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Praxair Inc. (PX) | 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 's common stock.

Rates of Return

Praxair Inc., monthly rates of return

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    Praxair Inc. (PX) NYSE Composite Index (NYC)
t Date PricePX,t1 DividendPX,t1 RPX,t2 PriceNYC,t RNYC,t3
  Jan 31, 2008 80.70     9,126.16  
1. Feb 29, 2008 80.28   -0.52% 8,962.46 -1.79%
2. Mar 31, 2008 84.23 0.375 5.39% 8,797.29 -1.84%
3. Apr 30, 2008 91.31   8.41% 9,299.60 5.71%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2012 107.21   0.94% 8,260.43 0.47%
59. Dec 31, 2012 109.45 0.55 2.60% 8,443.51 2.22%
Average: 0.89%   0.05%
Standard Deviation: 6.32%   6.05%
    Praxair Inc. (PX) NYSE Composite Index (NYC)
t Date PricePX,t1 DividendPX,t1 RPX,t2 PriceNYC,t RNYC,t3
  Jan 31, 2008 80.70     9,126.16  
1. Feb 29, 2008 80.28   -0.52% 8,962.46 -1.79%
2. Mar 31, 2008 84.23 0.375 5.39% 8,797.29 -1.84%
3. Apr 30, 2008 91.31   8.41% 9,299.60 5.71%
4. May 31, 2008 95.06   4.11% 9,401.08 1.09%
5. Jun 30, 2008 94.24 0.375 -0.47% 8,660.48 -7.88%
6. Jul 31, 2008 93.73   -0.54% 8,438.64 -2.56%
7. Aug 31, 2008 89.84   -4.15% 8,382.08 -0.67%
8. Sep 30, 2008 71.74 0.375 -19.73% 7,532.80 -10.13%
9. Oct 31, 2008 65.15   -9.19% 6,061.09 -19.54%
10. Nov 30, 2008 59.05   -9.36% 5,599.30 -7.62%
11. Dec 31, 2008 59.36 0.375 1.16% 5,757.05 2.82%
12. Jan 31, 2009 62.26   4.89% 5,195.79 -9.75%
13. Feb 28, 2009 56.75   -8.85% 4,617.03 -11.14%
14. Mar 31, 2009 67.29 0.40 19.28% 4,978.98 7.84%
15. Apr 30, 2009 74.61   10.88% 5,513.36 10.73%
16. May 31, 2009 73.20   -1.89% 6,004.07 8.90%
17. Jun 30, 2009 71.07 0.40 -2.36% 5,905.15 -1.65%
18. Jul 31, 2009 78.18   10.00% 6,424.28 8.79%
19. Aug 31, 2009 76.62   -2.00% 6,643.24 3.41%
20. Sep 30, 2009 81.69 0.40 7.14% 6,910.88 4.03%
21. Oct 31, 2009 79.44   -2.75% 6,739.45 -2.48%
22. Nov 30, 2009 82.03   3.26% 7,092.36 5.24%
23. Dec 31, 2009 80.31 0.40 -1.61% 7,184.96 1.31%
24. Jan 31, 2010 75.32   -6.21% 6,883.78 -4.19%
25. Feb 28, 2010 75.14   -0.24% 7,035.04 2.20%
26. Mar 31, 2010 83.00 0.45 11.06% 7,447.80 5.87%
27. Apr 30, 2010 83.77   0.93% 7,474.40 0.36%
28. May 31, 2010 77.60   -7.37% 6,791.57 -9.14%
29. Jun 30, 2010 75.99 0.45 -1.49% 6,469.65 -4.74%
30. Jul 31, 2010 86.82   14.25% 6,998.99 8.18%
31. Aug 31, 2010 86.03   -0.91% 6,704.15 -4.21%
32. Sep 30, 2010 90.26 0.45 5.44% 7,281.07 8.61%
33. Oct 31, 2010 91.34   1.20% 7,513.35 3.19%
34. Nov 30, 2010 92.05   0.78% 7,430.94 -1.10%
35. Dec 31, 2010 95.47 0.45 4.20% 7,964.02 7.17%
36. Jan 31, 2011 93.04   -2.55% 8,139.16 2.20%
37. Feb 28, 2011 99.38   6.81% 8,438.55 3.68%
38. Mar 31, 2011 101.60 0.50 2.74% 8,404.98 -0.40%
39. Apr 30, 2011 106.42   4.74% 8,671.41 3.17%
40. May 31, 2011 105.84   -0.55% 8,477.28 -2.24%
41. Jun 30, 2011 108.39 0.50 2.88% 8,319.10 -1.87%
42. Jul 31, 2011 103.64   -4.38% 8,079.44 -2.88%
43. Aug 31, 2011 98.49   -4.97% 7,528.39 -6.82%
44. Sep 30, 2011 93.48 0.50 -4.58% 6,791.65 -9.79%
45. Oct 31, 2011 101.67   8.76% 7,563.38 11.36%
46. Nov 30, 2011 102.00   0.32% 7,484.50 -1.04%
47. Dec 31, 2011 106.90 0.50 5.29% 7,477.03 -0.10%
48. Jan 31, 2012 106.20   -0.65% 7,838.48 4.83%
49. Feb 29, 2012 109.00   2.64% 8,113.24 3.51%
50. Mar 31, 2012 114.64 0.55 5.68% 8,206.93 1.15%
51. Apr 30, 2012 115.70   0.92% 8,119.06 -1.07%
52. May 31, 2012 106.24   -8.18% 7,463.96 -8.07%
53. Jun 30, 2012 108.73 0.55 2.86% 7,801.84 4.53%
54. Jul 31, 2012 103.76   -4.57% 7,863.93 0.80%
55. Aug 31, 2012 105.50   1.68% 8,014.93 1.92%
56. Sep 30, 2012 103.88 0.55 -1.01% 8,251.00 2.95%
57. Oct 31, 2012 106.21   2.24% 8,221.40 -0.36%
58. Nov 30, 2012 107.21   0.94% 8,260.43 0.47%
59. Dec 31, 2012 109.45 0.55 2.60% 8,443.51 2.22%
Average: 0.89%   0.05%
Standard Deviation: 6.32%   6.05%

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

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

3 Rate of return on NYC (the market portfolio proxy) during period t

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Systematic Risk (β) Estimation

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VariancePX 39.89
VarianceNYC 36.59
CovariancePX,NYC 27.89
Correlation CoefficientPX,NYC1 0.73
βPX2 0.76
αPX3 0.85

Calculations

1 CovariancePX,NYC ÷ (Standard DeviationPX × Standard DeviationNYC)
= 27.89 ÷ (6.32 × 6.05)

2 CovariancePX,NYC ÷ VarianceNYC
= 27.89 ÷ 36.59

3 AveragePX – βPX × AverageNYC
= 0.89 – 0.76 × 0.05

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Expected Rate of Return

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Assumptions
Rate of return on LT Treasury Composite1 RF 2.77%
Expected rate of return on market portfolio2 E(RM) 13.09%
Systematic risk (β) of 's common stock βPX 0.76
 
Expected rate of return on 's common stock3 E(RPX) 10.63%

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(RPX) = RF + βPX [E(RM) – RF]
= 2.77% + 0.76 [13.09% – 2.77%]
= 10.63%

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