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.
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Rates of Return
Twenty-First Century Fox Inc. (FOX) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceFOX,t1 | DividendFOX,t1 | RFOX,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jul 31, 2012 | ||||||
1. | Aug 31, 2012 | |||||
2. | Sep 30, 2012 | |||||
3. | Oct 31, 2012 | |||||
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | May 31, 2018 | |||||
71. | Jun 30, 2018 | |||||
Average (R): | ||||||
Standard deviation: |
Twenty-First Century Fox Inc. (FOX) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceFOX,t1 | DividendFOX,t1 | RFOX,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jul 31, 2012 | ||||||
1. | Aug 31, 2012 | |||||
2. | Sep 30, 2012 | |||||
3. | Oct 31, 2012 | |||||
4. | Nov 30, 2012 | |||||
5. | Dec 31, 2012 | |||||
6. | Jan 31, 2013 | |||||
7. | Feb 28, 2013 | |||||
8. | Mar 31, 2013 | |||||
9. | Apr 30, 2013 | |||||
10. | May 31, 2013 | |||||
11. | Jun 30, 2013 | |||||
12. | Jul 31, 2013 | |||||
13. | Aug 31, 2013 | |||||
14. | Sep 30, 2013 | |||||
15. | Oct 31, 2013 | |||||
16. | Nov 30, 2013 | |||||
17. | Dec 31, 2013 | |||||
18. | Jan 31, 2014 | |||||
19. | Feb 28, 2014 | |||||
20. | Mar 31, 2014 | |||||
21. | Apr 30, 2014 | |||||
22. | May 31, 2014 | |||||
23. | Jun 30, 2014 | |||||
24. | Jul 31, 2014 | |||||
25. | Aug 31, 2014 | |||||
26. | Sep 30, 2014 | |||||
27. | Oct 31, 2014 | |||||
28. | Nov 30, 2014 | |||||
29. | Dec 31, 2014 | |||||
30. | Jan 31, 2015 | |||||
31. | Feb 28, 2015 | |||||
32. | Mar 31, 2015 | |||||
33. | Apr 30, 2015 | |||||
34. | May 31, 2015 | |||||
35. | Jun 30, 2015 | |||||
36. | Jul 31, 2015 | |||||
37. | Aug 31, 2015 | |||||
38. | Sep 30, 2015 | |||||
39. | Oct 31, 2015 | |||||
40. | Nov 30, 2015 | |||||
41. | Dec 31, 2015 | |||||
42. | Jan 31, 2016 | |||||
43. | Feb 29, 2016 | |||||
44. | Mar 31, 2016 | |||||
45. | Apr 30, 2016 | |||||
46. | May 31, 2016 | |||||
47. | Jun 30, 2016 | |||||
48. | Jul 31, 2016 | |||||
49. | Aug 31, 2016 | |||||
50. | Sep 30, 2016 | |||||
51. | Oct 31, 2016 | |||||
52. | Nov 30, 2016 | |||||
53. | Dec 31, 2016 | |||||
54. | Jan 31, 2017 | |||||
55. | Feb 28, 2017 | |||||
56. | Mar 31, 2017 | |||||
57. | Apr 30, 2017 | |||||
58. | May 31, 2017 | |||||
59. | Jun 30, 2017 | |||||
60. | Jul 31, 2017 | |||||
61. | Aug 31, 2017 | |||||
62. | Sep 30, 2017 | |||||
63. | Oct 31, 2017 | |||||
64. | Nov 30, 2017 | |||||
65. | Dec 31, 2017 | |||||
66. | Jan 31, 2018 | |||||
67. | Feb 28, 2018 | |||||
68. | Mar 31, 2018 | |||||
69. | Apr 30, 2018 | |||||
70. | May 31, 2018 | |||||
71. | Jun 30, 2018 | |||||
Average (R): | ||||||
Standard deviation: |
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
t | Date | RFOX,t | RS&P 500,t | (RFOX,t–RFOX)2 | (RS&P 500,t–RS&P 500)2 | (RFOX,t–RFOX)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Aug 31, 2012 | |||||
2. | Sep 30, 2012 | |||||
3. | Oct 31, 2012 | |||||
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | May 31, 2018 | |||||
71. | Jun 30, 2018 | |||||
