©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004 -2008 All rights reserved P r o v i d i n g W E A L T H C A R E ARE YOU MODELING.

©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004 -2008 All rights reserved

P r o v i d i n g W E A L T H C A R E

ARE YOU MODELING WHAT YOU ARE YOU MODELING WHAT YOU INTENDED?INTENDED?

Presented by:

David B. Loeper, CIMA®, CIMC®

©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved

P r o v i d i n g W E A L T H C A R E PAGE 2

What are Capital Market Assumptions (CMAs) Anyway?

For Purposes of Monte Carlo Simulation OR Optimization:

The Average (mean, arithmetic mean) of Millions of Returns• Center of the distribution

The Standard Deviation of Returns (uncertainty)• Extent and frequency returns vary from the mean

The Correlation of Returns to Other Assets• Degree of association between two random variables



What are Capital Market Assumptions (CMAs) Anyway?

For Purposes of Monte Carlo Simulation OR Optimization:

The Average (mean, arithmatic mean) of Millions of Returns• Center of the distribution

The Standard Deviation of Returns (uncertainty)• Extent and frequency returns vary from the mean

The Correlation of Returns to Other Assets• Degree of association between two random variables

Together, these define the shape of a RANDOM distribution and ARE NOT A FIXED

RELATIONSHIP in A Monte Carlo TRIAL



Statisticians draw these distributions as a bell curve(Log normal distributions have a slightly longer tail at one end)

Extent

FrequencyMean

Standard Deviation



Statisticians draw these distributions as a bell curveThe bell curve can define AN ASSET CLASS

High RiskAsset Class

LowRisk

AssetClass

Low Mean & Risk

High Mean & Risk



Statisticians draw these distributions as a bell curveThe bell curve can define AN ASSET CLASSOr A PORTFOLIO when two or more classes are combined (based on the correlation between the two)

50%

Mean

More EfficientPortfolio

High RiskAsset Class

LowRisk

AssetClass

Low Mean

High Mean

50%

Degree of Covariance



Imagine the “bell” flipped over and filled with a million numbers

Extent

FrequencyMean

10 1114

24

7

1 188 129

-3

-11

-22

28

35

45

9 1311 192

5 10-1 12 16 26

-913

274 752-38

-45 61-5-21

-28

381811

26141284 41 48



Imagine the “bell” flipped over and filled with a million numbersThe CMAs define the population of numbers in the “bell”

Extent

FrequencyMean

10

-3

1114

24

52

-11

-22-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21-28

13274

381811

7

26141284 41 48



The CMAs define the population of numbers in the “bell”If we stirred them, blind folded you, & asked you to pickA SMALL percentage of the numbersWhat’s your chance of picking?….

Extent

FrequencyMean

10

-3

1114

24

52

-11

-22-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21-28

13274

381811

7

26141284 41 48

Just these?



The CMAs define the population of numbers in the “bell”If we stirred them, blind folded you, & asked you to pickA SMALL percentage of the numbersWhat’s your chance of picking?….

Extent

FrequencyMean

10

-3

1114

24

52

-11

-22-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21-28

13274

381811

7

26141284 41 48

Just these?

Or, Just

these?



The CMAs define the population of numbers in the “bell”What’s your chance of picking?….

Extent

FrequencyMean

10

-3

1114

24

52

-11

-22-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21-28

13274

381811

7

26141284 41 48

Just these?

Or, Just

these?

Monte Carlo Simulates this

random “picking”

BASED ON THE BELL

(bowl) DEFINED BY

THE CMAs



The CMAs define the population of numbers in the “bell”

Extent

FrequencyMean

10

-3

1114

24

52

-11

-22-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21-28

13274

381811

7

26141284 41 48

Just these?

5% Chance

Or, Just these?

5% Chance

In Seeking RATIONAL confidence,

WITHOUT undue sacrifice, do we advise clients to

live their life based on

REMOTE EXTREMES

THAT NEVER HAPPENED?




Extent

FrequencyMean

10

-3

1114

24

52

-11

-22-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21-28

13274

381811

7

26141284 41 48

Just these?

5% Chance

Or, Just these?

5% Chance

In Seeking RATIONAL confidence,

WITHOUT undue sacrifice do we advise clients to

live their life based on

REMOTE EXTREMES?

Or REASONABLE CONFIDENCE?

