Stock Analysis on Net

lululemon athletica inc. (NASDAQ:LULU)

Capital Asset Pricing Model (CAPM) 

Microsoft Excel

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like lululemon athletica inc. common stock.


Rates of Return

lululemon athletica inc., monthly rates of return

Microsoft Excel
lululemon athletica inc. (LULU) Standard & Poor’s 500 (S&P 500)
t Date PriceLULU,t1 DividendLULU,t1 RLULU,t2 PriceS&P 500,t RS&P 500,t3
Feb 28, 2018 $81.10 2,713.83
1. Mar 31, 2018 $89.12 9.89% 2,640.87 -2.69%
2. Apr 30, 2018 $99.80 11.98% 2,648.05 0.27%
3. May 31, 2018 $105.05 5.26% 2,705.27 2.16%
. . . . . . .
. . . . . . .
. . . . . . .
70. Dec 31, 2023 $511.29 14.43% 4,769.83 4.42%
71. Jan 31, 2024 $453.82 -11.24% 4,845.65 1.59%
Average (R): 3.03% 0.95%
Standard deviation: 11.02% 5.18%
lululemon athletica inc. (LULU) Standard & Poor’s 500 (S&P 500)
t Date PriceLULU,t1 DividendLULU,t1 RLULU,t2 PriceS&P 500,t RS&P 500,t3
Feb 28, 2018 $81.10 2,713.83
1. Mar 31, 2018 $89.12 9.89% 2,640.87 -2.69%
2. Apr 30, 2018 $99.80 11.98% 2,648.05 0.27%
3. May 31, 2018 $105.05 5.26% 2,705.27 2.16%
4. Jun 30, 2018 $124.85 18.85% 2,718.37 0.48%
5. Jul 31, 2018 $119.95 -3.92% 2,816.29 3.60%
6. Aug 31, 2018 $154.93 29.16% 2,901.52 3.03%
7. Sep 30, 2018 $162.49 4.88% 2,913.98 0.43%
8. Oct 31, 2018 $140.73 -13.39% 2,711.74 -6.94%
9. Nov 30, 2018 $132.55 -5.81% 2,760.17 1.79%
10. Dec 31, 2018 $121.61 -8.25% 2,506.85 -9.18%
11. Jan 31, 2019 $147.81 21.54% 2,704.10 7.87%
12. Feb 28, 2019 $150.42 1.77% 2,784.49 2.97%
13. Mar 31, 2019 $163.87 8.94% 2,834.40 1.79%
14. Apr 30, 2019 $176.35 7.62% 2,945.83 3.93%
15. May 31, 2019 $165.59 -6.10% 2,752.06 -6.58%
16. Jun 30, 2019 $180.21 8.83% 2,941.76 6.89%
17. Jul 31, 2019 $191.09 6.04% 2,980.38 1.31%
18. Aug 31, 2019 $184.67 -3.36% 2,926.46 -1.81%
19. Sep 30, 2019 $192.53 4.26% 2,976.74 1.72%
20. Oct 31, 2019 $204.27 6.10% 3,037.56 2.04%
21. Nov 30, 2019 $225.69 10.49% 3,140.98 3.40%
22. Dec 31, 2019 $231.67 2.65% 3,230.78 2.86%
23. Jan 31, 2020 $239.39 3.33% 3,225.52 -0.16%
24. Feb 29, 2020 $217.41 -9.18% 2,954.22 -8.41%
25. Mar 31, 2020 $189.55 -12.81% 2,584.59 -12.51%
26. Apr 30, 2020 $223.48 17.90% 2,912.43 12.68%
