Monte-carlo

Given the Mean Annual Return of two investments (like Stocks and Bonds) and the annualized Volatility (or Standard Deviation) of each and a degree of Correlation between the two … the Monte Carlo (MC) sheet picks random annual returns* for each, over the next umpteen years and, assuming some split between the two investment types - like 75% of the former and 25% of the latter (and an annual rebalancing to maintain this split), sees how much would be left of your portfolio if you withdraw a given percentage of the original portfolio (this amount increasing annually with inflation) … and it does this hundreds of times to see what fraction of these iterations would yield a portfolio less than 10% of the original portfolio value, or less than 20% … or even more than 110% … or even 0% - meaning your portfolio went to $zero :^( (These percentages are the BreakPoints.) See: http://home.golden.net/~pjponzo/Monte-Carlo.htm for "the Math" P.S. You can also stick in a negative withdrawal rate and see what'd happen as you add to your portfolio, increasing annually with inflation … in which case you may want to carefully change the BreakPoints in T2 to T13. See the next sheet: Explain-2 Since it takes some time, you can ask for just ONE run (of umpteen hundred iterations… you decide how may hundreds or a collection of runs, using three different Stock/Bond splits and three different Withdrawal Rates (that makes NINE scenarios, eh?). There's also a chart of some sample portfolios. The red graph on this chart is the deterministic portfolio evolution: it uses an Annualized Return then sets both Standard Deviations to zero. The Monte Carlo simulations fluctuate about this graph. P.S. The software needs the Average (or Mean) annual returns. If you know the Annualized returns, you can Click a Button and get 'em changed to Average. * Note: the (random) returns are Log-normally distributed … but you can also ask for a Normal distribution. This spreadsheet began life as a child of Richard Pritz with help from Peter Van and Peter Ponzo.

ualized Volatility

n years and, of the latter -

ly with inflation)

to your portfolio, increasing akPoints in T2 to T13. you decide how may hundreds)

te about this graph. zed returns, you

a Normal distribution. Peter Ponzo.

If you should decide to use a negative withdrawal rate (meaning that you're adding annually to your portfolio) then it's unlikely that you'll be interested in how often the Final portfolio was greater than 0%, 500%,1000%, etc. of the Original portfolio. They MIGHT all be!!

So, you'll want to know how often your Final portolio was greater than (for example) 1000%, 3000%, etc. of your Original portfolio. To allow you to do this, change the percentage in cell T2 and the increment in cell R5 … like so: Now the spreadsheet will calculate how often the final portfolio was less than (for example) 1000%, 3000%, etc. Neat, eh?

Note: You can ask for Simple or Latin Hypercube sampling (when you choose Normal or Lognormal). Just enter S or H ... or even s or h. See: http://home.golden.net/~pjponzo/latin-hypercube.htm

se Normal or Lognormal). golden.net/~pjponzo/latin-hypercube.htm

Okay, here's another variant:

A standard Monte Carlo simulation uses a fixed Mean Return and Standard Deviation and Distribution (Normal? Log-norm over the 10, 20, 30, etc. years considered by the simulation You don't like that? Then how about selecting, for your Stock gain, at random, monthly gains from a collection of monthly gains of the S&P 50 from Jan, 1926 to May, 2001? (At last count, there's 905 of 'em and they live in column AI as "1+Monthly Return" You like that? Remember, that includes the 1929 crash!! You can put your own (1+MonthlyReturn) data in column AI. Just be sure to first delete the data that's there! If you'd like to see the effect of that choice (where you don't assume some fixed Mean, Standard Deviation or Distribution, but use real, live historical returns), then instead of typing N or L in cell B9, type S (for S&P, eh?) or T

The MC software will, when calculating an annual Stock gain, multiply together a dozen (consecutive) monthly selections (at random, of course) from the collection of S&P 500 gains (which live in column AI) or TSE gains (in column If you enter T in cell B9, then the bond component is selected from Cdn longBond gains (in column AM ... and twelve (consecutive) monthly gains from the same year are multiplied together to get the annual Bond gain. Otherwise, the annual Bond gain, will be the standard Log-normal distribution with your choice of Mean and Standard Deviation. P.S. For the past umpteen years (since 1926) appropriate, nominal (as opposed to inflation-adjusted) "annual" numbers ar Average U.S. Stock Return: 12.6% Standard Deviation: 20% Bonds - 5 year U.S. treasuries: Average Return: 5.5% Standard Deviation: 6% Correlation: 8% TSE average Stock Return (since 1948): 11.5% Standard Deviation: 15% See Richard's page for more data: http://www.geocities.com/snarkll/

d Distribution (Normal? Log-normal?)

n of monthly gains of the S&P 500, I as "1+Monthly Return")

ete the data that's there! andard Deviation or Distribution, &P, eh?) or T (for TSE).

consecutive) monthly selections SE gains (in column AK). (in column AM) get the annual Bond gain.

on-adjusted) "annual" numbers are:

Stocks Bonds ** If B2/C2 are Annualized Returns ** Average Annual Return = 12.6% 6.7% Annual Standard Deviation = 19.5% 8.4% Enter the Volatilities: Stocks & Bonds Correlation = 5% Enter the Correlation: Stocks & Bonds Annual Inflation = 2.0% Enter Inflation Rate (=Withdrawal increase) Years = 30 Enter the number of Years to consider Iterations/100 = 10 Enter just the number of Hundreds Simple or Hypercube? S Change only the data in the boxes