<18% Chance or 82% Confidence of EXCEEDING




Extent

FrequencyMean

10

-3

1114

24

52

-11

-22-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21-28

13274

381811

7

26141284 41 48

Just these?

Or, Just

these?

But, IF WE MAKE POOR

ASSUMPTIONS in the SHAPE of

the Bell, we could be CREATING:

UNDUE SACRIFICE

orTOO MUCH

UNCERTAINTY

10%<18% Chance



The CMAs define the population of numbers in the “bell”IN THIS CASE, 82% Confidence is likely FAR worse than any market we have ever seen! SACRIFICE!!

Extent

FrequencyMean

10

-3

1114

24

-11

-22-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21-28

13274

381811

7

26141284 41 48

Missing only a few returns (some

HIGH ones) changes ALL of

the odds

7%Only 50% Confidence of

EXCEEDING What Had Been 82%

Remote outcome no

longer within population

52



The CMAs define the population of numbers in the “bell” 82% Confidence of DOING ABOVE AVERAGE?!TOO MUCH UNCERTAINTY

Extent

Frequency

Mean

10

-3

1114

24

-11

-22-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21-28

13274

381811

7

26141284 41 48

Missing only a few returns (some

LOW ones) changes ALL of

the odds

13% 82% Confidence of EXCEEDING What Had Been only 50%

Remote outcome no

longer within population

Higher Confidence of

previously remote extreme



CRITICAL POINTS TO UNDERSTAND

With more COMPLETE populations, we can understand:

Where reasonable confidence falls

Remote extremes (those possible but never seen events)

It is intuitive that if you select a small sample, it is very unlikely they will ALL be one extreme or the other

Extent

FrequencyMean

10

-3

11

14

24

52

-11

-22

-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21

-28

13274

381811

7

26141284 41 48



CRITICAL POINTS TO UNDERSTAND

With more COMPLETE populations, we can understand:

Where reasonable confidence falls

Remote extremes (those possible but never seen events)

It is intuitive that if you select a small sample, it is very unlikely they will all be one extreme or the other

Extent

FrequencyMean

10

-3

11

14

24

52

-11

-22

-38

-45

7

1 18

28

35

45

61

8

9

12

1311 19

9

2

5 10-1 12 16 26

-9

-5-21

-28

13274

381811

7

26141284 41 48

What is harder to understand is how unlikely it is that a LARGER sample would be representative of the entire population…Thus skewed…or fooled?



We Can Easily Be Fooled (by randomness)

How Many Of You Think a Compound Return for Large Cap should be 10% or less?





30 Years 1974- 2003: 12.08%

30 Years 1973-2002: 10.55%

30 Years 1927-1956:

Think we should be careful in using a 30 year data set? ONE year changed compound return by

1.5%!!!!





30 Years 1974- 2003: 12.08%30 Years 1973-2002: 10.55%30 Years 1927-1956: 10.06% (expecting depression as NORM?)

20% of Historical 30 Year Periods <10%50% of Historical 30 Year Periods >10.82%51% of Historical 30 Year Periods >10.85% (monthly data)Our CMAs: 12.32% (mean) & 18.38% SD= 10.85% CompoundOur CMAs at 77th %-tile: 8.30% at 87th%-tile: 7.17%Worst 30 Years of History (annual data): 8.47% (1929-1958)Worst 30 Years of History (monthly data): 7.17%









RANDOMNESS Doesn’t Look Random!






RANDOMNESS Fooling Us? Have you been fooled by?…

RECENT low returns?Previously high returns (14% assumptions 5 years ago)Data sets that are too small to have any confidence in

assumptions? (20-30 Years? 10 Years?)• One trading discipline (MLM index)• “New” asset classes (foreign stocks, mid cap, growth/value,

hedge funds)

“Seeing Cycles or Streaks” in Random Data?• Roulette Wheel Spun 15 reds in a row!

– “Red Streak” Or “Black is Overdue”(As if the ball remembers where it fell)

• Growth & Value “Cycle”



Familiar with Growth & Value Cycles?

Relative Trailing 3 Year Returns - Growth vs. Value

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

Jan-

81

Jan-

82

Jan-

83

Jan-

84

Jan-

85

Jan-

86

Jan-

87

Jan-

88

Jan-

89

Jan-

90

Jan-

91

Jan-

92

Jan-

93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

3 Year Period Ending

Pe

form

an

ce

vs

. La

rge

Ca

p

Growth

ValueValue Outperforms

Growth OutperformsHEADS

TAILSHeadsTails

Heads vs. Tails

Ra

nd

om

Re

turn

s

Trailing 12 Flips

Flip# 12 24 36 48 60 72 84 96

Heads vs.TailsRANDOMNESS?

