.	Mar 31, 2021	$65.17		-19.08%	3,972.89	4.24%
15.	Apr 30, 2021	$72.93		11.91%	4,181.17	5.24%
16.	May 31, 2021	$58.81		-19.36%	4,204.11	0.55%
17.	Jun 30, 2021	$77.36		31.54%	4,297.50	2.22%
18.	Jul 31, 2021	$81.91		5.88%	4,395.26	2.27%
19.	Aug 31, 2021	$80.05		-2.27%	4,522.68	2.90%
20.	Sep 30, 2021	$70.30		-12.18%	4,307.54	-4.76%
21.	Oct 31, 2021	$74.91		6.56%	4,605.38	6.91%
22.	Nov 30, 2021	$103.42		38.06%	4,567.00	-0.83%
23.	Dec 31, 2021	$91.64		-11.39%	4,766.18	4.36%
24.	Jan 31, 2022	$69.54		-24.12%	4,515.55	-5.26%
25.	Feb 28, 2022	$85.32		22.69%	4,373.94	-3.14%
26.	Mar 31, 2022	$69.25		-18.83%	4,530.41	3.58%
27.	Apr 30, 2022	$58.92		-14.92%	4,131.93	-8.80%
28.	May 31, 2022	$52.05		-11.66%	4,132.15	0.01%
29.	Jun 30, 2022	$41.89		-19.52%	3,785.38	-8.39%
30.	Jul 31, 2022	$45.00		7.42%	4,130.29	9.11%
31.	Aug 31, 2022	$62.70		39.33%	3,955.00	-4.24%
32.	Sep 30, 2022	$59.75		-4.70%	3,585.62	-9.34%
33.	Oct 31, 2022	$53.24		-10.90%	3,871.98	7.99%
34.	Nov 30, 2022	$52.14		-2.07%	4,080.11	5.38%
35.	Dec 31, 2022	$44.83		-14.02%	3,839.50	-5.90%
36.	Jan 31, 2023	$50.70		13.09%	4,076.60	6.18%
37.	Feb 28, 2023	$55.96		10.37%	3,970.15	-2.61%
38.	Mar 31, 2023	$60.91		8.85%	4,109.31	3.51%
39.	Apr 30, 2023	$64.34		5.63%	4,169.48	1.46%
40.	May 31, 2023	$70.08		8.92%	4,179.83	0.25%
41.	Jun 30, 2023	$77.22		10.19%	4,376.86	4.71%
42.	Jul 31, 2023	$91.26		18.18%	4,588.96	4.85%
43.	Aug 31, 2023	$80.03		-12.31%	4,507.66	-1.77%
44.	Sep 30, 2023	$78.15		-2.35%	4,288.05	-4.87%
45.	Oct 31, 2023	$70.96		-9.20%	4,193.80	-2.20%
46.	Nov 30, 2023	$70.46		-0.70%	4,567.80	8.92%
47.	Dec 31, 2023	$71.96		2.13%	4,769.83	4.42%
48.	Jan 31, 2024	$68.43		-4.91%	4,845.65	1.59%
49.	Feb 29, 2024	$85.43		24.84%	5,096.27	5.17%
50.	Mar 31, 2024	$87.42		2.33%	5,254.35	3.10%
51.	Apr 30, 2024	$82.85		-5.23%	5,035.69	-4.16%
52.	May 31, 2024	$92.78		11.99%	5,277.51	4.80%
53.	Jun 30, 2024	$97.67		5.27%	5,460.48	3.47%
54.	Jul 31, 2024	$89.88		-7.98%	5,522.30	1.13%
55.	Aug 31, 2024	$104.53		16.30%	5,648.40	2.28%
56.	Sep 30, 2024	$109.65		4.90%	5,762.48	2.02%
57.	Oct 31, 2024	$120.21		9.63%	5,705.45	-0.99%
58.	Nov 30, 2024	$128.55		6.94%	6,032.38	5.73%
59.	Dec 31, 2024	$117.53		-8.57%	5,881.63	-2.50%
Average (R):				3.94%		1.16%
Standard deviation:				17.71%		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 TTD during period t