Enter N , L , S or T 5.0% Probability 95% Final exceeds 92% 87% 0% Original

120%

76%

80% 60%

55%

62%

77%

3500% 3000% 2500% 2000%

92%

87%

76%

50% 75% 100%

61%

40%

1000% 500% 0%

45% 40% 35% 30% 25% 20% 15% 10% 5% 0%

Row 2 Row 3 Row 4 Row 5 Row 6 Row 7 Row 8 Row 9 Row 10 Row 11 Row 12 Row

20%

1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2

7.0% 6.0% 50% 55% 76% Stock Percentage 75% 62% 77% 100% 61% 76% Run ONE: just 50% Stock, 7.0% Withdrawal Rate Run all NINE Stock Percentages/Withdrawal Rates

95%

4000%

1500%

Annual Withdrawal (Investment)

100%

4500%

0 1 2 3 4 5 6 7 8 9

L

5000%

Percentage of Iterations

Normal, Log-normal, etc.?

5500%

0% 7.0%

6.0%

5.0%

Final portfolio

Avg Return = 12.66%

Created by Richard Pritz with the assistance of Peter Vann & Peter Ponzo.

some SAMPLE scenarios Average Annual Return = 12.6% 6.7% Annual Standard Deviation = 19.5% Correlation =

8.4%

5%

Annual Inflation = 2.0% Years =

30

Iterations/100 =

10

Change only the data in the Normal, Log-normal, etc.? S Annual Withdrawal (Investment)

8.0%

7.0%

6.0%

50%

59%

73%

89%

75%

62%

75%

84%

100%

65%

73%

82%

Stock Percentage

Normal, Log-normal, etc.?

T

Annual Withdrawal (Investment)

8.0%

7.0%

6.0%

50%

54%

72%

90%

75%

63%

76%

90%

100%

66%

75%

85%

Stock Percentage

Normal, Log-normal, etc.?

N

Annual Withdrawal (Investment) Stock Percentage

boxes

Enter N , L , S or T 8.0%

7.0%

6.0%

50%

28%

47%

73%

75%

40%

54%

73%

100%

47%

56%

69%

Std Dev = 18.65%

Normal, Log-normal, etc.?

L

Annual Withdrawal (Investment) Stock Percentage

Enter N , L , S or T 8.0%

7.0%

6.0%

50%

45%

68%

87%

75%

58%

72%

86%

100%

60%

70%

84%

100.0%

Iterations =

100

BreakPoints

Years

12.0%

0%

12

0

Expected Final Portfolio = 2238.29%

43.0%

500%

43

1

Suggested Increment = 230.00%

22.0%

1000%

22

2

Actual Increment Used = 500.00%

11.0%

1500%

11

3

SUGGESTED INCREMENT = 1100.00%

5.0%

2000%

5

4

2.0%

2500%

2

5

0.0%

3000%

0

6

2.0%

3500%

2

7

1.0%

4000%

1

8

0.0%

4500%

0

9

0.0%

5000%

0

10

2.0%

5500%

2

11

0.0%

0%

0

12

1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9

Annualized Return = 10.92%

13 14

Deterministic Gain = 10.9%

Current Stock Percentage

100.0%

15

Current Withdrawal Rate

5.0%

16

Annualized Stock Gain

10.9%

17

Annualized Bond Gain

6.3%

18

Mixed Annual Gain

10.9%

19

Err:504

Row 5 Row 6 Row 7 Row 8 Row 9 Row 10 Row 11 Row 12 Row 13 Row 14

9

Check Sum

Final portfolio

Average of 100 simulations

20

Number of Iterations vs Percentage of Original Portfolio

21

100% stock, 5.0% annual withdrawal

22

Probability Final portfolio exceeds 0% of Original portfolio (after 30 years)

23

Stock: Gain=12.6% SD=19.5% Bond: Gain=6.7% SD=8.4% Inflation=2.0% Correlation=5.0%

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

53 54 55 56 57 58 59 60

Labels

Blanks

Table-Lookup Values: Deterministic Mean = 0, SD =Withdraw$ 1

Sample Portfolios

S&P Gains

<=0%

0.0025

-2.807

100.0%

5.0%

1.000

1.000

1.000

1.000

1.000

1.000

S&P data 905 10.9% 19.5% 12.6%

<=500%

0.0050

-2.576

105.8%

5.1%

1.015

0.912

1.083

1.065

0.810

0.962

<=1000%

0.0075

-2.432

112.2%

5.2%

0.859

1.054

1.202

1.293

0.852

0.943

<=1500%

0.0100

-2.326

119.1%

5.3%

0.638

1.149

1.041

1.364

0.987

1.025

<=2000%

0.0125

-2.241

126.7%

5.4%

0.607

1.353

1.267

1.373

1.113

1.018

Above:

