Transcript Capital Market Assumptions

ARE YOU MODELING WHAT YOU
INTENDED?
Presented by:
David B. Loeper, CIMA®, CIMC®
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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
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PAGE 2
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
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PAGE 3
Statisticians draw these distributions as a bell curve
(Log normal distributions have a slightly longer tail at one end)
Mean
Frequency
Extent
Standard Deviation
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PAGE 4
Statisticians draw these distributions as a bell curve
The bell curve can define AN ASSET CLASS
Low Mean & Risk
Low
Risk
Asset
Class
High Risk
Asset Class
High Mean & Risk
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PAGE 5
Statisticians draw these distributions as a bell curve
The bell curve can define AN ASSET CLASS
Or A PORTFOLIO when two or more classes are combined
(based on the correlation between the two) Low Mean
More Efficient
Portfolio
Mean
Degree of Covariance
Low
Risk
Asset
Class
High Risk
Asset Class
High Mean
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PAGE 6
Imagine the “bell” flipped over and filled with a million
numbers
-28
-45
4 8 12 14 26 41 48 61
-21 -5
-38
38 52
11 18
-22 -9 4 7
27 45
13
-11 -1 5 10 12 16 26 35
-3 2
9 11 13 19 28
24
Mean
1 8
18
12
14
7 9
10 11
Frequency
Extent
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PAGE 7
Imagine the “bell” flipped over and filled with a million
numbers
The CMAs define the population of numbers in the “bell”
-28
-45
4 8 12 14 26 41 48 61
-21 -5
-38
38 52
11 18
-22 -9 4 7
27 45
13
-11 -1 5 10 12 16 26 35
-3 2
9 11 13 19 28
24
Mean
1 8
18
12
14
7 9
10 11
Frequency
Extent
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PAGE 8
The CMAs define the population of numbers in the “bell”
If we stirred them, blind folded you, & asked you to pick
A SMALL percentage of the numbers
What’s your chance of picking?….
-28
-45
4 8 12 14 26 41 48 61
-21 -5
-38
38 52
11 18
-22 -9 4 7
27 45
13
-11 -1 5 10 12 16 26 35
-3 2
Just
these?
9 11 13 19 28
24
Mean
1 8
18
12
14
7 9
10 11
Frequency
Extent
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PAGE 9
The CMAs define the population of numbers in the “bell”
If we stirred them, blind folded you, & asked you to pick
A SMALL percentage of the numbers
What’s your chance of picking?….
-28
-45
4 8 12 14 26 41 48 61
-21 -5
-38
38 52
11 18
-22 -9 4 7
27 45
13
-11 -1 5 10 12 16 26 35
-3 2
Just
these?
9 11 13 19 28
24
Mean
1 8
18
12
14
7 9
10 11
Or,
Just
these?
Frequency
Extent
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PAGE 10
The CMAs define the population of numbers in the “bell”
What’s your chance of picking?….
-28
-45
4 8 12 14 26 41 48 61
-21 -5
-38
38 52
11 18
-22 -9 4 7
27 45
13
-11 -1 5 10 12 16 26 35
-3 2
Just
these?
9 11 13 19 28
24
Mean
1 8
18
12
14
7 9
10 11
Extent
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Or,
Just
these?
Frequency
Monte Carlo
Simulates this
random
“picking”
BASED ON
THE BELL
(bowl)
DEFINED BY
THE CMAs
PAGE 11
The CMAs define the population of numbers in the “bell”
In Seeking
RATIONAL
confidence,
WITHOUT undue
-28
-45
4 8 12 14 26 41 48 61
-21 -5
-38
38 52
11 18
sacrifice, do we
-22 -9 4 7
27 45
13
-11 -1 5 10 12 16 26 35
advise clients to
-3 2 9 11 13 19 28
24
live their life
Mean
1 8
18
Or,
Just
Frequency
12
Just
14
7 9
based on
10 11
these?
these?
5%
5% Chance
REMOTE
Chance
EXTREMES
Extent
THAT NEVER
HAPPENED?
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PAGE 12
The CMAs define the population of numbers in the “bell”
In Seeking
RATIONAL
<18% Chance or 82%
confidence,
Confidence of EXCEEDING
WITHOUT undue
-28
-45
4 8 12 14 26 41 48 61
-21 -5
-38
38 52
11 18
sacrifice do we
-22 -9 4 7
27 45
13
-11 -1 5 10 12 16 26 35
advise clients to
-3 2 9 11 13 19 28
24
live their life
Mean
1 8
18
Or,
Just
Frequency
12
Just
14
7 9
based on
10 11
these?
these?
