Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like AutoZone Inc. common stock.
Rates of Return
AutoZone Inc. (AZO) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceAZO,t1 | DividendAZO,t1 | RAZO,t2 | PriceS&P 500,t | RS&P 500,t3 |
Sep 30, 2017 | $595.11 | 2,519.36 | ||||
1. | Oct 31, 2017 | $589.50 | -0.94% | 2,575.26 | 2.22% | |
2. | Nov 30, 2017 | $686.76 | 16.50% | 2,647.58 | 2.81% | |
3. | Dec 31, 2017 | $711.37 | 3.58% | 2,673.61 | 0.98% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Jul 31, 2023 | $2,481.72 | -0.47% | 4,588.96 | 4.85% | |
71. | Aug 31, 2023 | $2,531.33 | 2.00% | 4,507.66 | -1.77% | |
Average (R): | 2.31% | 0.95% | ||||
Standard deviation: | 7.25% | 5.08% |
AutoZone Inc. (AZO) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceAZO,t1 | DividendAZO,t1 | RAZO,t2 | PriceS&P 500,t | RS&P 500,t3 |
Sep 30, 2017 | $595.11 | 2,519.36 | ||||
1. | Oct 31, 2017 | $589.50 | -0.94% | 2,575.26 | 2.22% | |
2. | Nov 30, 2017 | $686.76 | 16.50% | 2,647.58 | 2.81% | |
3. | Dec 31, 2017 | $711.37 | 3.58% | 2,673.61 | 0.98% | |
4. | Jan 31, 2018 | $765.44 | 7.60% | 2,823.81 | 5.62% | |
5. | Feb 28, 2018 | $664.72 | -13.16% | 2,713.83 | -3.89% | |
6. | Mar 31, 2018 | $648.69 | -2.41% | 2,640.87 | -2.69% | |
7. | Apr 30, 2018 | $624.52 | -3.73% | 2,648.05 | 0.27% | |
8. | May 31, 2018 | $649.32 | 3.97% | 2,705.27 | 2.16% | |
9. | Jun 30, 2018 | $670.93 | 3.33% | 2,718.37 | 0.48% | |
10. | Jul 31, 2018 | $705.53 | 5.16% | 2,816.29 | 3.60% | |
11. | Aug 31, 2018 | $766.88 | 8.70% | 2,901.52 | 3.03% | |
12. | Sep 30, 2018 | $775.70 | 1.15% | 2,913.98 | 0.43% | |
13. | Oct 31, 2018 | $733.47 | -5.44% | 2,711.74 | -6.94% | |
14. | Nov 30, 2018 | $809.07 | 10.31% | 2,760.17 | 1.79% | |
15. | Dec 31, 2018 | $838.34 | 3.62% | 2,506.85 | -9.18% | |
16. | Jan 31, 2019 | $847.34 | 1.07% | 2,704.10 | 7.87% | |
17. | Feb 28, 2019 | $938.97 | 10.81% | 2,784.49 | 2.97% | |
18. | Mar 31, 2019 | $1,024.12 | 9.07% | 2,834.40 | 1.79% | |
19. | Apr 30, 2019 | $1,028.31 | 0.41% | 2,945.83 | 3.93% | |
20. | May 31, 2019 | $1,027.11 | -0.12% | 2,752.06 | -6.58% | |
21. | Jun 30, 2019 | $1,099.47 | 7.05% | 2,941.76 | 6.89% | |
22. | Jul 31, 2019 | $1,123.04 | 2.14% | 2,980.38 | 1.31% | |
23. | Aug 31, 2019 | $1,101.69 | -1.90% | 2,926.46 | -1.81% | |
24. | Sep 30, 2019 | $1,084.62 | -1.55% | 2,976.74 | 1.72% | |