Total (Σ): |
t | Date | RFOX,t | RS&P 500,t | (RFOX,t–RFOX)2 | (RS&P 500,t–RS&P 500)2 | (RFOX,t–RFOX)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Aug 31, 2012 | |||||
2. | Sep 30, 2012 | |||||
3. | Oct 31, 2012 | |||||
4. | Nov 30, 2012 | |||||
5. | Dec 31, 2012 | |||||
6. | Jan 31, 2013 | |||||
7. | Feb 28, 2013 | |||||
8. | Mar 31, 2013 | |||||
9. | Apr 30, 2013 | |||||
10. | May 31, 2013 | |||||
11. | Jun 30, 2013 | |||||
12. | Jul 31, 2013 | |||||
13. | Aug 31, 2013 | |||||
14. | Sep 30, 2013 | |||||
15. | Oct 31, 2013 | |||||
16. | Nov 30, 2013 | |||||
17. | Dec 31, 2013 | |||||
18. | Jan 31, 2014 | |||||
19. | Feb 28, 2014 | |||||
20. | Mar 31, 2014 | |||||
21. | Apr 30, 2014 | |||||
22. | May 31, 2014 | |||||
23. | Jun 30, 2014 | |||||
24. | Jul 31, 2014 | |||||
25. | Aug 31, 2014 | |||||
26. | Sep 30, 2014 | |||||
27. | Oct 31, 2014 | |||||
28. | Nov 30, 2014 | |||||
29. | Dec 31, 2014 | |||||
30. | Jan 31, 2015 | |||||
31. | Feb 28, 2015 | |||||
32. | Mar 31, 2015 | |||||
33. | Apr 30, 2015 | |||||
34. | May 31, 2015 | |||||
35. | Jun 30, 2015 | |||||
36. | Jul 31, 2015 | |||||
37. | Aug 31, 2015 | |||||
38. | Sep 30, 2015 | |||||
39. | Oct 31, 2015 | |||||
40. | Nov 30, 2015 | |||||
41. | Dec 31, 2015 | |||||
42. | Jan 31, 2016 | |||||
43. | Feb 29, 2016 | |||||
44. | Mar 31, 2016 | |||||
45. | Apr 30, 2016 | |||||
46. | May 31, 2016 | |||||
47. | Jun 30, 2016 | |||||
48. | Jul 31, 2016 | |||||
49. | Aug 31, 2016 | |||||
50. | Sep 30, 2016 | |||||
51. | Oct 31, 2016 | |||||
52. | Nov 30, 2016 | |||||
53. | Dec 31, 2016 | |||||
54. | Jan 31, 2017 | |||||
55. | Feb 28, 2017 | |||||
56. | Mar 31, 2017 | |||||
57. | Apr 30, 2017 | |||||
58. | May 31, 2017 | |||||
59. | Jun 30, 2017 | |||||
60. | Jul 31, 2017 | |||||
61. | Aug 31, 2017 | |||||
62. | Sep 30, 2017 | |||||
63. | Oct 31, 2017 | |||||
64. | Nov 30, 2017 | |||||
65. | Dec 31, 2017 | |||||
66. | Jan 31, 2018 | |||||
67. | Feb 28, 2018 | |||||
68. | Mar 31, 2018 | |||||
69. | Apr 30, 2018 | |||||
70. | May 31, 2018 | |||||
71. | Jun 30, 2018 | |||||
Total (Σ): |
Show all
VarianceFOX = Σ(RFOX,t–RFOX)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
CovarianceFOX, S&P 500 = Σ(RFOX,t–RFOX)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= ÷ (71 – 1)
=
Systematic Risk (β) Estimation
VarianceFOX | |
VarianceS&P 500 | |
CovarianceFOX, S&P 500 | |
Correlation coefficientFOX, S&P 5001 | |
βFOX2 | |
αFOX3 |
Calculations
1 Correlation coefficientFOX, S&P 500
= CovarianceFOX, S&P 500 ÷ (Standard deviationFOX × Standard deviationS&P 500)
= ÷ ( × )
=
2 βFOX
= CovarianceFOX, S&P 500 ÷ VarianceS&P 500
= ÷
=
3 αFOX
= AverageFOX – βFOX × AverageS&P 500
= – ×
=
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | |
Expected rate of return on market portfolio2 | E(RM) | |
Systematic risk (β) of Twenty-First Century Fox Inc. common stock | βFOX | |
Expected rate of return on Twenty-First Century Fox Inc. common stock3 | E(RFOX) |
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).
3 E(RFOX) = RF + βFOX [E(RM) – RF]
= + [ – ]
=