Airbnb Inc. (NASDAQ:ABNB)

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 Airbnb Inc. common stock.

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

Rates of Return

Airbnb Inc., monthly rates of return

		Airbnb Inc. (ABNB)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_ABNB,t¹	Dividend_ABNB,t¹	R_ABNB,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Dec 31, 2020	$146.80			3,756.07
1.	Jan 31, 2021	$183.63		25.09%	3,714.24	-1.11%
2.	Feb 28, 2021	$206.35		12.37%	3,811.15	2.61%
3.	Mar 31, 2021	$187.94		-8.92%	3,972.89	4.24%
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35.	Nov 30, 2023	$126.34		6.81%	4,567.80	8.92%
36.	Dec 31, 2023	$136.14		7.76%	4,769.83	4.42%
Average (R):				0.65%		0.79%
Standard deviation:				13.30%		5.04%

		Airbnb Inc. (ABNB)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_ABNB,t¹	Dividend_ABNB,t¹	R_ABNB,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Dec 31, 2020	$146.80			3,756.07
1.	Jan 31, 2021	$183.63		25.09%	3,714.24	-1.11%
2.	Feb 28, 2021	$206.35		12.37%	3,811.15	2.61%
3.	Mar 31, 2021	$187.94		-8.92%	3,972.89	4.24%
4.	Apr 30, 2021	$172.71		-8.10%	4,181.17	5.24%
5.	May 31, 2021	$140.40		-18.71%	4,204.11	0.55%
6.	Jun 30, 2021	$153.14		9.07%	4,297.50	2.22%
7.	Jul 31, 2021	$144.01		-5.96%	4,395.26	2.27%
8.	Aug 31, 2021	$154.99		7.62%	4,522.68	2.90%
9.	Sep 30, 2021	$167.75		8.23%	4,307.54	-4.76%
10.	Oct 31, 2021	$170.66		1.73%	4,605.38	6.91%
11.	Nov 30, 2021	$172.54		1.10%	4,567.00	-0.83%
12.	Dec 31, 2021	$166.49		-3.51%	4,766.18	4.36%
13.	Jan 31, 2022	$153.97		-7.52%	4,515.55	-5.26%
14.	Feb 28, 2022	$151.49		-1.61%	4,373.94	-3.14%
15.	Mar 31, 2022	$171.76		13.38%	4,530.41	3.58%
16.	Apr 30, 2022	$153.21		-10.80%	4,131.93	-8.80%
17.	May 31, 2022	$120.87		-21.11%	4,132.15	0.01%
18.	Jun 30, 2022	$89.08		-26.30%	3,785.38	-8.39%
19.	Jul 31, 2022	$110.98		24.58%	4,130.29	9.11%
20.	Aug 31, 2022	$113.12		1.93%	3,955.00	-4.24%
21.	Sep 30, 2022	$105.04		-7.14%	3,585.62	-9.34%
22.	Oct 31, 2022	$106.91		1.78%	3,871.98	7.99%
23.	Nov 30, 2022	$102.14		-4.46%	4,080.11	5.38%
24.	Dec 31, 2022	$85.50		-16.29%	3,839.50	-5.90%
25.	Jan 31, 2023	$111.11		29.95%	4,076.60	6.18%
26.	Feb 28, 2023	$123.28		10.95%	3,970.15	-2.61%
27.	Mar 31, 2023	$124.40		0.91%	4,109.31	3.51%
28.	Apr 30, 2023	$119.67		-3.80%	4,169.48	1.46%
29.	May 31, 2023	$109.77		-8.27%	4,179.83	0.25%
30.	Jun 30, 2023	$128.16		16.75%	4,376.86	4.71%
31.	Jul 31, 2023	$152.19		18.75%	4,588.96	4.85%
32.	Aug 31, 2023	$131.55		-13.56%	4,507.66	-1.77%
33.	Sep 30, 2023	$137.21		4.30%	4,288.05	-4.87%
34.	Oct 31, 2023	$118.29		-13.79%	4,193.80	-2.20%
35.	Nov 30, 2023	$126.34		6.81%	4,567.80	8.92%
36.	Dec 31, 2023	$136.14		7.76%	4,769.83	4.42%
Average (R):				0.65%		0.79%
Standard deviation:				13.30%		5.04%

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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 ABNB during period t

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

Variance and Covariance

Airbnb Inc., calculation of variance and covariance of returns

t	Date	R_ABNB,t	R_{S&P 500,t}	(R_ABNB,t–R_ABNB)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ABNB,t–R_ABNB)×(R_{S&P 500,t}–R_{S&P 500})
1.	Jan 31, 2021	25.09%	-1.11%	597.48	3.62	-46.54
2.	Feb 28, 2021	12.37%	2.61%	137.54	3.31	21.33
3.	Mar 31, 2021	-8.92%	4.24%	91.52	11.93	-33.04
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35.	Nov 30, 2023	6.81%	8.92%	37.95	66.06	50.07
36.	Dec 31, 2023	7.76%	4.42%	50.58	13.20	25.84
Total (Σ):				6,195.02	889.77	1,107.74