<=2500%

0.0150

-2.170

135.0%

5.5%

0.592

1.340

0.991

1.552

1.260

1.046

Annual Return

<=3000%

0.0175

-2.108

144.1%

5.6%

0.466

1.295

1.085

1.408

1.268

1.048

Standard Dev

<=3500%

0.0200

-2.054

154.1%

5.7%

0.507

1.317

0.933

1.944

1.573

1.025

Mean Return

<=4000%

0.0225

-2.005

165.1%

5.9%

0.440

1.492

1.046

2.709

2.090

1.025

<=4500%

0.0250

-1.960

177.1%

6.0%

0.446

1.565

0.985

3.378

1.651

0.972

<=5000%

0.0275

-1.919

190.4%

6.1%

0.548

2.272

1.240

4.053

1.718

1.035

<=5500%

0.0300

-1.881

204.9%

6.2%

0.709

2.145

1.731

6.112

1.601

1.020

>5500%

0.0325

-1.845

220.9%

6.3%

0.842

2.551

2.003

7.516

1.840

0.981

0.0350

-1.812

238.6%

6.5%

0.776

2.332

1.756

7.096

2.474

1.054

0.0375

-1.780

258.0%

6.6%

0.971

2.480

1.834

7.661

2.352

1.009

0.0400

-1.751

279.5%

6.7%

1.042

2.603

1.603

9.113

2.503

1.020

0.0425

-1.722

303.1%

6.9%

1.079

2.697

1.499

11.224

3.114

1.061

0.0450

-1.695

329.2%

7.0%

1.118

2.725

1.449

12.174

3.299

0.993

0.0475

-1.670

358.0%

7.1%

1.060

4.047

1.574

17.829

3.525

1.067

0.0500

-1.645

389.8%

7.3%

1.161

4.082

1.525

16.314

4.287

1.052

0.0525

-1.621

425.0%

7.4%

1.656

3.596

2.048

11.922

5.224

1.045

0.0550

-1.598

463.8%

7.6%

2.124

2.927

1.879

13.682

5.787

0.950

0.0575

-1.576

506.7%

7.7%

2.399

3.183

1.456

12.890

7.338

1.072

0.0600

-1.555

554.1%

7.9%

2.643

2.837

1.239

14.846

7.532

1.028

0.0625

-1.534

606.5%

8.0%

2.696

2.840

1.254

19.740

6.563

0.996

0.0650

-1.514

664.5%

8.2%

2.773

3.051

1.013

17.110

6.236

0.988

0.0675

-1.495

728.7%

8.4%

3.038

3.784

1.194

20.888

6.605

1.110

0.0700

-1.476

799.7%

8.5%

3.873

4.479

1.090

23.336

8.673

1.035

0.0725

-1.457

878.3%

8.7%

3.584

4.808

1.239

39.126

11.827

1.020

0.0750

-1.440

965.4%

8.9%

3.967

6.107

1.491

42.574

12.105

0.962

0.0775

-1.422

1061.7%

9.1%

4.861

6.759

1.563

52.167

11.780

1.014

0.0800

-1.405

1168.4%

9.2%

0.0825

-1.388

1.026

0.0850

-1.372

1.017

0.0875

-1.356

1.129

0.0900

-1.341

1.005

0.0925

-1.326

1.058

0.0950

-1.311

0.998

0.0975

-1.296

0.999

0.1000

-1.282

1.018

0.1025

-1.267

0.964

0.1050

-1.254

1.114

0.1075

-1.240

1.047

0.1100

-1.227

1.103

0.1125

-1.213

0.952

0.1150

-1.200

0.803

0.1175

-1.188

0.875

0.1200

-1.175

1.028

0.1225

-1.163

1.064

0.1250

-1.150

1.026

0.1275

-1.138

1.081

0.1300

-1.126

0.992

0.1325

-1.115

0.990

1.080

0.1350

-1.103

0.838

0.1375

-1.092

1.039

0.1400

-1.080

1.014

0.1425

-1.069

0.872

0.1450

-1.058

0.915

0.1475

-1.047

0.991

0.1500

-1.036

0.929

0.1525

-1.026

1.050

0.1550

-1.015

1.119

0.1575

-1.005

0.933

0.1600

-0.994

0.907

0.1625

-0.984

0.872

0.1650

-0.974

1.142

0.1675

-0.964

0.928

0.1700

-0.954

1.018

0.1725

-0.944

0.703

0.1750

-0.935

1.090

0.1775

-0.925

0.920

0.1800

-0.915

0.860

0.1825

-0.906

0.973

0.1850

-0.896

1.057

0.1875

-0.887

0.884

0.1900

-0.878

0.800

0.1925

-0.869

0.780

0.1950

-0.860

0.998

0.1975

-0.851

1.382

0.2000

-0.842

1.387

0.2025

-0.833

0.965

0.2050

-0.824

0.865

0.2075

-0.815

0.958

0.2100

-0.806

1.057

0.2125

-0.798

1.009

0.2150

-0.789

0.823

0.2175

-0.781

1.035

0.2200

-0.772

1.426

0.2225

-0.764

1.168

0.2250

-0.755

1.134

0.2275

-0.747

0.914

0.2300

-0.739

1.121

0.2325

-0.731

0.888

0.2350

-0.722

0.915

0.2375

-0.714

1.113

0.2400

-0.706

1.025

0.2425

-0.698

1.107

0.2450

-0.690

0.968

0.2475

-0.682

1.000

0.2500

-0.674

0.975

0.2525

-0.667

0.926

0.2550

-0.659

1.023

0.2575

-0.651

0.887

0.2600

-0.643

1.061

0.2625

-0.636

0.997

0.2650

-0.628

0.971

0.2675

-0.620

1.094

0.2700

-0.613

0.999

0.2725

-0.605

0.959

0.2750

-0.598

0.966

0.2775

-0.590

0.971