RandomnessDOES NOT appear to be

Random!



Your Advice (output) is only as good as the input… (Capital Market Assumptions)

If we are going to make the most of the one life each client has, then we must:

»Have comfort & confidence in achieving thegoals each client VALUES»Which therefore requires avoiding undue sacrifice to their lifestyle»And would include avoiding unnecessary investment risk (risk=concern=contradiction to comfort)

These are the premises of what we call: Wealthcare



Capital Market Assumptions SHOULD NOT CONTRADICT Wealthcare PREMISES…If we are too conservative, the price to the client’s life is: NEARLY

CERTAIN UNDUE LIFESTYLE SACRIFICE

REMEMBER:

1. How we were fooled by recent history?

2. How missing a few data points changed ALL the outcomes

3. How ONE YEAR of data changed the trailing returns (1.5%)

4. How reasonably large samples can be very skewed?

5. How our brains are “wired” to see streaks & cycles in random data?

To avoid UNDUE SACRIFICE, we should avoid being too conservative



Client Desires Maximum Income and has no desire to leave more than $1 million estate:Which is Wealthcare? PRICE OF BEING TOO CONSERVATIVE!

$43,000 retirement income and 83% chance of exceeding$1 million estate with (Our CMAs):

-90% chance of exceeding $450k estate?-75% chance of exceeding $1.5 million estate?

OR…

$24,000 retirement income, also 83% confidence but 2% lower return assumption than our CMAs:

-96.5% chance of exceeding $1 million?-90% chance of exceeding $1.5 million?



Client Desires Maximum Income and has no desire to leave more than $1 million estate:Which is Wealthcare? PRICE OF TOO CONSERVATIVE!

$43,000 retirement income and 83% chance of exceeding$1 million estate with (Our CMAs):

-90% chance of exceeding $450k estate?-75% chance of exceeding $1.5 million estate?

OR…

$24,000 retirement income, also 83% confidence but 2% lower return assumption than our CMAs:

chance of exceeding $1 million?-90% chance of exceeding $1.5 million?Being too conservative prioritizes estate above all else!

With $43k income starting in 1926, they’d have an $875K

estate

With $24k income starting in 1926, they’d have a

$2.6 million estate



I’d be very uncomfortable targeting low 80ish confidence with return assumptions less than ours…Nearly certain sacrifice!

I’m fairly confident of our assumptions for stocks, bonds & cash because there is a lot of data to validate & test reasonableness

Funny thing, a lot of the advisors that think our assumptions are “too high” (currently) or “too low” (eight years ago) despite all the data, turn around and complain about our assumptions for “new classes” despite NOT having enough data to validate & test these “new classes”

Isn’t a premise of Wealthcare having RATIONAL CONFIDENCE?

What happens to CONFIDENCE in DELIVERING the client’s goals when we make ASSUMPTIONS about “classes” we do not have the data to validate???



I’d be very uncomfortable targeting low 80ish confidence with return assumptions less than ours…Nearly certain sacrifice!

I’m fairly confident of our assumptions for stocks, bonds & cash because there is a lot of data to validate & test reasonableness

Funny thing, a lot of the advisors that think our assumptions are “too high” (currently) or “too low” (five years ago) despite all the data, turn around and complain about our assumptions for “new classes” despite NOT having enough data to validate & test these “new classes”

Isn’t a premise of Wealthcare having RATIONAL CONFIDENCE?

What happens to CONFIDENCE in DELIVERING the client’s goals when we make ASSUMPTIONS about “classes” we do not have the data to validate and test reasonableness???



First Question Would Be…What Explains 90%+ Of The Variance Of Returns? (to see if targeted confidence is in the ballpark?)

ANSWER: Asset Allocation

Source: Two Studies by Brinson, Beebower & Hood

Asset Allocation TO WHAT?

STOCKS, BONDS & CASH

LESS THAN 10% of variance was explained by small cap, midcap, growth, value, foreign, real estate, etc.



First Question Would Be…What Explains 90%+ Of The Variance Of Returns? (to see if targeted confidence is in the ballpark?)

