Stock Simulations

8/3/2019 Stock Simulations

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Current Year 2001 $393

Current Accumulation $100

Years Spent Saving 20

Stock Allocation 100%

Safe Asset Return 3.5%Stock Average Return 9.5%

Stock SD 18.0%

Year Accumulation Stock Return

2001 0 $100 26.9% $9

2002 1 $109 -8.8% $(3)

2003 2 $106 -34.0% $(12)

2004 3 $94 21.2% $41

2005 4 $135 27.5% $54

2006 5 $189 28.2% $49

2007 6 $238 -9.8% $(72)2008 7 $166 19.0% $25

2009 8 $191 4.5% $22

2010 9 $213 -8.6% $(41)

2011 10 $172 19.4% $44

2012 11 $216 13.4% $(23)

2013 12 $193 14.4% $(4)

2014 13 $189 30.2% $45

2015 14 $234 -19.8% $40

2016 15 $274 -23.1% $32

2017 16 $306 -2.4% $72

2018 17 $377 14.4% $27

2019 18 $405 12.8% $(1)2020 19 $404 -12.5% $(11)

2021 20 $393 -22.5% $(57)

2022 21 $336 30.9% $76

2023 22 $412 18.9% $78

2024 23 $489 14.8% $72

2025 24 $562 -9.5% $(53)

2026 25 $509 16.6% $84

2027 26 $593 6.6% $39

2028 27 $632 -8.4% $(53)

2029 28 $579 -1.4% $(8)

2030 29 $571 45.4% $259

2031 30 $830 -4.7% $(39)2032 31 $791 -14.6% $(116)

2033 32 $675 -12.6% $(85)

2034 33 $590 8.4% $49

2035 34 $640 30.0% $192

2036 35 $832 22.9% $191

2037 36 $1,023 -26.8% $(274)

2038 37 $749 16.6% $124

FinalAccumulation

Years fromnow

CapitalGain

0 2 4 6 8 10 12 14 16 18 20

$-

$50

$100

$150

$200

$250

$300

$350

$400

$450

Accumulation


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2039 38 $873 -4.2% $(37)

2040 39 $836 0.9% $8

2041 40 $843 32.7% $276

2042 41 $1,119 0.8% $8

2043 42 $1,127 -15.4% $(173)

2044 43 $954 -7.6% $(72)

2045 44 $882 23.1% $2042046 45 $1,085 12.0% $130

2047 46 $1,216 67.3% $818

2048 47 $2,034 4.3% $88

2049 48 $2,121 33.5% $711

2050 49 $2,832 18.3% $518

2051 50 $3,350 27.6% $924

2052 51 $4,274 4.9% $210

2053 52 $4,484 29.0% $1,300

2054 53 $5,784 11.4% $657

2055 54 $6,440 -29.5% ###

2056 55 $4,539 -35.4% ###

2057 56 $2,933 -6.1% $(178)2058 57 $2,756 7.3% $200

2059 58 $2,956 -8.0% $(235)

2060 59 $2,721 8.0% $217

2061 60 $2,938 6.2% $183

2062 61 $3,121 4.0% $126

2063 62 $3,247 12.1% $392

2064 63 $3,638 11.2% $408

2065 64 $4,046 28.6% $1,158

2066 65 $5,204 6.3% $328


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Simulation Parameters

Asset Asset

Stocks 9 18 A

Long Term Bonds 5 10 B

Short Term Bonds 4 2 C

Risk Free Asset 3.5 0 rf

Correlation matrix for the Assets

Asset A B C rf

A 1 -0.2 -0.1 0

B -0.2 1 -0.1 0

C -0.1 -0.1 1 0

rf 0 0 0 1

Initial Wealth $100

Length 20

1

ExpectedReturn

StandardDeviation


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85.38 99.13 103.02 90.29 104.67 115.33 124.73

109.97 106 123.83 139.81 121.2 139.19 119.78

122.89 151.69 171.98 192.97 184.13 194.13 203.06

90.38 91.26 93.88 101.65 116.35 141.83 159.65

94.26 101.45 138.87 149.42 183.28 189.53 236.25

107.17 132.58 150.16 135.68 138.97 151.43 173.38

125.05 184.86 207.87 245.42 283.57 292.96 360.7

83.7 103.16 141.16 166.06 195.98 231.37 234.07

102.02 105.82 101.72 113.35 132.43 135.68 123.37

106.6 122.3 119.22 119.92 161.22 166.88 171.99


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Portfolio Weights

1

0

0

0

Monte Carlo

1000

Number ofRepetitions


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130.98 161.17 156.14 183.67 192.8 218.85 256.55 272.23 315.39

