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Microsoft Excel LibreOffice Calc

Capital Asset Pricing Model (CAPM)

Difficulty: Intermediate

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Time Warner's common stock.


Rates of Return

Time Warner Inc., monthly rates of return

Microsoft Excel LibreOffice Calc
Time Warner Inc. (TWX) Standard & Poor's 500 (S&P 500)
t Date PriceTWX,t1 DividendTWX,t1 RTWX,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2013 50.52 1,498.11
1. Feb 28, 2013 53.17 0.2875 5.81% 1,514.68 1.11%
2. Mar 31, 2013 57.62 8.37% 1,569.19 3.60%
3. Apr 30, 2013 59.78 3.75% 1,597.57 1.81%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2017 91.51 -6.90% 2,647.58 2.81%
59. Dec 31, 2017 91.47 -0.04% 2,673.61 0.98%
Average: 1.35% 1.02%
Standard Deviation: 6.00% 2.71%
Time Warner Inc. (TWX) Standard & Poor's 500 (S&P 500)
t Date PriceTWX,t1 DividendTWX,t1 RTWX,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2013 50.52 1,498.11
1. Feb 28, 2013 53.17 0.2875 5.81% 1,514.68 1.11%
2. Mar 31, 2013 57.62 8.37% 1,569.19 3.60%
3. Apr 30, 2013 59.78 3.75% 1,597.57 1.81%
4. May 31, 2013 58.37 0.2875 -1.88% 1,630.74 2.08%
5. Jun 30, 2013 57.82 -0.94% 1,606.28 -1.50%
6. Jul 31, 2013 62.26 7.68% 1,685.73 4.95%
7. Aug 31, 2013 60.53 0.2875 -2.32% 1,632.97 -3.13%
8. Sep 30, 2013 65.81 8.72% 1,681.55 2.97%
9. Oct 31, 2013 68.74 4.45% 1,756.54 4.46%
10. Nov 30, 2013 65.71 0.2875 -3.99% 1,805.81 2.80%
11. Dec 31, 2013 69.72 6.10% 1,848.36 2.36%
12. Jan 31, 2014 62.83 -9.88% 1,782.59 -3.56%
13. Feb 28, 2014 67.13 0.3175 7.35% 1,859.45 4.31%
14. Mar 31, 2014 65.33 -2.68% 1,872.34 0.69%
15. Apr 30, 2014 66.46 1.73% 1,883.95 0.62%
16. May 31, 2014 69.83 0.3175 5.55% 1,923.57 2.10%
17. Jun 30, 2014 70.25 0.60% 1,960.23 1.91%
18. Jul 31, 2014 83.02 18.18% 1,930.67 -1.51%
19. Aug 31, 2014 77.03 0.3175 -6.83% 2,003.37 3.77%
20. Sep 30, 2014 75.21 -2.36% 1,972.29 -1.55%
21. Oct 31, 2014 79.47 5.66% 2,018.05 2.32%
22. Nov 30, 2014 85.12 0.3175 7.51% 2,067.56 2.45%
23. Dec 31, 2014 85.42 0.35% 2,058.90 -0.42%
24. Jan 31, 2015 77.93 -8.77% 1,994.99 -3.10%
25. Feb 28, 2015 81.86 0.35 5.49% 2,104.50 5.49%
26. Mar 31, 2015 84.44 3.15% 2,067.89 -1.74%
27. Apr 30, 2015 84.41 -0.04% 2,085.51 0.85%
28. May 31, 2015 84.48 0.35 0.50% 2,107.39 1.05%
29. Jun 30, 2015 87.41 3.47% 2,063.11 -2.10%
30. Jul 31, 2015 88.04 0.72% 2,103.84 1.97%
31. Aug 31, 2015 71.10 0.35 -18.84% 1,972.18 -6.26%
32. Sep 30, 2015 68.75 -3.31% 1,920.03 -2.64%
33. Oct 31, 2015 75.34 9.59% 2,079.36 8.30%
34. Nov 30, 2015 69.98 0.35 -6.65% 2,080.41 0.05%
35. Dec 31, 2015 64.67 -7.59% 2,043.94 -1.75%
36. Jan 31, 2016 70.44 8.92% 1,940.24 -5.07%
37. Feb 29, 2016 66.20 0.4025 -5.45% 1,932.23 -0.41%
38. Mar 31, 2016 72.55 9.59% 2,059.74 6.60%
39. Apr 30, 2016 75.14 3.57% 2,065.30 0.27%
40. May 31, 2016 75.66 0.4025 1.23% 2,096.95 1.53%
41. Jun 30, 2016 73.54 -2.80% 2,098.86 0.09%
42. Jul 31, 2016 76.65 4.23% 2,173.60 3.56%
43. Aug 31, 2016 78.41 0.4025 2.82% 2,170.95 -0.12%
44. Sep 30, 2016 79.61 1.53% 2,168.27 -0.12%
45. Oct 31, 2016 88.99 11.78% 2,126.15 -1.94%
46. Nov 30, 2016 91.82 0.4025 3.63% 2,198.81 3.42%
47. Dec 31, 2016 96.53 5.13% 2,238.83 1.82%
48. Jan 31, 2017 96.85 0.33% 2,278.87 1.79%
49. Feb 28, 2017 98.21 0.4025 1.82% 2,363.64 3.72%
50. Mar 31, 2017 97.71 -0.51% 2,362.72 -0.04%
51. Apr 30, 2017 99.27 1.60% 2,384.20 0.91%
52. May 31, 2017 99.49 0.4025 0.63% 2,411.80 1.16%
53. Jun 30, 2017 100.41 0.92% 2,423.41 0.48%
54. Jul 31, 2017 102.42 0.4025 2.40% 2,470.30 1.93%
55. Aug 31, 2017 101.10 -1.29% 2,471.65 0.05%
56. Sep 30, 2017 102.45 1.34% 2,519.36 1.93%
57. Oct 31, 2017 98.29 0.4025 -3.67% 2,575.26 2.22%
58. Nov 30, 2017 91.51 -6.90% 2,647.58 2.81%
59. Dec 31, 2017 91.47 -0.04% 2,673.61 0.98%
Average: 1.35% 1.02%
Standard Deviation: 6.00% 2.71%

Show All

1 Data in USD $ per share of common stock, adjusted for splits and stock dividends.

2 Rate of return on common stock of TWX during period t

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


Systematic Risk (β) Estimation

Microsoft Excel LibreOffice Calc
VarianceTWX 36.04
VarianceS&P 500 7.32
CovarianceTWX, S&P 500 7.00
Correlation CoefficientTWX, S&P 5001 0.43
βTWX2 0.96
αTWX3 0.37

Calculations

1 CovarianceTWX, S&P 500 ÷ (Standard DeviationTWX × Standard DeviationS&P 500)
= 7.00 ÷ (6.00 × 2.71)

2 CovarianceTWX, S&P 500 ÷ VarianceS&P 500
= 7.00 ÷ 7.32

3 AverageTWX – βTWX × AverageS&P 500
= 1.350.96 × 1.02


Expected Rate of Return

Microsoft Excel LibreOffice Calc
Assumptions
Rate of return on LT Treasury Composite1 RF 3.34%
Expected rate of return on market portfolio2 E(RM) 12.31%
Systematic risk (β) of Time Warner's common stock βTWX 0.96
Expected rate of return on Time Warner's common stock3 E(RTWX) 11.93%

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).

Calculations

2 See Details »

3 E(RTWX) = RF + βTWX [E(RM) – RF]
= 3.34% + 0.96 [12.31% – 3.34%]
= 11.93%