27. May 31, 2020 $300.10 34.28% 3,044.31 4.53%
28. Jun 30, 2020 $312.01 3.97% 3,100.29 1.84%
29. Jul 31, 2020 $325.59 4.35% 3,271.12 5.51%
30. Aug 31, 2020 $375.67 15.38% 3,500.31 7.01%
31. Sep 30, 2020 $329.37 -12.32% 3,363.00 -3.92%
32. Oct 31, 2020 $319.29 -3.06% 3,269.96 -2.77%
33. Nov 30, 2020 $370.22 15.95% 3,621.63 10.75%
34. Dec 31, 2020 $348.03 -5.99% 3,756.07 3.71%
35. Jan 31, 2021 $328.68 -5.56% 3,714.24 -1.11%
36. Feb 28, 2021 $311.68 -5.17% 3,811.15 2.61%
37. Mar 31, 2021 $306.71 -1.59% 3,972.89 4.24%
38. Apr 30, 2021 $335.27 9.31% 4,181.17 5.24%
39. May 31, 2021 $323.13 -3.62% 4,204.11 0.55%
40. Jun 30, 2021 $364.97 12.95% 4,297.50 2.22%
41. Jul 31, 2021 $400.17 9.64% 4,395.26 2.27%
42. Aug 31, 2021 $400.17 0.00% 4,522.68 2.90%
43. Sep 30, 2021 $404.70 1.13% 4,307.54 -4.76%
44. Oct 31, 2021 $466.01 15.15% 4,605.38 6.91%
45. Nov 30, 2021 $454.41 -2.49% 4,567.00 -0.83%
46. Dec 31, 2021 $391.45 -13.86% 4,766.18 4.36%
47. Jan 31, 2022 $333.76 -14.74% 4,515.55 -5.26%
48. Feb 28, 2022 $319.94 -4.14% 4,373.94 -3.14%
49. Mar 31, 2022 $365.23 14.16% 4,530.41 3.58%
50. Apr 30, 2022 $354.63 -2.90% 4,131.93 -8.80%
51. May 31, 2022 $292.69 -17.47% 4,132.15 0.01%
52. Jun 30, 2022 $272.61 -6.86% 3,785.38 -8.39%
53. Jul 31, 2022 $310.51 13.90% 4,130.29 9.11%
54. Aug 31, 2022 $299.96 -3.40% 3,955.00 -4.24%
55. Sep 30, 2022 $279.56 -6.80% 3,585.62 -9.34%
56. Oct 31, 2022 $329.04 17.70% 3,871.98 7.99%
57. Nov 30, 2022 $380.31 15.58% 4,080.11 5.38%
58. Dec 31, 2022 $320.38 -15.76% 3,839.50 -5.90%
59. Jan 31, 2023 $306.88 -4.21% 4,076.60 6.18%
60. Feb 28, 2023 $309.20 0.76% 3,970.15 -2.61%
61. Mar 31, 2023 $364.19 17.78% 4,109.31 3.51%
62. Apr 30, 2023 $379.93 4.32% 4,169.48 1.46%
63. May 31, 2023 $331.93 -12.63% 4,179.83 0.25%
64. Jun 30, 2023 $378.50 14.03% 4,376.86 4.71%
65. Jul 31, 2023 $378.53 0.01% 4,588.96 4.85%
66. Aug 31, 2023 $381.26 0.72% 4,507.66 -1.77%
67. Sep 30, 2023 $385.61 1.14% 4,288.05 -4.87%
68. Oct 31, 2023 $393.48 2.04% 4,193.80 -2.20%
69. Nov 30, 2023 $446.80 13.55% 4,567.80 8.92%
70. Dec 31, 2023 $511.29 14.43% 4,769.83 4.42%
71. Jan 31, 2024 $453.82 -11.24% 4,845.65 1.59%
Average (R): 3.03% 0.95%
Standard deviation: 11.02% 5.18%