158.34 196.4 217.41 237.11 227.8 271.09 293.59 317.94 324.71

184.45 185.76 210.14 237.92 274.29 311.98 374.43 412.32 510.48

171.17 146.33 154.49 169.88 206.3 232.99 261.64 289.56 297.2

300.68 351.14 396.88 411.34 377.79 435.12 516.89 668.71 677.2

205.59 235.02 259.79 241.77 281.04 326.96 392.09 382.86 371.93

428.31 475.45 472.18 546.56 562.65 684.36 715.52 831.98 1007.51

250.28 262.26 268.64 322.81 308.01 381.75 397.95 442.39 528.38

133.94 138.44 156.22 172.06 197.46 225.47 245.08 254.24 259.22

188.29 192.13 230.02 273.08 289.68 262.4 286.18 282.66 276.99


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8/36

357.67 321.16 396.11 473.34 557.59 553.33 603.93 544.15 599.32

332.37 377.75 397.49 431.44 499.82 523.32 594.39 650.29 573.81

604.07 558.06 634.7 653.85 632.19 667.95 708.19 780.97 901.25

315.08 339.43 350.08 372.77 387.97 377.63 340.58 316.04 356.8

824.86 967.23 927.75 1130.77 1374.87 1487.03 1672.24 1474.83 1688.21

397.8 412.51 442.77 473.14 358.77 416.04 415.42 503.13 463.96

1171.53 1285.45 1398.2 1630.31 1543.03 1527.58 1870.76 2322.44 2921.78

552.74 612.06 647.72 779.49 866.07 965.84 1234.47 1462.05 1671.83

281.61 295.74 313.39 365.24 400.61 369.13 416.06 448.63 454.79

303.76 369.22 410.1 446.71 429.63 477.31 601.79 735.26 813.66


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83.47

327.94

447.22

559.55

690.23

785.61

911.75

1027.63

1147.72

1297.79

1489.85

1682.341905.18

2113.97

2422.77

2817.34

3364.77

4116.45

5095.73

7000.28

42392.82


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11/36

83.47 0

83.47 0.2

50 327.94 0.2

50 327.94 0.42

50 447.22 0.42

50 447.22 0.45

50 559.55 0.45

50 559.55 0.38

50 690.23 0.38

50 690.23 0.52

50 785.61 0.52

50 785.61 0.4

50 911.75 0.450 911.75 0.43

50 1027.63 0.43

50 1027.63 0.42

50 1147.72 0.42

50 1147.72 0.33

50 1297.79 0.33

50 1297.79 0.26

50 1489.85 0.26

50 1489.85 0.26

1682.34 0.261682.34 0.22

1905.18 0.22

1905.18 0.24

2113.97 0.24

2113.97 0.16

2422.77 0.16

2422.77 0.13

2817.34 0.13

2817.34 0.09

3364.77 0.09

3364.77 0.07

4116.45 0.07

4116.45 0.05

5095.73 0.05

5095.73 0.03


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7000.28 0.03

7000.28 0

42392.82 0

42392.82 0


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Asset Portfolio Weights ER SD