25. | Oct 31, 2019 | $1,144.38 | 5.51% | 3,037.56 | 2.04% | |
26. | Nov 30, 2019 | $1,177.92 | 2.93% | 3,140.98 | 3.40% | |
27. | Dec 31, 2019 | $1,191.31 | 1.14% | 3,230.78 | 2.86% | |
28. | Jan 31, 2020 | $1,057.96 | -11.19% | 3,225.52 | -0.16% | |
29. | Feb 29, 2020 | $1,032.51 | -2.41% | 2,954.22 | -8.41% | |
30. | Mar 31, 2020 | $846.00 | -18.06% | 2,584.59 | -12.51% | |
31. | Apr 30, 2020 | $1,020.32 | 20.61% | 2,912.43 | 12.68% | |
32. | May 31, 2020 | $1,147.86 | 12.50% | 3,044.31 | 4.53% | |
33. | Jun 30, 2020 | $1,128.12 | -1.72% | 3,100.29 | 1.84% | |
34. | Jul 31, 2020 | $1,207.42 | 7.03% | 3,271.12 | 5.51% | |
35. | Aug 31, 2020 | $1,196.31 | -0.92% | 3,500.31 | 7.01% | |
36. | Sep 30, 2020 | $1,177.64 | -1.56% | 3,363.00 | -3.92% | |
37. | Oct 31, 2020 | $1,128.98 | -4.13% | 3,269.96 | -2.77% | |
38. | Nov 30, 2020 | $1,137.65 | 0.77% | 3,621.63 | 10.75% | |
39. | Dec 31, 2020 | $1,185.44 | 4.20% | 3,756.07 | 3.71% | |
40. | Jan 31, 2021 | $1,118.37 | -5.66% | 3,714.24 | -1.11% | |
41. | Feb 28, 2021 | $1,159.92 | 3.72% | 3,811.15 | 2.61% | |
42. | Mar 31, 2021 | $1,404.30 | 21.07% | 3,972.89 | 4.24% | |
43. | Apr 30, 2021 | $1,464.12 | 4.26% | 4,181.17 | 5.24% | |
44. | May 31, 2021 | $1,406.60 | -3.93% | 4,204.11 | 0.55% | |
45. | Jun 30, 2021 | $1,492.22 | 6.09% | 4,297.50 | 2.22% | |
46. | Jul 31, 2021 | $1,623.57 | 8.80% | 4,395.26 | 2.27% | |
47. | Aug 31, 2021 | $1,549.15 | -4.58% | 4,522.68 | 2.90% | |
48. | Sep 30, 2021 | $1,697.99 | 9.61% | 4,307.54 | -4.76% | |
49. | Oct 31, 2021 | $1,784.84 | 5.11% | 4,605.38 | 6.91% | |
50. | Nov 30, 2021 | $1,817.07 | 1.81% | 4,567.00 | -0.83% | |
51. | Dec 31, 2021 | $2,096.39 | 15.37% | 4,766.18 | 4.36% | |
52. | Jan 31, 2022 | $1,986.35 | -5.25% | 4,515.55 | -5.26% | |
53. | Feb 28, 2022 | $1,863.39 | -6.19% | 4,373.94 | -3.14% | |
54. | Mar 31, 2022 | $2,044.58 | 9.72% | 4,530.41 | 3.58% | |
55. | Apr 30, 2022 | $1,955.47 | -4.36% | 4,131.93 | -8.80% | |
56. | May 31, 2022 | $2,059.65 | 5.33% | 4,132.15 | 0.01% | |
57. | Jun 30, 2022 | $2,149.12 | 4.34% | 3,785.38 | -8.39% | |
58. | Jul 31, 2022 | $2,137.39 | -0.55% | 4,130.29 | 9.11% | |
59. | Aug 31, 2022 | $2,119.21 | -0.85% | 3,955.00 | -4.24% | |
60. | Sep 30, 2022 | $2,141.93 | 1.07% | 3,585.62 | -9.34% | |
61. | Oct 31, 2022 | $2,532.88 | 18.25% | 3,871.98 | 7.99% | |