0.2800

-0.583

1.098

0.2825

-0.575

1.041

0.2850

-0.568

1.070

0.2875

-0.561

1.085

0.2900

-0.553

1.028

0.2925

-0.546

1.026

0.2950

-0.539

1.078

0.2975

-0.532

1.047

0.3000

-0.524

1.039

0.3025

-0.517

1.067

0.3050

-0.510

1.022

0.3075

-0.503

1.027

0.3100

-0.496

0.925

0.3125

-0.489

1.055

0.3150

-0.482

1.033

0.3175

-0.475

1.070

0.3200

-0.468

1.015

0.3225

-0.461

1.003

0.3250

-0.454

1.078

0.3275

-0.447

1.013

0.3300

-0.440

0.997

0.3325

-0.433

1.039

0.3350

-0.426

1.019

0.3375

-0.419

0.992

0.3400

-0.412

0.919

0.3425

-0.406

0.998

0.3450

-0.399

0.950

0.3475

-0.392

1.105

0.3500

-0.385

0.952

0.3525

-0.379

0.860

0.3550

-0.372

0.902

0.3575

-0.365

0.913

0.3600

-0.358

0.954

0.3625

-0.352

1.015

0.3650

-0.345

1.067

0.3675

-0.338

0.751

0.3700

-0.332

1.145

0.3725

-0.325

0.967

0.3750

-0.319

1.250

0.3775

-0.312

1.074

0.3800

-0.305

0.977

0.3825

-0.299

1.017

0.3850

-0.292

1.078

0.3875

-0.286

0.973

0.3900

-0.279

1.040

0.3925

-0.273

0.933

0.3950

-0.266

1.039

0.3975

-0.260

0.866

0.4000

-0.253

0.997

0.4025

-0.247

1.073

0.4050

-0.240

0.939

0.4075

-0.234

1.111

0.4100

-0.228

0.935

0.4125

-0.221

1.167

0.4150

-0.215

0.988

0.4175

-0.208

0.960

0.4200

-0.202

1.027

0.4225

-0.196

0.966

0.4250

-0.189

1.013

0.4275

-0.183

1.012

0.4300

-0.176

0.998

0.4325

-0.170

0.771

0.4350

-0.164

1.081

0.4375

-0.157

1.034

0.4400

-0.151

1.035

0.4425

-0.145

1.012

0.4450

-0.138

1.042

0.4475

-0.132

0.968

0.4500

-0.126

1.001

0.4525

-0.119

0.954

0.4550

-0.113

0.994

0.4575

-0.107

1.007

0.4600

-0.100

0.939

0.4625

-0.094

1.018

0.4650

-0.088

1.058

0.4675

-0.082

1.058

0.4700

-0.075

1.001

0.4725

-0.069

0.993

0.4750

-0.063

0.934

0.4775

-0.056

0.972

0.4800

-0.050

0.959

0.4825

-0.044

1.016

0.4850

-0.038

0.984

0.4875

-0.031

0.935

0.4900

-0.025

0.960

0.4925

-0.019

1.080

0.4950

-0.013

1.022

0.4975

-0.006

1.034

0.5000

0.000

1.016

0.5025

0.006

1.029

0.5050

0.013

1.068

0.5075

0.019

0.998

0.5100

0.025

1.055

0.5125

0.031

1.074

0.5150

0.038

1.058

0.5175

0.044

1.055

0.5200

0.050

1.004

0.5225

0.056

1.055

0.5250

0.063

1.022

0.5275

0.069

0.947

0.5300

0.075

1.017

0.5325

0.082

1.026

0.5350

0.088

0.989

0.5375

0.094

0.935

0.5400

0.100

1.062

0.5425

0.107

1.017

0.5450

0.113

1.004

0.5475

0.119

1.020

0.5500

0.126

0.990

0.5525

0.132

1.051

0.5550

0.138

1.054

0.5575

0.145

0.981

0.5600

0.151

1.016

0.5625

0.157

0.999

0.5650

0.164

1.002

0.5675

0.170

1.013

0.5700

0.176

1.037

0.5725

0.183

1.016

0.5750

0.189

1.068

0.5775

0.196

0.956

0.5800

0.202

1.090

0.5825

0.208

1.020

0.5850

0.215

0.999

0.5875

0.221

0.982

0.5900

0.228

1.064

0.5925

0.234

1.044

0.5950

0.240

1.032

0.5975

0.247

1.040

0.6000

0.253

1.012

0.6025

0.260

1.071

0.6050

0.266

0.936

0.6075

0.273

1.048

0.6100

0.279

1.039

0.6125

0.286

1.029

0.6150

0.292

0.963

0.6175

0.299

0.976

0.6200

0.305

0.933

0.6225

0.312

0.900

0.6250

0.319

0.994

0.6275

0.325

0.997

0.6300

0.332

1.046

0.6325

0.338

1.026

0.6350

0.345

0.992

0.6375

0.352

0.985

0.6400

0.358

0.964

0.6425

0.365

1.001

0.6450

0.372

1.055

0.6475

0.379

1.038

0.6500

0.385

0.980

0.6525

0.392

0.989

0.6550

0.399

1.024

0.6575

0.406

0.983

0.6600

0.412

1.023

0.6625

0.419

0.962

0.6650

0.426

0.961

0.6675

0.433

1.079

0.6700

0.440

1.029

0.6725

0.447

1.088

0.6750

0.454

1.005

0.6775

0.461

0.949

0.6800

0.468

1.016

0.6825

0.475

0.972

0.6850

0.482

1.071

0.6875

0.489

0.904

0.6900

0.496

1.035

0.6925

0.503

1.004

0.6950

0.510

0.970

0.6975

0.517

1.033

0.7000

0.524

0.982

0.7025

0.532

0.974

0.7050

0.539

1.001

0.7075

