Twenty-First Century Fox Inc. (NASDAQ:FOX)

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 Twenty-First Century Fox Inc. common stock.

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

Rates of Return

Twenty-First Century Fox Inc., monthly rates of return

		Twenty-First Century Fox Inc. (FOX)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_FOX,t¹	Dividend_FOX,t¹	R_FOX,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jul 31, 2012	$23.02			1,379.32
1.	Aug 31, 2012	$23.39		1.61%	1,406.58	1.98%
2.	Sep 30, 2012	$24.51	$0.085	5.15%	1,440.67	2.42%
3.	Oct 31, 2012	$23.93		-2.37%	1,412.16	-1.98%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	May 31, 2018	$38.55		5.44%	2,705.27	2.16%
71.	Jun 30, 2018	$49.69		28.90%	2,718.37	0.48%
Average (R):				1.45%		1.00%
Standard deviation:				7.59%		2.71%

		Twenty-First Century Fox Inc. (FOX)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_FOX,t¹	Dividend_FOX,t¹	R_FOX,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jul 31, 2012	$23.02			1,379.32
1.	Aug 31, 2012	$23.39		1.61%	1,406.58	1.98%
2.	Sep 30, 2012	$24.51	$0.085	5.15%	1,440.67	2.42%
3.	Oct 31, 2012	$23.93		-2.37%	1,412.16	-1.98%
4.	Nov 30, 2012	$24.64		2.97%	1,416.18	0.28%
5.	Dec 31, 2012	$25.51		3.53%	1,426.19	0.71%
6.	Jan 31, 2013	$27.74		8.74%	1,498.11	5.04%
7.	Feb 28, 2013	$28.81		3.86%	1,514.68	1.11%
8.	Mar 31, 2013	$30.51	$0.085	6.20%	1,569.19	3.60%
9.	Apr 30, 2013	$30.97		1.51%	1,597.57	1.81%
10.	May 31, 2013	$32.11		3.68%	1,630.74	2.08%
11.	Jun 30, 2013	$32.58		1.46%	1,606.28	-1.50%
12.	Jul 31, 2013	$29.88		-8.29%	1,685.73	4.95%
13.	Aug 31, 2013	$31.33		4.85%	1,632.97	-3.13%
14.	Sep 30, 2013	$33.51	$0.125	7.36%	1,681.55	2.97%
15.	Oct 31, 2013	$34.08		1.70%	1,756.54	4.46%
16.	Nov 30, 2013	$33.49		-1.73%	1,805.81	2.80%
17.	Dec 31, 2013	$35.17		5.02%	1,848.36	2.36%
18.	Jan 31, 2014	$31.82		-9.53%	1,782.59	-3.56%
19.	Feb 28, 2014	$33.54		5.41%	1,859.45	4.31%
20.	Mar 31, 2014	$31.97	$0.125	-4.31%	1,872.34	0.69%
21.	Apr 30, 2014	$32.02		0.16%	1,883.95	0.62%
22.	May 31, 2014	$35.41		10.59%	1,923.57	2.10%
23.	Jun 30, 2014	$35.15		-0.73%	1,960.23	1.91%
24.	Jul 31, 2014	$31.67		-9.90%	1,930.67	-1.51%
25.	Aug 31, 2014	$35.42		11.84%	2,003.37	3.77%
26.	Sep 30, 2014	$34.29	$0.125	-2.84%	1,972.29	-1.55%
27.	Oct 31, 2014	$34.48		0.55%	2,018.05	2.32%
28.	Nov 30, 2014	$36.80		6.73%	2,067.56	2.45%
29.	Dec 31, 2014	$38.41		4.38%	2,058.90	-0.42%
30.	Jan 31, 2015	$33.16		-13.67%	1,994.99	-3.10%
31.	Feb 28, 2015	$35.00		5.55%	2,104.50	5.49%
32.	Mar 31, 2015	$33.84	$0.15	-2.89%	2,067.89	-1.74%
33.	Apr 30, 2015	$34.08		0.71%	2,085.51	0.85%