62. | Nov 30, 2022 | $2,579.00 | 1.82% | 4,080.11 | 5.38% | |
63. | Dec 31, 2022 | $2,466.18 | -4.37% | 3,839.50 | -5.90% | |
64. | Jan 31, 2023 | $2,438.85 | -1.11% | 4,076.60 | 6.18% | |
65. | Feb 28, 2023 | $2,486.54 | 1.96% | 3,970.15 | -2.61% | |
66. | Mar 31, 2023 | $2,458.15 | -1.14% | 4,109.31 | 3.51% | |
67. | Apr 30, 2023 | $2,663.31 | 8.35% | 4,169.48 | 1.46% | |
68. | May 31, 2023 | $2,386.84 | -10.38% | 4,179.83 | 0.25% | |
69. | Jun 30, 2023 | $2,493.36 | 4.46% | 4,376.86 | 4.71% | |
70. | Jul 31, 2023 | $2,481.72 | -0.47% | 4,588.96 | 4.85% | |
71. | Aug 31, 2023 | $2,531.33 | 2.00% | 4,507.66 | -1.77% | |
Average (R): | 2.31% | 0.95% | ||||
Standard deviation: | 7.25% | 5.08% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of AZO during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RAZO,t | RS&P 500,t | (RAZO,t–RAZO)2 | (RS&P 500,t–RS&P 500)2 | (RAZO,t–RAZO)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Oct 31, 2017 | -0.94% | 2.22% | 10.60 | 1.61 | -4.13 |
2. | Nov 30, 2017 | 16.50% | 2.81% | 201.24 | 3.45 | 26.35 |
3. | Dec 31, 2017 | 3.58% | 0.98% | 1.61 | 0.00 | 0.04 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Jul 31, 2023 | -0.47% | 4.85% | 7.73 | 15.17 | -10.83 |
71. | Aug 31, 2023 | 2.00% | -1.77% | 0.10 | 7.41 | 0.85 |
Total (Σ): | 3,675.51 | 1,807.09 | 1,305.66 |
t | Date | RAZO,t | RS&P 500,t | (RAZO,t–RAZO)2 | (RS&P 500,t–RS&P 500)2 | (RAZO,t–RAZO)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Oct 31, 2017 | -0.94% | 2.22% | 10.60 | 1.61 | -4.13 |
2. | Nov 30, 2017 | 16.50% | 2.81% | 201.24 | 3.45 | 26.35 |
3. | Dec 31, 2017 | 3.58% | 0.98% | 1.61 | 0.00 | 0.04 |
4. | Jan 31, 2018 | 7.60% | 5.62% | 27.96 | 21.78 | 24.68 |
5. | Feb 28, 2018 | -13.16% | -3.89% | 239.36 | 23.48 | 74.97 |
6. | Mar 31, 2018 | -2.41% | -2.69% | 22.32 | 13.25 | 17.19 |
7. | Apr 30, 2018 | -3.73% | 0.27% | 36.47 | 0.46 | 4.10 |
8. | May 31, 2018 | 3.97% | 2.16% | 2.75 | 1.46 | 2.01 |
9. | Jun 30, 2018 | 3.33% | 0.48% | 1.03 | 0.22 | -0.47 |
10. | Jul 31, 2018 | 5.16% | 3.60% | 8.09 | 7.03 | 7.54 |
11. | Aug 31, 2018 | 8.70% | 3.03% | 40.74 | 4.31 | 13.25 |
12. | Sep 30, 2018 | 1.15% | 0.43% | 1.35 | 0.27 | 0.61 |
13. | Oct 31, 2018 | -5.44% | -6.94% | 60.17 | 62.28 | 61.21 |
14. | Nov 30, 2018 | 10.31% | 1.79% | 63.91 | 0.70 | 6.67 |
