Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Monsanto Co. common stock.
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Rates of Return
Monsanto Co. (MON) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceMON,t1 | DividendMON,t1 | RMON,t2 | PriceS&P 500,t | RS&P 500,t3 |
Sep 30, 2011 | ||||||
1. | Oct 31, 2011 | |||||
2. | Nov 30, 2011 | |||||
3. | Dec 31, 2011 | |||||
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Jul 31, 2017 | |||||
71. | Aug 31, 2017 | |||||
Average (R): | ||||||
Standard deviation: |
Monsanto Co. (MON) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceMON,t1 | DividendMON,t1 | RMON,t2 | PriceS&P 500,t | RS&P 500,t3 |
Sep 30, 2011 | ||||||
1. | Oct 31, 2011 | |||||
2. | Nov 30, 2011 | |||||
3. | Dec 31, 2011 | |||||
4. | Jan 31, 2012 | |||||
5. | Feb 29, 2012 | |||||
6. | Mar 31, 2012 | |||||
7. | Apr 30, 2012 | |||||
8. | May 31, 2012 | |||||
9. | Jun 30, 2012 | |||||
10. | Jul 31, 2012 | |||||
11. | Aug 31, 2012 | |||||
12. | Sep 30, 2012 | |||||
13. | Oct 31, 2012 | |||||
14. | Nov 30, 2012 | |||||
15. | Dec 31, 2012 | |||||
16. | Jan 31, 2013 | |||||
17. | Feb 28, 2013 | |||||
18. | Mar 31, 2013 | |||||
19. | Apr 30, 2013 | |||||
20. | May 31, 2013 | |||||
21. | Jun 30, 2013 | |||||
22. | Jul 31, 2013 | |||||
23. | Aug 31, 2013 | |||||
24. | Sep 30, 2013 | |||||
25. | Oct 31, 2013 | |||||
26. | Nov 30, 2013 | |||||
27. | Dec 31, 2013 | |||||
28. | Jan 31, 2014 | |||||
29. | Feb 28, 2014 | |||||
30. | Mar 31, 2014 | |||||
31. | Apr 30, 2014 | |||||
32. | May 31, 2014 | |||||
33. | Jun 30, 2014 | |||||
34. | Jul 31, 2014 | |||||
35. | Aug 31, 2014 | |||||
36. | Sep 30, 2014 | |||||
37. | Oct 31, 2014 | |||||
38. | Nov 30, 2014 | |||||
39. | Dec 31, 2014 | |||||
40. | Jan 31, 2015 | |||||
41. | Feb 28, 2015 | |||||
42. | Mar 31, 2015 | |||||
43. | Apr 30, 2015 | |||||
44. | May 31, 2015 | |||||
45. | Jun 30, 2015 | |||||
46. | Jul 31, 2015 | |||||
47. | Aug 31, 2015 | |||||
48. | Sep 30, 2015 | |||||
49. | Oct 31, 2015 | |||||
50. | Nov 30, 2015 | |||||
51. | Dec 31, 2015 | |||||
52. | Jan 31, 2016 | |||||
53. | Feb 29, 2016 | |||||
54. | Mar 31, 2016 | |||||
55. | Apr 30, 2016 | |||||
56. | May 31, 2016 | |||||
57. | Jun 30, 2016 | |||||
58. | Jul 31, 2016 | |||||
59. | Aug 31, 2016 | |||||
60. | Sep 30, 2016 | |||||
61. | Oct 31, 2016 | |||||
62. | Nov 30, 2016 | |||||
63. | Dec 31, 2016 | |||||
64. | Jan 31, 2017 | |||||
65. | Feb 28, 2017 | |||||
66. | Mar 31, 2017 | |||||
67. | Apr 30, 2017 | |||||
68. | May 31, 2017 | |||||
69. | Jun 30, 2017 | |||||
70. | Jul 31, 2017 | |||||
71. | Aug 31, 2017 | |||||
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 MON during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RMON,t | RS&P 500,t | (RMON,t–RMON)2 | (RS&P 500,t–RS&P 500)2 | (RMON,t–RMON)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Oct 31, 2011 | |||||
2. | Nov 30, 2011 | |||||
3. | Dec 31, 2011 | |||||
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Jul 31, 2017 | |||||