34.	May 31, 2015	$33.60		-1.41%	2,107.39	1.05%
35.	Jun 30, 2015	$32.55		-3.13%	2,063.11	-2.10%
36.	Jul 31, 2015	$34.49		5.96%	2,103.84	1.97%
37.	Aug 31, 2015	$27.39		-20.59%	1,972.18	-6.26%
38.	Sep 30, 2015	$26.98	$0.15	-0.95%	1,920.03	-2.64%
39.	Oct 31, 2015	$30.69		13.75%	2,079.36	8.30%
40.	Nov 30, 2015	$29.51		-3.84%	2,080.41	0.05%
41.	Dec 31, 2015	$27.16		-7.96%	2,043.94	-1.75%
42.	Jan 31, 2016	$26.97		-0.70%	1,940.24	-5.07%
43.	Feb 29, 2016	$27.02		0.19%	1,932.23	-0.41%
44.	Mar 31, 2016	$27.88	$0.15	3.74%	2,059.74	6.60%
45.	Apr 30, 2016	$30.26		8.54%	2,065.30	0.27%
46.	May 31, 2016	$28.88		-4.56%	2,096.95	1.53%
47.	Jun 30, 2016	$27.05		-6.34%	2,098.86	0.09%
48.	Jul 31, 2016	$26.64		-1.52%	2,173.60	3.56%
49.	Aug 31, 2016	$24.54		-7.88%	2,170.95	-0.12%
50.	Sep 30, 2016	$24.22	$0.18	-0.57%	2,168.27	-0.12%
51.	Oct 31, 2016	$26.27		8.46%	2,126.15	-1.94%
52.	Nov 30, 2016	$28.11		7.00%	2,198.81	3.42%
53.	Dec 31, 2016	$28.04		-0.25%	2,238.83	1.82%
54.	Jan 31, 2017	$31.38		11.91%	2,278.87	1.79%
55.	Feb 28, 2017	$29.92		-4.65%	2,363.64	3.72%
56.	Mar 31, 2017	$32.39	$0.18	8.86%	2,362.72	-0.04%
57.	Apr 30, 2017	$30.54		-5.71%	2,384.20	0.91%
58.	May 31, 2017	$27.12		-11.20%	2,411.80	1.16%
59.	Jun 30, 2017	$28.34		4.50%	2,423.41	0.48%
60.	Jul 31, 2017	$29.10		2.68%	2,470.30	1.93%
61.	Aug 31, 2017	$27.59		-5.19%	2,471.65	0.05%
62.	Sep 30, 2017	$26.38	$0.18	-3.73%	2,519.36	1.93%
63.	Oct 31, 2017	$26.15		-0.87%	2,575.26	2.22%
64.	Nov 30, 2017	$31.94		22.14%	2,647.58	2.81%
65.	Dec 31, 2017	$34.53		8.11%	2,673.61	0.98%
66.	Jan 31, 2018	$36.90		6.86%	2,823.81	5.62%
67.	Feb 28, 2018	$36.82		-0.22%	2,713.83	-3.89%
68.	Mar 31, 2018	$36.69	$0.18	0.14%	2,640.87	-2.69%
69.	Apr 30, 2018	$36.56		-0.35%	2,648.05	0.27%
70.	May 31, 2018	$38.55		5.44%	2,705.27	2.16%
71.	Jun 30, 2018	$49.69		28.90%	2,718.37	0.48%
Average (R):				1.45%		1.00%
Standard deviation:				7.59%		2.71%

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 FOX during period t

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

Variance and Covariance

Twenty-First Century Fox Inc., calculation of variance and covariance of returns

t	Date	R_FOX,t	R_{S&P 500,t}	(R_FOX,t–R_FOX)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_FOX,t–R_FOX)×(R_{S&P 500,t}–R_{S&P 500})
1.	Aug 31, 2012	1.61%	1.98%	0.03	0.96	0.16
2.	Sep 30, 2012	5.15%	2.42%	13.71	2.04	5.29
3.	Oct 31, 2012	-2.37%	-1.98%	14.55	8.85	11.35
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	May 31, 2018	5.44%	2.16%	15.96	1.36	4.65
71.	Jun 30, 2018	28.90%	0.48%	753.44	0.26	-14.05
Total (Σ):				4,030.79	514.30	633.77