0.546

1.065

0.7100

0.553

1.022

0.7125

0.561

1.026

0.7150

0.568

1.034

0.7175

0.575

1.018

0.7200

0.583

1.049

0.7225

0.590

1.020

0.7250

0.598

1.020

0.7275

0.605

1.007

0.7300

0.613

1.049

0.7325

0.620

1.051

0.7350

0.628

0.945

0.7375

0.636

1.012

0.7400

0.643

1.044

0.7425

0.651

1.059

0.7450

0.659

1.009

0.7475

0.667

1.017

0.7500

0.674

1.051

0.7525

0.682

1.064

0.7550

0.690

1.016

0.7575

0.698

0.984

0.7600

0.706

1.051

0.7625

0.714

0.970

0.7650

0.722

0.977

0.7675

0.731

1.071

0.7700

0.739

1.048

0.7725

0.747

1.001

0.7750

0.755

0.990

0.7775

0.764

1.010

0.7800

0.772

1.042

0.7825

0.781

1.018

0.7850

0.789

0.972

0.7875

0.798

1.050

0.7900

0.806

0.960

0.7925

0.815

1.034

0.7950

0.824

1.049

0.7975

0.833

1.020

0.8000

0.842

0.993

0.8025

0.851

0.982

0.8050

0.860

1.002

0.8075

0.869

1.057

0.8100

0.878

1.038

0.8125

0.887

0.995

0.8150

0.896

0.989

0.8175

0.906

0.979

0.8200

0.915

0.976

0.8225

0.925

1.008

0.8250

0.935

0.987

0.8275

0.944

1.027

0.8300

0.954

0.950

0.8325

0.964

1.003

0.8350

0.974

1.054

0.8375

0.984

1.020

0.8400

0.994

1.005

0.8425

1.005

1.054

0.8450

1.015

1.011

0.8475

1.026

1.033

0.8500

1.036

1.052

0.8525

1.047

1.042

0.8550

1.058

1.003

0.8575

1.069

1.059

0.8600

1.080

0.973

0.8625

1.092

1.085

0.8650

1.103

0.983

0.8675

1.115

1.091

0.8700

1.126

1.053

0.8725

1.138

1.020

0.8750

1.150

1.010

0.8775

1.163

0.997

0.8800

1.175

1.040

0.8825

1.188

1.006

0.8850

1.200

1.084

0.8875

1.213

1.062

0.8900

1.227

0.998

0.8925

1.240

1.013

0.8950

1.254

0.972

0.8975

1.267

1.083

0.9000

1.282

1.002

0.9025

1.296

0.965

0.9050

1.311

1.041

0.9075

1.326

1.071

0.9100

1.341

1.000

0.9125

1.356

0.941

0.9150

1.372

1.041

0.9175

1.388

1.053

0.9200

1.405

0.967

0.9225

1.422

0.956

0.9250

1.440

1.007

0.9275

1.457

0.995

0.9300

1.476

1.037

0.9325

1.495

0.960

0.9350

1.514

0.974

0.9375

1.534

1.022

0.9400

1.555

1.039

0.9425

1.576

1.044

0.9450

1.598

1.000

0.9475

1.621

1.013

0.9500

1.645

0.950

0.9525

1.670

0.940

0.9550

1.695

0.970

0.9575

1.722

1.023

0.9600

1.751

0.961

0.9625

1.780

1.045

0.9650

1.812

0.986

0.9675

1.845

1.033

0.9700

1.881

1.034

0.9725

1.919

1.021

0.9750

1.960

1.028

0.9775

2.005

1.045

0.9800

2.054

1.018

0.9825

2.108

1.050

0.9850

2.170

1.027

0.9875

2.241

1.028

0.9900

2.326

1.054

0.9925

2.432

1.005

0.9950

2.576

1.005

0.9975

2.807

1.002 1.040 1.024 0.998 1.036 0.990 0.956 1.013 1.019 1.029 0.930 1.015

0.988 0.984 1.033 1.021 0.977 1.032 0.941 0.999 1.047 1.048 1.065 1.032 1.027 1.005 1.024 0.973 1.034 1.024 0.982 1.030 1.045 1.005 0.963 1.021 0.995 0.939 0.919 0.920 1.065 1.021 0.954 1.006 1.109 1.015 1.051 0.976 1.037 1.050 1.019 0.981 0.998 1.054 0.990 1.034 0.995 1.026 1.028 1.015 1.017 1.008 1.016

1.018 1.020 0.988 1.030 1.010 1.001 1.006 1.035 1.003 0.987 1.036 0.997 0.953 1.015 1.027 1.033 1.029 0.997 1.011 1.006 0.987 0.980 1.022 0.951 0.985 0.988 0.928 0.995 1.049 1.010 1.000 1.080 1.007 1.041 1.044 0.952 1.019 1.047 0.993 1.034 0.972 1.007 1.028 0.958 0.974 1.011 1.083 1.016 1.011 0.983 1.016

1.040 1.009 1.053 0.960 0.993 0.957 1.036 1.023 1.003 0.946 0.941 1.045 0.976 1.046 0.970 0.982 0.926 1.059 1.003 0.911 0.945 0.952 1.075 1.051 1.035 0.990 1.054 1.058 1.042 1.014 1.038 1.038 0.963 1.002 0.960 1.041 0.994 0.960 1.003 1.088 1.019 1.030 1.007 1.006 1.022 0.980 1.004 1.039 0.996 1.011 1.051

1.013 0.984 0.967 1.000 0.961 0.986 0.995 1.039 0.968 1.042 1.000 0.892 1.018 0.992 1.002 0.978 0.963 0.973 0.987 0.924 0.917 0.883 1.166 0.955 0.982 1.125 1.067 1.024 1.049 1.051 1.046 0.934 0.986 0.967 1.064 1.031 0.990 1.120 0.994 1.033 0.990 0.993 1.043 0.993 1.001 1.025 0.979 0.999 1.054 0.951 0.985