15. | Dec 31, 2018 | 3.62% | -9.18% | 1.70 | 102.59 | -13.22 |
16. | Jan 31, 2019 | 1.07% | 7.87% | 1.54 | 47.85 | -8.57 |
17. | Feb 28, 2019 | 10.81% | 2.97% | 72.27 | 4.09 | 17.19 |
18. | Mar 31, 2019 | 9.07% | 1.79% | 45.64 | 0.71 | 5.68 |
19. | Apr 30, 2019 | 0.41% | 3.93% | 3.62 | 8.88 | -5.67 |
20. | May 31, 2019 | -0.12% | -6.58% | 5.90 | 56.68 | 18.29 |
21. | Jun 30, 2019 | 7.05% | 6.89% | 22.39 | 35.31 | 28.12 |
22. | Jul 31, 2019 | 2.14% | 1.31% | 0.03 | 0.13 | -0.06 |
23. | Aug 31, 2019 | -1.90% | -1.81% | 17.76 | 7.62 | 11.63 |
24. | Sep 30, 2019 | -1.55% | 1.72% | 14.92 | 0.59 | -2.96 |
25. | Oct 31, 2019 | 5.51% | 2.04% | 10.22 | 1.19 | 3.49 |
26. | Nov 30, 2019 | 2.93% | 3.40% | 0.38 | 6.02 | 1.52 |
27. | Dec 31, 2019 | 1.14% | 2.86% | 1.38 | 3.64 | -2.24 |
28. | Jan 31, 2020 | -11.19% | -0.16% | 182.42 | 1.24 | 15.05 |
29. | Feb 29, 2020 | -2.41% | -8.41% | 22.26 | 87.65 | 44.17 |
30. | Mar 31, 2020 | -18.06% | -12.51% | 415.20 | 181.25 | 274.33 |
31. | Apr 30, 2020 | 20.61% | 12.68% | 334.62 | 137.67 | 214.63 |
32. | May 31, 2020 | 12.50% | 4.53% | 103.78 | 12.80 | 36.44 |
33. | Jun 30, 2020 | -1.72% | 1.84% | 16.26 | 0.79 | -3.58 |
34. | Jul 31, 2020 | 7.03% | 5.51% | 22.25 | 20.78 | 21.50 |
35. | Aug 31, 2020 | -0.92% | 7.01% | 10.45 | 36.67 | -19.58 |
36. | Sep 30, 2020 | -1.56% | -3.92% | 15.00 | 23.76 | 18.88 |
37. | Oct 31, 2020 | -4.13% | -2.77% | 41.53 | 13.82 | 23.96 |
38. | Nov 30, 2020 | 0.77% | 10.75% | 2.39 | 96.11 | -15.14 |
39. | Dec 31, 2020 | 4.20% | 3.71% | 3.56 | 7.62 | 5.21 |
40. | Jan 31, 2021 | -5.66% | -1.11% | 63.53 | 4.26 | 16.46 |
41. | Feb 28, 2021 | 3.72% | 2.61% | 1.97 | 2.75 | 2.33 |
42. | Mar 31, 2021 | 21.07% | 4.24% | 351.79 | 10.84 | 61.76 |
43. | Apr 30, 2021 | 4.26% | 5.24% | 3.79 | 18.42 | 8.36 |
44. | May 31, 2021 | -3.93% | 0.55% | 38.95 | 0.16 | 2.51 |
45. | Jun 30, 2021 | 6.09% | 2.22% | 14.25 | 1.61 | 4.79 |
46. | Jul 31, 2021 | 8.80% | 2.27% | 42.12 | 1.75 | 8.59 |
47. | Aug 31, 2021 | -4.58% | 2.90% | 47.56 | 3.79 | -13.43 |
48. | Sep 30, 2021 | 9.61% | -4.76% | 53.22 | 32.58 | -41.64 |
49. | Oct 31, 2021 | 5.11% | 6.91% | 7.85 | 35.56 | 16.71 |
50. | Nov 30, 2021 | 1.81% | -0.83% | 0.26 | 3.18 | 0.90 |
51. | Dec 31, 2021 | 15.37% | 4.36% | 170.55 | 11.63 | 44.53 |
52. | Jan 31, 2022 | -5.25% | -5.26% | 57.18 | 38.56 | 46.96 |
53. | Feb 28, 2022 | -6.19% | -3.14% | 72.30 | 16.71 | 34.75 |