ANSWER: Asset Allocation

Source: Two Studies by Brinson, Beebower & Hood

Asset Allocation TO WHAT?

STOCKS, BONDS & CASH

LESS THAN 10% of variance was explained by small cap, midcap, growth, value, foreign, real estate, etc.



Sample Client Confidence with 100% Large Cap as Investment Policy:

Based upon randomizing actual historical returns from ’26-’02 1000 times



How big a difference do you think it would make if the client were OVERWEIGHTED by 60% to Small Cap?


60% Small/40% Large82%



Shouldn’t it make a HUGE difference???It does…so long as we are planning on coin flip odds…


60% Small/40% Large82%

54% 60% Small/40% Large

45% 100% Large

Assuming you consider 9 pts of confidence “HUGE” near the median



Measuring with a micrometer…cutting with a chain saw…

Would You Get Different Results With These Allocations?

Asset Class #1 #2 #3 #4

Large 40% 10% 0% 20%Large Value 0% 15% 20% 10%Large Growth 0% 15% 20% 10%Small 60% 0% 40% 10%Small Value 0% 30% 10% 25%Small Growth 0% 30% 10% 25%

SHOULD YOU?SHOULD YOU?THEY ARE ALL THE SAME!THEY ARE ALL THE SAME!



Provided you use appropriate indices, your results would be statistical equivalents – 10 Years Ending 2002


Allocations: #1 #2 #3 #4

Large 40% 10% 0% 20%Large Value 0% 15% 20% 10%Large Growth 0% 15% 20% 10%Small 60% 0% 40% 10%Small Value 0% 30% 10% 25%Small Growth 0% 30% 10% 25%

Mean 9.46 9.35 9.39 9.37Compound 8.22 8.13 8.16 8.15Standard Deviation 16.59 16.46 16.52 16.49Sample Confidence 49% 48% 48% 48%

Are we getting better assumptions by slicing the pie into more pieces?



Or are we increasing our estimation error by limiting our data set?


Allocation: #1 #2 #3 #4

11 Years 2003:Mean 10.62 10.57 10.63 10.58Compound 9.45 9.41 9.46 9.42Standard Deviation 16.21 16.14 16.20 16.14Sample Confidence 64% 63% 64% 63%


Since the results are statistically the same between the allocations…





11 Years 2003:11 Years 2003 Mean: 10.62 10.57 10.63 10.58Sample Confidence 64% 63% 64% 63%



25 Years 2000: 18.13%

Sample Confidence 99%

Which “Error” Reduces My OVERALL Confidence More?

Ignoring Subclasses?





11 Years 2003:11 Year 2003 Mean: 10.62 10.57 10.63 10.58Sample Confidence 64% 63% 64% 63%

10 Year 2002:Mean 9.46 9.35 9.39 9.37Compound 8.22 8.13 8.16 8.15Standard Deviation 16.59 16.46 16.52 16.49Sample Confidence 49% 48% 48% 48%


25 Year Mean 2000: 18.13%

Sample Confidence 99%

Which “Error” Reduces My OVERALL Confidence More?

Ignoring Subclasses? +/- 1%

Or ignoring the effect of limiting

my sample population so I can

include Sub- Classes?

+/- 50%+/- 15%

+/- 35%



Making assumptions from limited data, usually has the opposite effect of excessive conservatism

Instead of nearly certain sacrifice…

We MIGHT be subjecting the client to:TOO MUCH UNCERTAINTY






If the effect of “new classes” on the overall portfolio is 1-2% standard deviation and/or 50-100 bps of return…

You could very well be assuming the value of the “new” class is the same as moving the 50th %-tile to the comfort zone!

HOW CAN YOU ASSUME THAT?!






If the effect of “new classes” on the overall portfolio is 1-2% standard deviation and/or 50-100 bps of return…

You could very well be assuming the value of the “new” class is the same a moving the 50th %-tile to the comfort zone!

HOW CAN YOU ASSUME THAT?!

The best evidence your assumptions are wrong about a class, come from Mean Variance Optimizers…



If the results of an MVO are “Wacky”

And you obviously need to constrain it because it shows:

Everyone holding stocks (we have good data) is stupid

But should own managed futures or hedge funds (we have little data) and is therefore “enlightened”

There is probably a stupid assumption in there somewhere…

But Dave, isn’t that why optimizers have constraint inputs?