Repetition Final Wealth Stocks 100% 9.0% 18.0%

1 $603 9.0% Risk Free Asset 0% 3.5% 0.0%

2 $138 1.6% Initial Wealth $100

3 $754 10.1% Length 20

4 $128 1.2% Repetitions 10005 $427 7.3% Results

6 $546 8.5% Mean SD

7 $809 10.5% Wealth $843 $854

8 $615 9.1% Average Return 9.0% 4.0%

9 $353 6.3%

10 $590 8.9%

11 $435 7.4%

12 $357 6.4%

13 $515 8.2%

14 $162 2.4%

15 $232 4.2%

16 $1,288 12.8%17 $133 1.4%

18 $412 7.1%

19 $274 5.0%

20 $180 2.9%

21 $265 4.9%

22 $182 3.0%

23 $789 10.3%

24 $332 6.0%

25 $400 6.9%

26 $373 6.6%

27 $1,840 14.6%

28 $594 8.9%29 $309 5.6%

30 $96 -0.2%

31 $811 10.5%

32 $561 8.6%

33 $479 7.8%

34 $1,032 11.7%

35 $419 7.2%

36 $451 7.5%

37 $1,067 11.8%

38 $642 9.3%

39 $278 5.1%

40 $620 9.1%41 $737 10.0%

42 $612 9.1%

43 $460 7.6%

44 $4,780 19.3%

45 $147 1.9%

46 $1,726 14.2%

47 $191 3.2%

AverageReturn

0 500 1000 1500 2000

Empirical Histogram for 1000 Repetitions

1 3 5 7 9 11 13 15 17 19

$10

$100

$1,000


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48 $434 7.3%

49 $359 6.4%

50 $437 7.4%

51 $747 10.1%

52 $1,223 12.5%

53 $408 7.0%

54 $437 7.4%55 $695 9.7%

56 $644 9.3%

57 $659 9.4%

58 $1,018 11.6%

59 $3,876 18.3%

60 $540 8.4%

61 $260 4.8%

62 $518 8.2%

63 $353 6.3%

64 $366 6.5%

65 $679 9.6%

66 $1,224 12.5%67 $131 1.4%

68 $2,791 16.6%

69 $384 6.7%

70 $225 4.1%

71 $1,458 13.4%

72 $537 8.4%

73 $683 9.6%

74 $135 1.5%

75 $335 6.0%

76 $935 11.2%

77 $1,006 11.5%

78 $280 5.1%79 $299 5.5%

80 $886 10.9%

81 $2,641 16.4%

82 $184 3.0%

83 $950 11.3%

84 $142 1.8%

85 $1,350 13.0%

86 $672 9.5%

87 $586 8.8%

88 $392 6.8%

89 $1,090 11.9%

90 $752 10.1%91 $256 4.7%

92 $242 4.4%

93 $554 8.6%

94 $794 10.4%

95 $1,106 12.0%

96 $1,475 13.5%

97 $379 6.7%

98 $737 10.0%


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99 $191 3.2%


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inal Wealth Percentile

Minimum $83

5 $162

10 $207

15 $254

20 $29525 $347

30 $392

35 $436

40 $482

45 $555

50 $619

55 $683

60 $752

65 $839

70 $948

75 $1,052

80 $1,21785 $1,383

90 $1,686

95 $2,189

100 $11,595


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18/36


19/36


20/36


21/36


22/36

83.18 0

83.18 83.18 0.64

161.66 60 50 161.66 0.64

206.83 125 50 161.66 1.11

Percentile Lines 253.54 125 50 206.83 1.11

50th 618.63 0.77 295.12 101 50 206.83 1.07618.63 0 347.17 67 50 253.54 1.07

392.44 70 50 253.54 1.2

25th 347.17 1.1 435.85 58 50 295.12 1.2

347.17 0 482.45 63 50 295.12 0.96

554.73 44 50 347.17 0.96

75th 1052.33 0.3 618.63 29 50 347.17 1.1

1052.33 0 683.45 21 50 392.44 1.1

752.05 28 50 392.44 1.15

839.47 22 50 435.85 1.15

947.55 19 50 435.85 1.07

1052.33 168 50 482.45 1.07

1217.29 7 50 482.45 0.691383.16 9 50 554.73 0.69

1685.72 16 50 554.73 0.78

2188.72 4 50 618.63 0.78

11594.97 5 50 618.63 0.77

2728.58 5 683.45 0.77

2855.72 10 683.45 0.73

2982.87 10 752.05 0.73

3110.01 6 752.05 0.57

3237.15 3 839.47 0.57

3364.29 4 839.47 0.46

3491.43 3 947.55 0.46

3618.57 2 947.55 0.483745.72 4 1052.33 0.48

3872.86 9 1052.33 0.3

4000 42 1217.29 0.3

3026.31 1 1217.29 0.3

1383.16 0.3

1383.16 0.17

1685.72 0.17

1685.72 0.1

2188.72 0.1

2188.72 0.01

11594.97 0.01

11594.97 02728.58 5

2728.58 10

2855.72 10

2855.72 10

2982.87 10

2982.87 6

3110.01 6


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3110.01 3

3237.15 3

3237.15 4

3364.29 4

3364.29 3

3491.43 3

3491.43 23618.57 2

3618.57 4

3745.72 4

3745.72 9

3872.86 9

3872.86 42

4000 42

4000 0

3026.31 0


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25/36

$100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00

1 $130.26 $93.94 $111.05 $99.19 $141.39 $149.95 $108.81

2 $133.70 $93.53 $103.93 $131.33 $169.31 $177.59 $113.52

3 $124.96 $98.72 $174.91 $113.44 $140.33 $151.49 $153.00

4 $141.04 $91.04 $241.57 $121.37 $132.69 $191.69 $168.12

5 $181.00 $112.58 $199.54 $136.66 $115.83 $197.35 $147.476 $174.46 $120.92 $207.33 $131.05 $114.03 $221.99 $169.60