t	Date	R_ABNB,t	R_{S&P 500,t}	(R_ABNB,t–R_ABNB)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ABNB,t–R_ABNB)×(R_{S&P 500,t}–R_{S&P 500})
1.	Jan 31, 2021	25.09%	-1.11%	597.48	3.62	-46.54
2.	Feb 28, 2021	12.37%	2.61%	137.54	3.31	21.33
3.	Mar 31, 2021	-8.92%	4.24%	91.52	11.93	-33.04
4.	Apr 30, 2021	-8.10%	5.24%	76.54	19.82	-38.95
5.	May 31, 2021	-18.71%	0.55%	374.53	0.06	4.67
6.	Jun 30, 2021	9.07%	2.22%	71.05	2.05	12.06
7.	Jul 31, 2021	-5.96%	2.27%	43.65	2.20	-9.81
8.	Aug 31, 2021	7.62%	2.90%	48.71	4.45	14.72
9.	Sep 30, 2021	8.23%	-4.76%	57.57	30.77	-42.09
10.	Oct 31, 2021	1.73%	6.91%	1.19	37.51	6.67
11.	Nov 30, 2021	1.10%	-0.83%	0.21	2.64	-0.74
12.	Dec 31, 2021	-3.51%	4.36%	17.23	12.75	-14.83
13.	Jan 31, 2022	-7.52%	-5.26%	66.67	36.59	49.39
14.	Feb 28, 2022	-1.61%	-3.14%	5.09	15.41	8.86
15.	Mar 31, 2022	13.38%	3.58%	162.19	7.77	35.50
16.	Apr 30, 2022	-10.80%	-8.80%	130.99	91.89	109.71
17.	May 31, 2022	-21.11%	0.01%	473.21	0.62	17.07
18.	Jun 30, 2022	-26.30%	-8.39%	726.09	84.31	247.42
19.	Jul 31, 2022	24.58%	9.11%	573.10	69.25	199.21
20.	Aug 31, 2022	1.93%	-4.24%	1.65	25.34	-6.46
21.	Sep 30, 2022	-7.14%	-9.34%	60.65	102.61	78.89
22.	Oct 31, 2022	1.78%	7.99%	1.29	51.79	8.17
23.	Nov 30, 2022	-4.46%	5.38%	26.08	21.02	-23.42
24.	Dec 31, 2022	-16.29%	-5.90%	286.84	44.72	113.26
25.	Jan 31, 2023	29.95%	6.18%	858.97	29.00	157.83
26.	Feb 28, 2023	10.95%	-2.61%	106.26	11.57	-35.06
27.	Mar 31, 2023	0.91%	3.51%	0.07	7.37	0.72
28.	Apr 30, 2023	-3.80%	1.46%	19.78	0.45	-3.00
29.	May 31, 2023	-8.27%	0.25%	79.53	0.29	4.83
30.	Jun 30, 2023	16.75%	4.71%	259.47	15.40	63.20
31.	Jul 31, 2023	18.75%	4.85%	327.79	16.45	73.43
32.	Aug 31, 2023	-13.56%	-1.77%	201.84	6.56	36.40
33.	Sep 30, 2023	4.30%	-4.87%	13.38	32.06	-20.71
34.	Oct 31, 2023	-13.79%	-2.20%	208.34	8.93	43.13
35.	Nov 30, 2023	6.81%	8.92%	37.95	66.06	50.07
36.	Dec 31, 2023	7.76%	4.42%	50.58	13.20	25.84
Total (Σ):				6,195.02	889.77	1,107.74

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Variance_ABNB = Σ(R_ABNB,t–R_ABNB)² ÷ (36 – 1)
= 6,195.02 ÷ (36 – 1)
= 177.00

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (36 – 1)
= 889.77 ÷ (36 – 1)
= 25.42

Covariance_{ABNB, S&P 500} = Σ(R_ABNB,t–R_ABNB)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (36 – 1)
= 1,107.74 ÷ (36 – 1)
= 31.65

Systematic Risk (β) Estimation

Variance_ABNB	177.00
Variance_{S&P 500}	25.42
Covariance_{ABNB, S&P 500}	31.65
Correlation coefficient_{ABNB, S&P 500}¹	0.47
β_ABNB²	1.24
α_ABNB³	-0.34%

Calculations

¹ Correlation coefficient_{ABNB, S&P 500}
= Covariance_{ABNB, S&P 500} ÷ (Standard deviation_ABNB × Standard deviation_{S&P 500})
= 31.65 ÷ (13.30% × 5.04%)
= 0.47

² β_ABNB
= Covariance_{ABNB, S&P 500} ÷ Variance_{S&P 500}
= 31.65 ÷ 25.42
= 1.24

³ α_ABNB
= Average_ABNB – β_ABNB × Average_{S&P 500}
= 0.65% – 1.24 × 0.79%
= -0.34%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.64%
Expected rate of return on market portfolio²	E(R_M)	13.68%
Systematic risk (β) of Airbnb Inc. common stock	β_ABNB	1.24

Expected rate of return on Airbnb Inc. common stock³	E(R_ABNB)	15.90%

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_ABNB) = R_F + β_ABNB [E(R_M) – R_F]
= 4.64% + 1.24 [13.68% – 4.64%]
= 15.90%