t	Date	R_FOX,t	R_{S&P 500,t}	(R_FOX,t–R_FOX)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_FOX,t–R_FOX)×(R_{S&P 500,t}–R_{S&P 500})
1.	Aug 31, 2012	1.61%	1.98%	0.03	0.96	0.16
2.	Sep 30, 2012	5.15%	2.42%	13.71	2.04	5.29
3.	Oct 31, 2012	-2.37%	-1.98%	14.55	8.85	11.35
4.	Nov 30, 2012	2.97%	0.28%	2.31	0.51	-1.08
5.	Dec 31, 2012	3.53%	0.71%	4.34	0.08	-0.60
6.	Jan 31, 2013	8.74%	5.04%	53.19	16.38	29.51
7.	Feb 28, 2013	3.86%	1.11%	5.80	0.01	0.26
8.	Mar 31, 2013	6.20%	3.60%	22.54	6.77	12.36
9.	Apr 30, 2013	1.51%	1.81%	0.00	0.66	0.05
10.	May 31, 2013	3.68%	2.08%	4.98	1.17	2.41
11.	Jun 30, 2013	1.46%	-1.50%	0.00	6.23	-0.04
12.	Jul 31, 2013	-8.29%	4.95%	94.79	15.60	-38.46
13.	Aug 31, 2013	4.85%	-3.13%	11.59	17.02	-14.05
14.	Sep 30, 2013	7.36%	2.97%	34.91	3.92	11.69
15.	Oct 31, 2013	1.70%	4.46%	0.06	12.00	0.87
16.	Nov 30, 2013	-1.73%	2.80%	10.11	3.27	-5.75
17.	Dec 31, 2013	5.02%	2.36%	12.73	1.85	4.85
18.	Jan 31, 2014	-9.53%	-3.56%	120.42	20.74	49.98
19.	Feb 28, 2014	5.41%	4.31%	15.66	10.99	13.12
20.	Mar 31, 2014	-4.31%	0.69%	33.14	0.09	1.74
21.	Apr 30, 2014	0.16%	0.62%	1.67	0.14	0.49
22.	May 31, 2014	10.59%	2.10%	83.51	1.23	10.12
23.	Jun 30, 2014	-0.73%	1.91%	4.76	0.83	-1.99
24.	Jul 31, 2014	-9.90%	-1.51%	128.80	6.27	28.42
25.	Aug 31, 2014	11.84%	3.77%	108.00	7.67	28.78
26.	Sep 30, 2014	-2.84%	-1.55%	18.37	6.49	10.92
27.	Oct 31, 2014	0.55%	2.32%	0.80	1.75	-1.18
28.	Nov 30, 2014	6.73%	2.45%	27.88	2.12	7.69
29.	Dec 31, 2014	4.38%	-0.42%	8.56	2.00	-4.14
30.	Jan 31, 2015	-13.67%	-3.10%	228.52	16.81	61.98
31.	Feb 28, 2015	5.55%	5.49%	16.81	20.19	18.42
32.	Mar 31, 2015	-2.89%	-1.74%	18.79	7.48	11.86
33.	Apr 30, 2015	0.71%	0.85%	0.55	0.02	0.11
34.	May 31, 2015	-1.41%	1.05%	8.16	0.00	-0.15
35.	Jun 30, 2015	-3.13%	-2.10%	20.92	9.59	14.17
36.	Jul 31, 2015	5.96%	1.97%	20.35	0.96	4.41
37.	Aug 31, 2015	-20.59%	-6.26%	485.51	52.62	159.84
38.	Sep 30, 2015	-0.95%	-2.64%	5.75	13.25	8.73
39.	Oct 31, 2015	13.75%	8.30%	151.35	53.32	89.83
40.	Nov 30, 2015	-3.84%	0.05%	28.02	0.89	5.01
41.	Dec 31, 2015	-7.96%	-1.75%	88.59	7.56	25.87
42.	Jan 31, 2016	-0.70%	-5.07%	4.61	36.84	13.04
43.	Feb 29, 2016	0.19%	-0.41%	1.60	1.99	1.78
44.	Mar 31, 2016	3.74%	6.60%	5.24	31.39	12.83
45.	Apr 30, 2016	8.54%	0.27%	50.24	0.53	-5.15
46.	May 31, 2016	-4.56%	1.53%	36.11	0.29	-3.22
47.	Jun 30, 2016	-6.34%	0.09%	60.61	0.82	7.05
48.	Jul 31, 2016	-1.52%	3.56%	8.79	6.58	-7.60
49.	Aug 31, 2016	-7.88%	-0.12%	87.08	1.25	10.43
50.	Sep 30, 2016	-0.57%	-0.12%	4.08	1.25	2.26
51.	Oct 31, 2016	8.46%	-1.94%	49.22	8.64	-20.62
52.	Nov 30, 2016	7.00%	3.42%	30.86	5.86	13.45
53.	Dec 31, 2016	-0.25%	1.82%	2.88	0.68	-1.40
54.	Jan 31, 2017	11.91%	1.79%	109.47	0.63	8.29
55.	Feb 28, 2017	-4.65%	3.72%	37.23	7.42	-16.62
56.	Mar 31, 2017	8.86%	-0.04%	54.88	1.07	-7.67
57.	Apr 30, 2017	-5.71%	0.91%	51.27	0.01	0.62
58.	May 31, 2017	-11.20%	1.16%	159.95	0.03	-2.04
59.	Jun 30, 2017	4.50%	0.48%	9.30	0.26	-1.57
60.	Jul 31, 2017	2.68%	1.93%	1.52	0.88	1.16
61.	Aug 31, 2017	-5.19%	0.05%	44.06	0.89	6.25
62.	Sep 30, 2017	-3.73%	1.93%	26.85	0.87	-4.84
63.	Oct 31, 2017	-0.87%	2.22%	5.38	1.50	-2.84
64.	Nov 30, 2017	22.14%	2.81%	428.20	3.28	37.50
65.	Dec 31, 2017	8.11%	0.98%	44.36	0.00	-0.09
66.	Jan 31, 2018	6.86%	5.62%	29.32	21.36	25.03
67.	Feb 28, 2018	-0.22%	-3.89%	2.77	23.92	8.15
68.	Mar 31, 2018	0.14%	-2.69%	1.72	13.58	4.84
69.	Apr 30, 2018	-0.35%	0.27%	3.25	0.52	1.31
70.	May 31, 2018	5.44%	2.16%	15.96	1.36	4.65
71.	Jun 30, 2018	28.90%	0.48%	753.44	0.26	-14.05
Total (Σ):				4,030.79	514.30	633.77