0.988 1.001 0.985 1.048 0.985 0.987 1.000 0.959 1.037 1.005 0.940 0.984 1.028 1.087 1.014 0.985 1.056 1.034 0.995 0.911 1.026 1.017 1.042 0.972 1.058 1.004 0.983 1.041 1.011 1.061 1.003 0.934 1.051 1.019 1.061 1.003 0.901 1.043 1.056 1.030 1.068 1.013 1.028 1.019 1.110 0.969 0.956 1.021 1.038 0.979 1.006

0.992 1.001 0.945 0.950 1.053 1.044 0.974 0.984 0.949 0.994 1.041 0.971 0.983 0.979 1.127 1.011 1.113 1.044 1.017 1.035 1.026 1.037 1.076 0.995 1.038 0.969 1.017 1.014 0.987 1.023 0.994 0.994 0.967 1.017 1.007 0.947 1.022 0.986 1.113 1.000 1.003 0.990 1.025 1.077 1.014 1.002 0.997 1.062 1.016 0.997 0.994

0.968 1.045 1.072 1.047 1.004 1.076 1.055 0.988 1.055 1.017 0.943 1.075 0.918 1.056 1.026 0.974 1.134 1.041 1.027 0.991 1.010 1.050 1.050 1.039 0.978 0.785 0.918 1.074 1.043 1.047 0.970 1.011 1.008 1.046 0.996 0.967 1.042 1.027 0.986 1.018 1.072 0.975 1.024 1.052 1.040 0.995 1.090 1.019 0.996 0.977 1.021

1.024 0.933 1.013 1.026 0.975 1.098 0.993 0.997 0.910 0.951 0.996 1.064 1.027 1.044 1.072 1.024 1.003 1.043 0.954 1.047 1.024 0.984 1.013 0.960 1.114 0.981 1.013 0.980 1.029 1.005 0.986 1.040 0.980 1.012 1.004 1.034 1.013 1.007 1.014 1.022 0.976 1.027 1.003 0.995 1.038 0.993 1.020 0.991 1.012 1.034 0.973

0.957 1.013 1.016 0.975 1.033 1.041 0.976 1.023 0.963 1.015 1.026 1.039 1.030 1.029 1.040 1.024 1.033 1.003 1.042 0.997 1.044 1.019 1.034 1.010 1.010 1.015 1.026 1.004 0.956 1.021 1.056 1.027 1.076 0.980 1.062 1.008 0.958 1.060 1.061 1.045 1.079 0.944 1.055 0.967 1.046 1.017 1.011 1.072 1.051 1.010 0.983

1.041 0.989 0.855 1.064 1.081 1.061 1.058 1.042 0.969 1.040 1.039 0.976 1.056 0.969 0.995 0.973 1.063 1.020 1.059 0.950 0.981 1.098 0.970 0.980 1.025 0.984 1.062 0.947 0.996 0.921 1.005 1.036 0.909 0.937 1.078 1.007

TSE data 642 10.4% 15.4% 11.5%

long Bond

1.072

Above:

0.997

Above:

0.7

0.971

Annual Return

1.005

Annual Return

0.6

0.964

Standard Dev

0.997

Standard Dev

0.5

1.003

Mean Return

1.007

Mean Return

0.4

TSE Gains 0.981 0.933 1.046 1.084

1.002 0.977 1.003 1.010

Cdn Bond data 642 6.7% 8.4% 7.0%

1.0 0.9 0.8

0.972

1.000

0.3

1.065

1.008

0.2

0.994

1.002

0.1

0.986

1.000

0.0

0.981

1.005

0.950

1.004

1.028

1.004

0.979

1.002

0.943

1.001

1.014

1.005

1.052

1.004

1.039

1.013

1.029

1.009

1.073

0.998

1.017

1.002

1.043

0.997

0.991

1.005

1.023

1.001

1.023

1.002

1.060

1.004

1.048

1.000

0.964

0.989

1.008

1.019

1.119

0.998

1.033

1.005

1.032

0.984

0.995

0.996

1.051

1.004

1.117

1.001

1.008

0.975

0.982

1.001

1.043

1.001

0.981

1.003

0.963

1.004

1.053

1.003

1.043

1.001

1.022

1.003

0.976

0.980

0.978

0.994

1.010

1.004

0.993

0.998

0.960

1.002

1.015

1.007

0.942

1.008

1.001

0.993

RR RRR RR RRR RR RR RRR RR RRR RR RRR RR RRR RR RR RRR R oooooooooooooo oooooooooooooooooooo oooooo ww www ww www ww ww www ww www ww www ww www ww ww www w