A lesson in Algebra…



The output is only as good as the input… (Capital Market Assumptions)

If you get wacky unconstrained allocations,IT MEANS YOUR INPUTS ARE WRONG!

If you have to constrain your optimizer to avoid “wacky” results, YOUR INPUTS ARE WRONG!

A lesson in Algebra… Solve this equation: 4x=4

x=1



Now, solve our simple equation but constrain x tobe < or = to .5 (just like an optimizer constraint)


A lesson in Algebra… Solve this equation: 4x=4 4x=4

x=1 If x is < or = to .5 then x =.5

OR 2=4


x=1 If x is < or = to .5 then

x =.5

OR 2=4




Now, solve our simple equation but constrain x tobe < or = to .5 (just like an optimizer constraint)



x=1 If x is < or = to .5 then x =.5

OR 2=4


x=1 If x is < or = to .5 then

x =.5

OR 2=4


ANY constrained allocation is as silly as

saying 2=4!



Finally, What About Forecasts? Mean Reversion?

Forecasts (mean reversion is just a forecast by another name) do not mix well with measuring confidence in random outcomes.

This is not to say you are unskilled at forecasting…

But, what is the confidence level measuring if it was based on a distribution created by a forecast?

Long Term Nature of Market

Worst of History

Best of History

Median 10.85%








Worst of History

Best of History

Median 10.85%

Best of history near “norm”?








Worst of History

Best of History

Median 10.85%

Best of history near “norm”?Worst of history near “norm”?

Effect of +/- 2.5%



Which mean are we reverting to?

Market Returns Ending in 2003:

5 Years, bottom 10%-tile of all 5 year periods» Raise Assumption?

10 Years, 51st %-tile of all 10 year periods» Keep the Same Assumption?

25 Years, top 16%-tile of all 25 year periods» Lower Assumption?



So, how can we be confident about our CMAs for all the asset classes???

WE CAN’T!!!

But…

The “main driver” is stocks, bonds and cash• There we have a lot of good data• We have reasonable confidence in the assumptions• And it is how we invest• Other classes with less evidence cannot by

definition do anything other than introduce more uncertainty (risk)

Isn’t Wealthcare about avoiding unnecessary risk?



How our assumptions are built…

For classes with a lot of good data (i.e. domestic stocks, bonds & cash)• Risk & Return= Average of 700+ 10 year periods• Correlations based on all historical data• Tested in engine (30,000 simulated years vs. 76 years of history)

• Extremes of simulations wider than history (based on SD)• Middle of simulated distribution near middle of historical

dataFor other assets…

• If possible, use a proxy (i.e. foreign stocks are still stocks)• Adjust for added uncertainty (i.e. currency risk for foreign,

limited data for alternative classes)• Use correlations but test with a Cholesky decomposition• Perform MVO test (i.e. adjust as needed to avoid excessive

assumed alpha but still shows some incremental value)



How our assumptions are built…

For classes with a lot of good data (i.e. domestic stocks, bonds & cash)• Risk & Return= Average of 700+ 10 year periods• Correlations based on all historical data• Tested in engine (30,000 simulated years vs. 76 years of history)

• Extremes of simulations wider than history (based on SD)• Middle of simulated distribution near middle of historical

dataFor other assets…

• If possible, use a proxy (i.e. foreign stocks are still stocks)• Adjust for added uncertainty (i.e. currency risk for foreign,

limited data for alternative classes)• Use correlations but test with a Cholesky decomposition• Perform MVO test (i.e. adjust as needed to avoid excessive

assumed alpha but still shows some incremental value)



In summary…

If we are really providing:

Confidence in exceeding goals, without undue sacrifice or unnecessary risk…

We cannot bet our clients’ future, or worse, misrepresent the confidence level based on:

» Skewed data» Lack of evidence» Hope or Prophesies… » These all contradict the premises of Wealthcare



In summary…

If we are really providing:

Confidence in exceeding goals, without undue sacrifice or unnecessary risk…

We cannot bet our clients’ future, or worse, misrepresent the confidence level based on:

» Skewed data» Lack of evidence» Hope or Prophesies… » These all contradict the premises of Wealthcare



Questions?

©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004 -2008 All rights reserved P r o v i d i n g W E A L T H C A R E ARE YOU MODELING.

Documents

r e page

copyright financeware

average mean

bell extent frequency

numbers extent frequency

frequency returns

arithmetic mean of millions

correlation of returns