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

Variance and Covariance

Trade Desk Inc., calculation of variance and covariance of returns

t	Date	R_TTD,t	R_{S&P 500,t}	(R_TTD,t–R_TTD)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_TTD,t–R_TTD)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2020	6.72%	-8.41%	7.74	91.63	-26.63
2.	Mar 31, 2020	-32.82%	-12.51%	1,351.60	186.96	502.68
3.	Apr 30, 2020	51.61%	12.68%	2,271.94	132.78	549.25
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58.	Nov 30, 2024	6.94%	5.73%	8.98	20.87	13.69
59.	Dec 31, 2024	-8.57%	-2.50%	156.60	13.40	45.80
Total (Σ):				18,189.84	1,618.62	2,372.85

t	Date	R_TTD,t	R_{S&P 500,t}	(R_TTD,t–R_TTD)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_TTD,t–R_TTD)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2020	6.72%	-8.41%	7.74	91.63	-26.63
2.	Mar 31, 2020	-32.82%	-12.51%	1,351.60	186.96	502.68
3.	Apr 30, 2020	51.61%	12.68%	2,271.94	132.78	549.25
4.	May 31, 2020	6.49%	4.53%	6.51	11.34	8.59
5.	Jun 30, 2020	30.46%	1.84%	703.01	0.46	17.97
6.	Jul 31, 2020	11.02%	5.51%	50.12	18.91	30.79
7.	Aug 31, 2020	6.65%	7.01%	7.32	34.17	15.82
8.	Sep 30, 2020	7.79%	-3.92%	14.82	25.85	-19.57
9.	Oct 31, 2020	9.19%	-2.77%	27.59	15.43	-20.63
10.	Nov 30, 2020	59.06%	10.75%	3,038.56	92.03	528.81
11.	Dec 31, 2020	-11.11%	3.71%	226.50	6.51	-38.39
12.	Jan 31, 2021	-4.37%	-1.11%	69.07	5.18	18.91
13.	Feb 28, 2021	5.14%	2.61%	1.45	2.10	1.74
14.	Mar 31, 2021	-19.08%	4.24%	530.15	9.50	-70.98
15.	Apr 30, 2021	11.91%	5.24%	63.46	16.66	32.51
16.	May 31, 2021	-19.36%	0.55%	543.00	0.38	14.28
17.	Jun 30, 2021	31.54%	2.22%	761.81	1.12	29.26
18.	Jul 31, 2021	5.88%	2.27%	3.76	1.24	2.16
19.	Aug 31, 2021	-2.27%	2.90%	38.59	3.02	-10.80
20.	Sep 30, 2021	-12.18%	-4.76%	259.89	35.02	95.41
21.	Oct 31, 2021	6.56%	6.91%	6.85	33.10	15.05
22.	Nov 30, 2021	38.06%	-0.83%	1,164.02	3.98	-68.05
23.	Dec 31, 2021	-11.39%	4.36%	235.06	10.24	-49.06
24.	Jan 31, 2022	-24.12%	-5.26%	787.22	41.21	180.12
25.	Feb 28, 2022	22.69%	-3.14%	351.59	18.47	-80.58
26.	Mar 31, 2022	-18.83%	3.58%	518.76	5.84	-55.03
27.	Apr 30, 2022	-14.92%	-8.80%	355.63	99.14	187.77
28.	May 31, 2022	-11.66%	0.01%	243.40	1.34	18.03
29.	Jun 30, 2022	-19.52%	-8.39%	550.42	91.26	224.13
30.	Jul 31, 2022	7.42%	9.11%	12.13	63.21	27.69
31.	Aug 31, 2022	39.33%	-4.24%	1,252.60	29.22	-191.30
32.	Sep 30, 2022	-4.70%	-9.34%	74.76	110.27	90.79
33.	Oct 31, 2022	-10.90%	7.99%	220.13	46.58	-101.26
34.	Nov 30, 2022	-2.07%	5.38%	36.09	17.76	-25.32
35.	Dec 31, 2022	-14.02%	-5.90%	322.61	49.82	126.78
36.	Jan 31, 2023	13.09%	6.18%	83.77	25.14	45.89
37.	Feb 28, 2023	10.37%	-2.61%	41.39	14.23	-24.27
38.	Mar 31, 2023	8.85%	3.51%	24.05	5.49	11.50
39.	Apr 30, 2023	5.63%	1.46%	2.86	0.09	0.51
40.	May 31, 2023	8.92%	0.25%	24.80	0.83	-4.55
41.	Jun 30, 2023	10.19%	4.71%	39.03	12.62	22.19
42.	Jul 31, 2023	18.18%	4.85%	202.79	13.58	52.47
43.	Aug 31, 2023	-12.31%	-1.77%	263.96	8.60	47.65
44.	Sep 30, 2023	-2.35%	-4.87%	39.57	36.40	37.95
45.	Oct 31, 2023	-9.20%	-2.20%	172.70	11.28	44.15
46.	Nov 30, 2023	-0.70%	8.92%	21.58	60.17	-36.04
47.	Dec 31, 2023	2.13%	4.42%	3.28	10.64	-5.91
48.	Jan 31, 2024	-4.91%	1.59%	78.27	0.18	-3.79
49.	Feb 29, 2024	24.84%	5.17%	436.88	16.09	83.83
50.	Mar 31, 2024	2.33%	3.10%	2.60	3.77	-3.13
51.	Apr 30, 2024	-5.23%	-4.16%	84.07	28.33	48.80
52.	May 31, 2024	11.99%	4.80%	64.71	13.26	29.29
53.	Jun 30, 2024	5.27%	3.47%	1.77	5.32	3.06
54.	Jul 31, 2024	-7.98%	1.13%	142.02	0.00	0.35
55.	Aug 31, 2024	16.30%	2.28%	152.73	1.26	13.87
56.	Sep 30, 2024	4.90%	2.02%	0.92	0.74	0.82
57.	Oct 31, 2024	9.63%	-0.99%	32.37	4.63	-12.24
58.	Nov 30, 2024	6.94%	5.73%	8.98	20.87	13.69
59.	Dec 31, 2024	-8.57%	-2.50%	156.60	13.40	45.80
Total (Σ):				18,189.84	1,618.62	2,372.85