7 $187.56 $146.15 $260.56 $104.34 $146.43 $262.51 $235.60

8 $254.71 $140.21 $243.40 $86.24 $156.83 $203.60 $232.81

9 $262.14 $116.38 $264.61 $80.42 $159.53 $293.61 $216.12

10 $259.82 $131.44 $335.93 $105.69 $168.06 $318.81 $217.27

11 $323.37 $114.93 $374.46 $76.99 $198.90 $429.15 $259.54

12 $456.18 $100.52 $421.45 $90.59 $262.27 $496.62 $248.19

13 $417.41 $82.01 $435.46 $87.17 $246.55 $567.90 $306.75

14 $483.86 $66.92 $493.77 $93.75 $344.44 $452.55 $434.79

15 $488.45 $58.91 $647.71 $107.12 $416.89 $377.68 $465.69

16 $410.17 $78.01 $842.39 $91.23 $392.97 $345.64 $582.52

17 $428.41 $67.13 $576.97 $71.17 $530.12 $435.67 $510.6718 $496.00 $106.06 $597.38 $79.36 $508.40 $566.36 $454.50

19 $572.64 $136.11 $663.25 $104.14 $370.98 $599.24 $619.42

20 $602.85 $137.69 $754.38 $127.88 $427.33 $545.84 $809.44

31 2,472.11 734.87 1100.76 1,352.53 710.81 1,953.48 3,433.04

32 2,724.72 744.16 1126.48 1,694.02 761.97 2,013.45 3,657.17

33 2,442.89 689.78 1202.67 1,986.48 810.74 1,800.39 5,211.00

34 2,507.11 892.09 1443.47 2,529.24 1,037.93 2,498.23 5,142.45

35 2,920.78 1,126.89 1921.51 2,559.72 844.71 2,574.28 5,256.23

36 3,759.75 1,201.71 2013.16 2,989.91 1,169.46 2,951.51 5,628.22

37 3,871.26 1,355.77 2492.67 2,107.17 1,335.32 3,176.64 5,392.59

38 4,754.53 1,308.83 2086.87 1,728.68 2,119.27 3,734.18 5,854.76

39 5,045.74 1,408.34 2664.88 1,404.74 2,624.62 5,959.59 7,258.13

40 5,649.14 1,211.00 3011.86 1,756.93 3,618.67 5,172.32 7,470.83

0.05 5,649.14 1.23 1.15 0.91 1.31

1,000.00

2,000.00

3,000.00

4,000.00

5,000.00

6,000.00


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0.00 1,000.00 2,000.00 3,000.00 4,000.00 5,000.00 6,000.00