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 LULU during period t

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


Variance and Covariance

lululemon athletica inc., calculation of variance and covariance of returns

Microsoft Excel
t Date RLULU,t RS&P 500,t (RLULU,tRLULU)2 (RS&P 500,tRS&P 500)2 (RLULU,tRLULU)×(RS&P 500,tRS&P 500)
1. Mar 31, 2018 9.89% -2.69% 47.06 13.26 -24.98
2. Apr 30, 2018 11.98% 0.27% 80.19 0.46 -6.10
3. May 31, 2018 5.26% 2.16% 4.98 1.46 2.70
. . . . . . .
. . . . . . .
. . . . . . .
70. Dec 31, 2023 14.43% 4.42% 130.06 12.04 39.57
71. Jan 31, 2024 -11.24% 1.59% 203.61 0.41 -9.08
Total (Σ): 8,497.00 1,876.53 2,520.47
t Date RLULU,t RS&P 500,t (RLULU,tRLULU)2 (RS&P 500,tRS&P 500)2 (RLULU,tRLULU)×(RS&P 500,tRS&P 500)
1. Mar 31, 2018 9.89% -2.69% 47.06 13.26 -24.98
2. Apr 30, 2018 11.98% 0.27% 80.19 0.46 -6.10
3. May 31, 2018 5.26% 2.16% 4.98 1.46 2.70
4. Jun 30, 2018 18.85% 0.48% 250.24 0.22 -7.41
5. Jul 31, 2018 -3.92% 3.60% 48.36 7.02 -18.42
6. Aug 31, 2018 29.16% 3.03% 682.93 4.30 54.18
7. Sep 30, 2018 4.88% 0.43% 3.42 0.27 -0.97
8. Oct 31, 2018 -13.39% -6.94% 269.64 62.30 129.61
9. Nov 30, 2018 -5.81% 1.79% 78.18 0.69 -7.37
10. Dec 31, 2018 -8.25% -9.18% 127.30 102.63 114.30
11. Jan 31, 2019 21.54% 7.87% 342.81 47.82 128.04
12. Feb 28, 2019 1.77% 2.97% 1.60 4.08 -2.55
13. Mar 31, 2019 8.94% 1.79% 34.96 0.70 4.96
14. Apr 30, 2019 7.62% 3.93% 21.04 8.87 13.66
15. May 31, 2019 -6.10% -6.58% 83.37 56.71 68.76
16. Jun 30, 2019 8.83% 6.89% 33.64 35.28 34.45
17. Jul 31, 2019 6.04% 1.31% 9.05 0.13 1.08
18. Aug 31, 2019 -3.36% -1.81% 40.82 7.63 17.65
19. Sep 30, 2019 4.26% 1.72% 1.51 0.59 0.94
20. Oct 31, 2019 6.10% 2.04% 9.42 1.19 3.35
21. Nov 30, 2019 10.49% 3.40% 55.61 6.01 18.28
22. Dec 31, 2019 2.65% 2.86% 0.14 3.63 -0.72
23. Jan 31, 2020 3.33% -0.16% 0.09 1.24 -0.34
24. Feb 29, 2020 -9.18% -8.41% 149.10 87.68 114.34
25. Mar 31, 2020 -12.81% -12.51% 251.02 181.30 213.33
26. Apr 30, 2020 17.90% 12.68% 221.15 137.63 174.46
27. May 31, 2020 34.28% 4.53% 976.92 12.78 111.75
28. Jun 30, 2020 3.97% 1.84% 0.88 0.78 0.83
29. Jul 31, 2020 4.35% 5.51% 1.75 20.77 6.03
30. Aug 31, 2020 15.38% 7.01% 152.58 36.65 74.77
31. Sep 30, 2020 -12.32% -3.92% 235.74 23.77 74.86
32. Oct 31, 2020 -3.06% -2.77% 37.08 13.83 22.65
33. Nov 30, 2020 15.95% 10.75% 166.97 96.07 126.66
34. Dec 31, 2020 -5.99% 3.71% 81.41 7.61 -24.90
35. Jan 31, 2021 -5.56% -1.11% 73.77 4.27 17.75
36. Feb 28, 2021 -5.17% 2.61% 67.26 2.74 -13.58
37. Mar 31, 2021 -1.59% 4.24% 21.38 10.83 -15.22
38. Apr 30, 2021 9.31% 5.24% 39.47 18.40 26.95
39. May 31, 2021 -3.62% 0.55% 44.22 0.16 2.69
40. Jun 30, 2021 12.95% 2.22% 98.39 1.61 12.58
41. Jul 31, 2021 9.64% 2.27% 43.76 1.75 8.74
42. Aug 31, 2021 0.00% 2.90% 9.18 3.79 -5.90
43. Sep 30, 2021 1.13% -4.76% 3.60 32.60 10.83
44. Oct 31, 2021 15.15% 6.91% 146.90 35.54 72.26
45. Nov 30, 2021 -2.49% -0.83% 30.45 3.19 9.86
46. Dec 31, 2021 -13.86% 4.36% 285.09 11.62 -57.55
47. Jan 31, 2022 -14.74% -5.26% 315.65 38.58 110.36
48. Feb 28, 2022 -4.14% -3.14% 51.41 16.72 29.32
49. Mar 31, 2022 14.16% 3.58% 123.80 6.89 29.20
50. Apr 30, 2022 -2.90% -8.80% 35.18 95.04 57.82
51. May 31, 2022 -17.47% 0.01% 420.05 0.90 19.42
52. Jun 30, 2022 -6.86% -8.39% 97.81 87.33 92.42
53. Jul 31, 2022 13.90% 9.11% 118.23 66.56 88.71
54. Aug 31, 2022 -3.40% -4.24% 41.30 27.01 33.40
55. Sep 30, 2022 -6.80% -9.34% 96.63 105.94 101.18
56. Oct 31, 2022 17.70% 7.99% 215.21 49.47 103.18
57. Nov 30, 2022 15.58% 5.38% 157.57 19.56 55.51
58. Dec 31, 2022 -15.76% -5.90% 352.96 46.92 128.69
59. Jan 31, 2023 -4.21% 6.18% 52.46 27.27 -37.83
60. Feb 28, 2023 0.76% -2.61% 5.17 12.70 8.10
61. Mar 31, 2023 17.78% 3.51% 217.72 6.51 37.66
62. Apr 30, 2023 4.32% 1.46% 1.67 0.26 0.66
63. May 31, 2023 -12.63% 0.25% 245.33 0.50 11.04
64. Jun 30, 2023 14.03% 4.71% 121.02 14.14 41.37
65. Jul 31, 2023 0.01% 4.85% 9.13 15.16 -11.76
66. Aug 31, 2023 0.72% -1.77% 5.33 7.42 6.29
67. Sep 30, 2023 1.14% -4.87% 3.57 33.93 11.00
68. Oct 31, 2023 2.04% -2.20% 0.98 9.93 3.11
69. Nov 30, 2023 13.55% 8.92% 110.71 63.44 83.81
70. Dec 31, 2023 14.43% 4.42% 130.06 12.04 39.57
71. Jan 31, 2024 -11.24% 1.59% 203.61 0.41 -9.08
Total (Σ): 8,497.00 1,876.53 2,520.47