Show all

Variance_TTD = Σ(R_TTD,t–R_TTD)² ÷ (59 – 1)
= 18,189.84 ÷ (59 – 1)
= 313.62

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_{TTD, S&P 500} = Σ(R_TTD,t–R_TTD)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 2,372.85 ÷ (59 – 1)
= 40.91

Systematic Risk (β) Estimation

Variance_TTD	313.62
Variance_{S&P 500}	27.91
Covariance_{TTD, S&P 500}	40.91
Correlation coefficient_{TTD, S&P 500}¹	0.44
β_TTD²	1.47
α_TTD³	2.24%

Calculations

¹ Correlation coefficient_{TTD, S&P 500}
= Covariance_{TTD, S&P 500} ÷ (Standard deviation_TTD × Standard deviation_{S&P 500})
= 40.91 ÷ (17.71% × 5.28%)
= 0.44

² β_TTD
= Covariance_{TTD, S&P 500} ÷ Variance_{S&P 500}
= 40.91 ÷ 27.91
= 1.47

³ α_TTD
= Average_TTD – β_TTD × Average_{S&P 500}
= 3.94% – 1.47 × 1.16%
= 2.24%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.70%
Expected rate of return on market portfolio²	E(R_M)	14.85%
Systematic risk (β) of Trade Desk Inc. common stock	β_TTD	1.47

Expected rate of return on Trade Desk Inc. common stock³	E(R_TTD)	19.58%

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_TTD) = R_F + β_TTD [E(R_M) – R_F]
= 4.70% + 1.47 [14.85% – 4.70%]
= 19.58%