54. | Mar 31, 2022 | 9.72% | 3.58% | 54.92 | 6.90 | 19.46 |
55. | Apr 30, 2022 | -4.36% | -8.80% | 44.50 | 95.00 | 65.02 |
56. | May 31, 2022 | 5.33% | 0.01% | 9.09 | 0.89 | -2.85 |
57. | Jun 30, 2022 | 4.34% | -8.39% | 4.13 | 87.29 | -18.98 |
58. | Jul 31, 2022 | -0.55% | 9.11% | 8.17 | 66.59 | -23.33 |
59. | Aug 31, 2022 | -0.85% | -4.24% | 10.01 | 26.99 | 16.43 |
60. | Sep 30, 2022 | 1.07% | -9.34% | 1.54 | 105.90 | 12.77 |
61. | Oct 31, 2022 | 18.25% | 7.99% | 254.07 | 49.49 | 112.14 |
62. | Nov 30, 2022 | 1.82% | 5.38% | 0.24 | 19.57 | -2.18 |
63. | Dec 31, 2022 | -4.37% | -5.90% | 44.72 | 46.90 | 45.80 |
64. | Jan 31, 2023 | -1.11% | 6.18% | 11.70 | 27.29 | -17.87 |
65. | Feb 28, 2023 | 1.96% | -2.61% | 0.13 | 12.69 | 1.27 |
66. | Mar 31, 2023 | -1.14% | 3.51% | 11.93 | 6.52 | -8.82 |
67. | Apr 30, 2023 | 8.35% | 1.46% | 36.40 | 0.26 | 3.10 |
68. | May 31, 2023 | -10.38% | 0.25% | 161.12 | 0.49 | 8.92 |
69. | Jun 30, 2023 | 4.46% | 4.71% | 4.62 | 14.16 | 8.09 |
70. | Jul 31, 2023 | -0.47% | 4.85% | 7.73 | 15.17 | -10.83 |
71. | Aug 31, 2023 | 2.00% | -1.77% | 0.10 | 7.41 | 0.85 |
Total (Σ): | 3,675.51 | 1,807.09 | 1,305.66 |
Show all
VarianceAZO = Σ(RAZO,t–RAZO)2 ÷ (71 – 1)
= 3,675.51 ÷ (71 – 1)
= 52.51
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,807.09 ÷ (71 – 1)
= 25.82
CovarianceAZO, S&P 500 = Σ(RAZO,t–RAZO)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,305.66 ÷ (71 – 1)
= 18.65
Systematic Risk (β) Estimation
VarianceAZO | 52.51 |
VarianceS&P 500 | 25.82 |
CovarianceAZO, S&P 500 | 18.65 |
Correlation coefficientAZO, S&P 5001 | 0.51 |
βAZO2 | 0.72 |
αAZO3 | 1.63% |
Calculations
1 Correlation coefficientAZO, S&P 500
= CovarianceAZO, S&P 500 ÷ (Standard deviationAZO × Standard deviationS&P 500)
= 18.65 ÷ (7.25% × 5.08%)
= 0.51
2 βAZO
= CovarianceAZO, S&P 500 ÷ VarianceS&P 500
= 18.65 ÷ 25.82
= 0.72
3 αAZO
= AverageAZO – βAZO × AverageS&P 500
= 2.31% – 0.72 × 0.95%
= 1.63%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.69% |
Expected rate of return on market portfolio2 | E(RM) | 13.79% |
Systematic risk (β) of AutoZone Inc. common stock | βAZO | 0.72 |
Expected rate of return on AutoZone Inc. common stock3 | E(RAZO) | 11.26% |
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(RAZO) = RF + βAZO [E(RM) – RF]
= 4.69% + 0.72 [13.79% – 4.69%]
= 11.26%