Show all

Variance_FOX = Σ(R_FOX,t–R_FOX)² ÷ (71 – 1)
= 4,030.79 ÷ (71 – 1)
= 57.58

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 514.30 ÷ (71 – 1)
= 7.35

Covariance_{FOX, S&P 500} = Σ(R_FOX,t–R_FOX)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 633.77 ÷ (71 – 1)
= 9.05

Systematic Risk (β) Estimation

Variance_FOX	57.58
Variance_{S&P 500}	7.35
Covariance_{FOX, S&P 500}	9.05
Correlation coefficient_{FOX, S&P 500}¹	0.44
β_FOX²	1.23
α_FOX³	0.22%

Calculations

¹ Correlation coefficient_{FOX, S&P 500}
= Covariance_{FOX, S&P 500} ÷ (Standard deviation_FOX × Standard deviation_{S&P 500})
= 9.05 ÷ (7.59% × 2.71%)
= 0.44

² β_FOX
= Covariance_{FOX, S&P 500} ÷ Variance_{S&P 500}
= 9.05 ÷ 7.35
= 1.23

³ α_FOX
= Average_FOX – β_FOX × Average_{S&P 500}
= 1.45% – 1.23 × 1.00%
= 0.22%

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 Twenty-First Century Fox Inc. common stock	β_FOX	1.23

Expected rate of return on Twenty-First Century Fox Inc. common stock³	E(R_FOX)	15.56%

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_FOX) = R_F + β_FOX [E(R_M) – R_F]
= 4.81% + 1.23 [13.54% – 4.81%]
= 15.56%