1.026

0.994

1.032

0.998

0.997

1.003

0.962

1.008

0.996

1.004

1.020

1.002

1.002

0.994

1.010

1.004

0.988

1.002

0.981

1.002

0.972

0.998

1.005

0.999

0.983

1.004

1.024

1.001

0.983

1.003

0.983

1.012

1.039

1.009

0.992

1.008

1.011

1.011

0.965

1.024

1.014

1.040

1.043

0.997

1.015

1.004

1.062

1.005

0.994

1.007

1.053

1.004

1.002

0.999

1.017

1.001

0.996

1.003

1.087

1.001

1.043

1.003

1.009

1.012

1.018

1.008

0.983

0.997

1.065

1.003

1.045

1.004

1.047

1.024

1.050

0.963

0.997

0.999

1.004

1.003

0.941

0.987

1.036

0.995

1.016

1.016

0.980

1.005

1.039

0.986

1.084

0.986

0.993

1.006

0.961

1.018

1.032

0.978

1.076

0.979

0.979

0.992

0.943

1.003

0.979

0.997

0.948

0.998

1.084

0.983

1.008

1.023

0.962

1.001

1.038

0.996

1.047

0.982

1.030

1.006

0.982

0.998

0.976

0.995

0.903

1.007

0.934

1.029

0.929

1.034

1.024

1.007

0.951

0.992

1.043

0.993

0.992

1.003

1.035

1.006

0.995

1.019

1.043

0.982

1.029

0.995

1.052

0.996

1.015

0.985

1.037

0.993

1.013

0.982

1.006

0.996

1.019

1.001

1.030

0.995

1.009

0.991

0.997

1.001

1.012

0.997

1.003

0.993

1.011

1.006

1.047

0.972

0.951

0.984

0.956

1.026

1.002

1.004

0.996

0.988

1.037

0.993

0.957

1.020

0.969

1.017

1.004

1.006

0.985

1.016

1.031

1.025

0.980

0.995

0.981

1.038

1.068

1.005

0.954

0.973

1.002

0.976

1.040

1.006

1.055

1.012

1.059

1.022

1.035

0.993

1.023

1.000

1.048

1.010

1.021

1.029

1.011

1.003

1.020

1.002

1.017

1.001

0.987

1.013

1.008

1.008

1.031

1.001

1.028

1.000

0.977

1.008

1.007

1.013

1.002

1.012

0.975

0.981

0.918

0.970

0.940

0.989

1.027

1.009

1.026

1.007

0.956

1.035

1.018

1.008

1.079

1.002

1.011

1.010

1.052

0.997

0.969

1.007

1.034

1.014

1.051

1.011

1.017

1.002

0.967

0.986

0.976

0.986

1.008

1.024

1.034

1.007

1.011

0.997

0.991

1.001

1.040

1.005

1.030

1.004

0.993

0.995

1.043

1.005

1.039

1.008

1.036

1.004

1.002

1.003

1.026

1.003

0.995

1.007

1.047

1.010

1.006

1.010

1.005

1.013

1.009

1.012

1.059

0.996

0.998

1.001

0.995

1.005

1.027

0.996

0.999

1.000

0.935

0.991

0.992

0.997

1.027

1.008

1.021

0.999

1.020

1.001

0.973

1.005

1.025

1.003

1.044

0.983

0.977

1.008

0.990

1.002

1.012

1.004

0.968

0.999

0.999

0.996

0.986

0.984

0.928

1.025

0.980

1.009

1.023

0.983

0.995

1.021

1.030

1.022

1.072

1.000

1.012

1.022

1.038

0.996

1.023

0.987

0.964

0.989

1.030

1.004

1.035

0.993

0.990

0.984

1.024

0.988

0.944

1.000

1.027

0.992

1.014

1.005

0.975

0.987

0.958

0.987

0.980

1.035

1.092

0.971

0.992

1.041

1.057

1.019

0.997

1.012

1.028

0.988

1.052

0.983

1.018

0.994

1.039

0.972

1.025

1.020

1.029

1.002

0.954

1.004

1.035

0.999

1.030

0.988

1.027

1.004

0.896

1.004

0.946

1.005

1.052

0.980

0.997

1.006

1.017

0.976

1.027

0.991

0.994

1.009

0.964

1.023

1.028

1.025

1.004

0.997

0.914

0.989

0.904

1.020

0.984

1.023

1.050

0.998

1.028

1.018

1.049

1.001

0.975

1.049

1.045

1.056

1.033

1.038

1.033

0.988

1.001

1.015

1.044

0.985

0.990

0.966

0.981

1.014

1.022

0.988

0.989

1.039

0.995

1.024

0.968

1.032

0.937

1.021

1.029

1.005

1.098

0.988

1.092

0.989

1.037

0.973

0.977

1.003

1.013

0.999

1.019

0.996

0.991

1.002

1.027

1.011

1.049

1.004

0.988

1.026

0.965

1.024

1.067

1.002

1.028

1.002

1.020

1.001

0.985

0.997

1.012

0.997

0.961

0.975

0.956

1.005

1.016

1.007

1.064

0.998

0.983

1.016

1.048

1.018

1.066

1.003

0.891

1.001

1.014

1.002

1.026

1.007

1.030

0.966

0.971

0.953

0.911

0.999

0.937

0.961

0.983

0.994

1.020

0.991

0.900

1.022

0.910

1.048

1.099

1.036

0.935

1.016

1.001

1.050

1.165

1.019

1.030

0.980

0.988

0.958

1.023

1.037

1.024

0.992

1.029

0.969

1.002

1.004

0.990

0.981

0.944

1.041

0.958

0.987

1.056

1.016

0.978

1.025

1.096

1.009

1.035

0.998

0.985

1.012

1.024

1.009

1.003

1.005

0.986

1.006

1.000

1.019

1.000

1.014

0.985

1.014

0.967

1.031

0.932

1.039

1.106