Show all

VarianceLULU = Σ(RLULU,tRLULU)2 ÷ (71 – 1)
= 8,497.00 ÷ (71 – 1)
= 121.39

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (71 – 1)
= 1,876.53 ÷ (71 – 1)
= 26.81

CovarianceLULU, S&P 500 = Σ(RLULU,tRLULU)×(RS&P 500,tRS&P 500) ÷ (71 – 1)
= 2,520.47 ÷ (71 – 1)
= 36.01


Systematic Risk (β) Estimation

Microsoft Excel
VarianceLULU 121.39
VarianceS&P 500 26.81
CovarianceLULU, S&P 500 36.01
Correlation coefficientLULU, S&P 5001 0.63
βLULU2 1.34
αLULU3 1.75%

Calculations

1 Correlation coefficientLULU, S&P 500
= CovarianceLULU, S&P 500 ÷ (Standard deviationLULU × Standard deviationS&P 500)
= 36.01 ÷ (11.02% × 5.18%)
= 0.63

2 βLULU
= CovarianceLULU, S&P 500 ÷ VarianceS&P 500
= 36.01 ÷ 26.81
= 1.34

3 αLULU
= AverageLULU – βLULU × AverageS&P 500
= 3.03%1.34 × 0.95%
= 1.75%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.67%
Expected rate of return on market portfolio2 E(RM) 13.79%
Systematic risk (β) of lululemon athletica inc. common stock βLULU 1.34
 
Expected rate of return on lululemon athletica inc. common stock3 E(RLULU) 16.91%

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).

2 See details »

3 E(RLULU) = RF + βLULU [E(RM) – RF]
= 4.67% + 1.34 [13.79%4.67%]
= 16.91%