71. | Aug 31, 2017 | |||||
Total (Σ): |
t | Date | RMON,t | RS&P 500,t | (RMON,t–RMON)2 | (RS&P 500,t–RS&P 500)2 | (RMON,t–RMON)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Oct 31, 2011 | |||||
2. | Nov 30, 2011 | |||||
3. | Dec 31, 2011 | |||||
4. | Jan 31, 2012 | |||||
5. | Feb 29, 2012 | |||||
6. | Mar 31, 2012 | |||||
7. | Apr 30, 2012 | |||||
8. | May 31, 2012 | |||||
9. | Jun 30, 2012 | |||||
10. | Jul 31, 2012 | |||||
11. | Aug 31, 2012 | |||||
12. | Sep 30, 2012 | |||||
13. | Oct 31, 2012 | |||||
14. | Nov 30, 2012 | |||||
15. | Dec 31, 2012 | |||||
16. | Jan 31, 2013 | |||||
17. | Feb 28, 2013 | |||||
18. | Mar 31, 2013 | |||||
19. | Apr 30, 2013 | |||||
20. | May 31, 2013 | |||||
21. | Jun 30, 2013 | |||||
22. | Jul 31, 2013 | |||||
23. | Aug 31, 2013 | |||||
24. | Sep 30, 2013 | |||||
25. | Oct 31, 2013 | |||||
26. | Nov 30, 2013 | |||||
27. | Dec 31, 2013 | |||||
28. | Jan 31, 2014 | |||||
29. | Feb 28, 2014 | |||||
30. | Mar 31, 2014 | |||||
31. | Apr 30, 2014 | |||||
32. | May 31, 2014 | |||||
33. | Jun 30, 2014 | |||||
34. | Jul 31, 2014 | |||||
35. | Aug 31, 2014 | |||||
36. | Sep 30, 2014 | |||||
37. | Oct 31, 2014 | |||||
38. | Nov 30, 2014 | |||||
39. | Dec 31, 2014 | |||||
40. | Jan 31, 2015 | |||||
41. | Feb 28, 2015 | |||||
42. | Mar 31, 2015 | |||||
43. | Apr 30, 2015 | |||||
44. | May 31, 2015 | |||||
45. | Jun 30, 2015 | |||||
46. | Jul 31, 2015 | |||||
47. | Aug 31, 2015 | |||||
48. | Sep 30, 2015 | |||||
49. | Oct 31, 2015 | |||||
50. | Nov 30, 2015 | |||||
51. | Dec 31, 2015 | |||||
52. | Jan 31, 2016 | |||||
53. | Feb 29, 2016 | |||||
54. | Mar 31, 2016 | |||||
55. | Apr 30, 2016 | |||||
56. | May 31, 2016 | |||||
57. | Jun 30, 2016 | |||||
58. | Jul 31, 2016 | |||||
59. | Aug 31, 2016 | |||||
60. | Sep 30, 2016 | |||||
61. | Oct 31, 2016 | |||||
62. | Nov 30, 2016 | |||||
63. | Dec 31, 2016 | |||||
64. | Jan 31, 2017 | |||||
65. | Feb 28, 2017 | |||||
66. | Mar 31, 2017 | |||||
67. | Apr 30, 2017 | |||||
68. | May 31, 2017 | |||||
69. | Jun 30, 2017 | |||||
70. | Jul 31, 2017 | |||||
71. | Aug 31, 2017 | |||||
Total (Σ): |
Show all
VarianceMON = Σ(RMON,t–RMON)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
CovarianceMON, S&P 500 = Σ(RMON,t–RMON)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= ÷ (71 – 1)
=
Systematic Risk (β) Estimation
VarianceMON | |
VarianceS&P 500 | |
CovarianceMON, S&P 500 | |
Correlation coefficientMON, S&P 5001 | |
βMON2 | |
αMON3 |
Calculations
1 Correlation coefficientMON, S&P 500
= CovarianceMON, S&P 500 ÷ (Standard deviationMON × Standard deviationS&P 500)
= ÷ ( × )
=
2 βMON
= CovarianceMON, S&P 500 ÷ VarianceS&P 500
= ÷
=
3 αMON
= AverageMON – βMON × 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 Monsanto Co. common stock | βMON | |
Expected rate of return on Monsanto Co. common stock3 | E(RMON) |
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(RMON) = RF + βMON [E(RM) – RF]
= + [ – ]
=