1.003

0.993

0.998

1.017

0.989

1.018

1.006

0.975

1.014

0.990

1.012

1.058

1.009

1.004

1.019

0.974

1.004

1.002

0.999

0.972

1.004

1.053

1.005

1.049

0.982

0.944

1.000

1.011

1.006

1.064

1.003

1.019

1.007

1.048

1.008

1.004

1.013

1.062

1.009

1.035

1.008

1.048

0.980

0.948

1.003

1.050

0.996

1.039

0.997

1.036

0.996

1.025

1.013

1.064

1.029

1.014

1.006

1.028

1.004

1.071

0.999

0.965

0.983

1.093

0.990

1.037

0.950

0.903

1.026

1.082

0.981

1.073

0.952

1.120

0.957

1.085

0.975

0.824

1.115

1.042

1.054

1.059

1.019

1.051

0.937

1.069

1.005

1.012

0.971

1.023

0.995

0.993

1.025

1.076

1.034

0.949

0.991

0.983

0.983

0.982

1.005

1.075

0.915

0.990

1.019

1.032

1.008

1.001

0.900

0.957

1.031

0.969

0.966

0.869

1.071

0.980

1.162

1.097

0.955

0.977

0.974

0.916

1.070

0.939

1.009

0.957

1.032

0.977

1.014

0.990

0.937

0.904

1.038

1.036

1.120

1.147

1.043

0.999

1.070

1.109

1.043

1.042

1.046

1.071

0.968

1.039

1.045

1.033

1.017

1.036

1.049

1.088

1.000

1.037

0.990

1.015

0.976

1.014

0.988

1.005

1.053

1.010

1.012

0.946

1.005

1.083

0.994

1.009

1.017

0.969

0.976

0.983

0.966

0.989

0.994

0.977

0.971

0.963

1.019

1.001

1.038

0.966

1.047

1.119

1.029

1.005

1.043

0.985

1.037

1.009

1.021

1.018

1.031

1.083

0.945

1.002

1.037

1.012

1.042

1.010

1.067

1.042

1.000

0.995

1.007

1.026

1.018

1.017

0.996

0.937

1.028

1.018

1.039

1.071

1.031

1.020

0.975

0.981

1.052

1.006

1.043

1.072

1.027

1.012

0.991

1.016

1.016

0.992

1.013

0.953

1.025

1.034

0.983

0.987

1.001

1.021

1.031

1.005

1.010

1.011

1.033

1.093

0.994

1.046

1.018

1.072

0.939

0.995

1.000

0.994

1.020

1.018

0.972

1.079

0.992

0.992

0.956

0.980

1.084

0.775

0.986

0.989

1.021

1.065

1.058

0.969

1.019

1.050

0.966

1.038

0.990

1.009

1.007

0.976

1.029

1.063

0.986

0.983

0.991

0.977

1.024

1.003

1.035

1.036

0.993

0.973

1.005

1.034

1.023

1.070

0.980

0.989

1.014

1.007

1.033

1.015

1.036

1.026

1.029

1.019

1.006

1.058

1.008

1.013

0.984

0.987

1.039

0.996

0.987

1.009

1.017

1.011

0.980

0.935

0.962

0.997

0.988

0.991

0.963

0.919

1.062

1.076

1.020

0.994

1.004

1.007

1.005

0.943

0.957

0.948

1.039

0.977

1.044

1.026

1.024

1.039

1.032

1.007

1.035

1.061

1.009

1.014

1.006

0.995

1.008

1.027

0.973

0.982

1.024

1.023

1.025

0.997

1.040

0.967

1.048

1.039

1.002

0.983

1.026

1.024

1.012

1.026

1.003

0.998

0.981

0.957

0.989

0.985

1.037

1.012

1.034

1.004

1.067

1.018

1.009

0.991

0.977

0.973

1.025

1.013

0.978

0.987

1.018

1.025

0.996

0.988

1.051

1.046

1.000

1.048

1.007

1.053

1.021

1.028

1.022

1.025

1.023

1.001

1.044

1.045

0.992

0.967

1.026

1.067

0.997

0.984

1.038

1.037

1.032

1.055

0.960

0.973

0.923

0.982

1.013

0.986

0.974

1.016

0.944

0.933

0.990

1.039

1.061

1.043

0.995

1.004

0.986

0.986

1.012

0.956

1.015

1.033

0.987

0.954

1.056

1.028

1.021

1.049

1.031

0.993

1.037

1.042

1.015

1.021

0.964

1.020

1.031

0.981

1.019

1.006

1.007

0.985

1.071

1.047

1.007

1.014

1.014

1.055

0.961

0.995

0.997

1.010

0.995

1.036

1.021

1.021

1.001

0.964

1.018

0.978

1.031

1.045

1.018

1.031

1.073

1.059

1.046

1.076

0.970

0.987

0.976

1.032

1.035

1.009

0.987

0.952

1.006

1.022

1.008

1.070

1.053

1.011

1.045

1.069

0.977

0.963

1.047

1.067

1.025

0.973

1.007

0.953

1.003

1.031

1.023

1.001

1.004

1.060

1.016

1.068

0.994

1.015

1.021

0.991

1.009

0.973

0.993

0.942

0.981

0.799

1.076

1.017

0.991

1.107

0.996

1.023

1.035

1.025

1.004

1.038

0.972

0.939

1.020

1.047

0.992

1.064

0.983

0.977

0.995

1.027

0.993

1.011

1.010

0.986

0.980

1.000

0.958

1.044

1.033

1.038

0.992

1.120

0.994

1.008

1.046

1.077

1.007

1.038

0.998

0.988

1.015

0.991

1.009

1.104

1.012

1.021

1.009

1.082

1.001

0.924

1.009

0.929

1.022

0.916

1.009

1.015

0.992

1.044

1.013

0.867

0.993

0.944

0.984

1.045

0.990

1.028

1.017

0.950

1.001