0.00


27/36


28/36

$100.00 $100.00 $100.00

$121.86 $95.96 $124.56 0.02

$149.99 $95.61 $129.32 0.05 18

$136.67 $121.34 $125.53 0.08 30

$192.09 $112.84 $124.17 0.12 69

$211.26 $123.86 $144.82 0.15 54$195.83 $166.50 $190.22 0.18 69

$151.91 $158.89 $224.10 0.21 78

$134.09 $128.40 $259.88 0.24 68

$122.26 $143.78 $253.16 0.27 57

$105.69 $153.40 $272.22 0.31 59

$128.80 $166.96 $245.35 0.34 55

$196.65 $162.89 $255.91 0.37 60

$209.52 $213.27 $230.96 0.4 54

$245.11 $249.11 $324.60 0.43 30

$186.89 $257.65 $355.19 0.46 29

$187.21 $238.82 $370.02 0.49 35

$289.09 $254.37 $480.09 0.53 30$351.81 $326.33 $509.53 0.56 30

$411.07 $379.24 $543.86 0.59 16

$614.56 $353.34 $590.06 0.62 17

0.65 23

0.68 22

0.72 13

0.75 15

0.78 12

0.81 8

0.84 12

0.87 12

0.91 60.94 8

3,804.70 1,086.13 1,052.20 0.97 3

3,760.84 1,190.84 1,347.30 1 8

3,506.17 1,421.48 1,401.61

4,980.68 1,573.43 1,208.85

3,606.51 1,494.53 1,179.30

3,123.43 1,852.48 1,084.47

2,676.82 3,193.97 1,220.87

3,755.40 2,819.33 1,470.70

3,901.06 3,297.43 1,607.32

3,937.28 4,819.21 1,264.03

1.50 0.93 1.08


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30/36


31/36

0.02 0

0.02 18

0.05 18

0.05 30

0.08 30

0.08 690.12 69

0.12 54

0.15 54

0.15 69

0.18 69

0.18 78

0.21 78

0.21 68

0.24 68

0.24 57

0.27 57

0.27 590.31 59

0.31 55

0.34 55

0.34 60

0.37 60

0.37 54

0.4 54

0.4 30

0.43 30

0.43 29

0.46 29

0.46 350.49 35

0.49 30

0.53 30

0.53 30

0.56 30

0.56 16

0.59 16

0.59 17

0.62 17

0.62 23

0.65 23

0.65 220.68 22

0.68 13

0.72 13

0.72 15

0.75 15

0.75 12

0.78 12


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0.78 8

0.81 8

0.81 12

0.84 12

0.84 12

0.87 12

0.87 60.91 6

0.91 8

0.94 8

0.94 3

0.97 3

0.97 8

1 8

1 0


33/36


34/36

AveRet 9%

SDRet 18%

Year

0 $100.00 $100.00

1 0% $97.47 $107.182 29% $104.06 $114.89

3 -16% $111.60 $123.14

4 10% $140.10 $131.99

5 -7% $159.14 $141.47

6 47% $161.90 $151.63

7 27% $189.94 $162.53

8 -2% $202.29 $174.21

9 -10% $218.61 $186.72

10 14% $200.14 $200.14

Arithmetic Average 9.2%

Geometric Average 7.2%Difference 2.0%

0 1 2 3 4 5 6 7 8 9 10

$-

$50

$100

$150

$200

$250

Column C Column D


35/36

FLOYD NORRISAs Earnings Plunge, the Market's P/E Ratio Sets a Record

The bubble burst a long time ago, and now stock market valuations are far more reasonable.

So goes the Wall Street line. But a look at the numbers raises questions about that happy conclusion. Theprice-earnings ratio of the Standard & Poor's 500-stock index reached its highest level ever yesterday, at35.99. That figure, based on reported profits over the last 12 months, exceeded the record of 35.82 set onApril 12, 1999.

How can that be? Share prices are down a lot from the peak in 2000, but so are profits. Profits surged in1999 and early 2000, keeping the P/E ratio from reaching new highs even as the market did. But sincethen the profit figures have been plunging precipitously.

It should also be noted that the historical earnings figures now being used include only a handful ofcompanies that have reported third-quarter results. Chances are that many third- and fourth-quarterreports will be dreadful, leading to even higher price-earnings ratios.

The second quarter was bad enough. According to calculations by Bloomberg Financial Markets, S.& P.profits for the period were lower than they were in the second quarter of 1990, just before the last

recession began.

Wall Street thinks such numbers are unfair. They are based on historical profits, while investors should belooking at future earnings. Though they exclude extraordinary items, they include write-offs thatcompanies think are best ignored. Wall Street focuses instead on estimates for 2002 pro-forma operatingearnings, which exclude whatever the company wants excluded. The S.& P. is trading at 19 times thatforecast, which Wall Street says is cheap given the current low level of interest rates.

Wall Street's argument is reasonable in part. A company's future operations should matter most toinvestors, and many write-offs now being taken represent losses that should have been taken in prioryears, not this one. But, says Thomas Coleman of Aequilibrium Investments, a money management firmbased in London, focusing on pro-forma operating earnings in the aggregate ignores a lot of losses, andthose losses are real. Moreover, the difference between reported profits and operating profits has grownover a sustained period, as companies have become more adept at making operating numbers look

better. That distorts historical comparisons based on operating profits.

In a study to be released next week, economists at the Jerome Levy Economics Institute at Bard Collegeestimate that overall earnings of the S.& P. 500 are overstated 20 percent. Like Mr. Coleman, they raisethe same issue of operating vs. total profits, but add that the 1990's boom in stock options also led to arising exaggeration of earnings because few companies treated the value of the options as an operatingexpense.

Does this matter? In the short term, probably not. Valuation is not very useful in market timing. Theimportant issue in the coming months will be the economic outlook, and share prices will probably do wellif investors continue to expect an early end to the recession. That hope has driven the S.& P. back towhere it was before Sept. 11.

But it is worth noting that the extraordinary high multiples of the late 1990's coincided with expectations ofrapid growth for the economy and for corporate profits. If those expectations come down, lower valuationsmay come to seem appropriate even after the recession ends. Instead of growing faster than profits, ashappened in the last decade, stock prices could fail to keep up with earnings.


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