5%
5% Chance
REMOTE
Chance
EXTREMES?
Extent
Or
REASONABLE
CONFIDENCE?
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PAGE 13
The CMAs define the population of numbers in the “bell”
But, IF WE
MAKE POOR
ASSUMPTIONS
in the SHAPE of
the Bell, we could
be CREATING:
10%
<18% Chance
-28
-45
4 8 12 14 26 41 48 61
-21 -5
-38
38 52
11 18
-22 -9 4 7
27 45
13
-11 -1 5 10 12 16 26 35
-3 2
Just
these?
9 11 13 19 28
24
Mean
1 8
18
12
14
7 9
10 11
Extent
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Or,
Just
these?
Frequency
UNDUE
SACRIFICE
or
TOO MUCH
UNCERTAINTY
PAGE 14
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!!
Missing only a
Only 50% Confidence of
few returns (some
7% EXCEEDING What Had Been 82%
HIGH ones)
-28
-45
4 8 12 14 26 41 48 61
-21 -5
changes ALL of
-38
38 52
11 18
-22 -9 4 7
27 45
13
the odds
-11 -1 5 10 12 16 26 35
-3 2
9 11 13 19 28
Mean
1 8
12
14
7 9
10 11
24
18
Remote
outcome no
longer within
population
Frequency
Extent
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PAGE 15
The CMAs define the population of numbers in the “bell”
82% Confidence of DOING ABOVE AVERAGE?!
TOO MUCH UNCERTAINTY
Missing only a
13%
82% Confidence of EXCEEDING
What Had Been only 50%
-28
-45
4 8 12 14 26 41 48
-21 -5
-38
38
11 18
-22 -9 4 7
27 45
13
-11 -1 5 10 12 16 26 35
Remote
outcome no
longer within
population
-3 2
9 11 13 19 28
24
Mean
18
8
1
12
14
7 9
10 11
61
Higher
Confidence of
previously
remote Frequency
extreme
few returns (some
LOW ones)
changes ALL of
the odds
Extent
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PAGE 16
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
-45
-28
-38
-21
4
-5
-22 -9
4
-11 -1
-3
8
2
14
11
7
5
12
10 12
18
16
7
27
9
10
26
11 13 19
12
61
52
45
35
28
24
Mean
8
41 48
38
13
9
1
26
18
Frequency
14
11
Extent
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PAGE 17
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
-45
-28
-38
-21
4
-5
-22 -9
4
-11 -1
-3
8
2
14
11
7
5
12
10 12
18
16
7
27
9
10
26
11 13 19
12
61
52
45
35
28
24
Mean
8
41 48
38
13
9
1
26
18
14
11
Extent
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Frequency
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?
PAGE 18
We Can Easily Be Fooled (by randomness)
How Many Of You Think a Compound Return for Large Cap
should be 10% or less?
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PAGE 19
We Can Easily Be Fooled (by randomness)
How Many Of You Think a Compound Return for Large Cap
should be 10% or less?
Think we should be careful in using
30 Years 1974- 2003: 12.08%
a 30 year data set? ONE year
30 Years 1973-2002: 10.55%
changed compound return by
30 Years 1927-1956:
1.5%!!!!
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PAGE 20
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: 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% Compound
Our 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%
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PAGE 21
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: 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% Compound
Our 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%
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PAGE 22
RANDOMNESS Doesn’t Look Random!
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: 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% Compound
Our 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%
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PAGE 23
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”
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PAGE 24
Familiar with Growth
RANDOMNESS?
& Value Cycles?
Heads vs.Tails
Peformance vs. Large
CapReturns
Random
Relative Trailing 3 Year Returns - Growth
Value
Headsvs.vs.
Tails
15.00%
10.00%
Growth
Heads
Tails
Value
Randomness
DOES NOT
appear to be
Random!
TAILS
Value Outperforms
5.00%
0.00%
-5.00%
HEADS
Growth Outperforms
nJa 81
nJa 82
nJa 83
nJa 84
nJa 85
nJa 86
nJa 87
nJa 88
nJa 89
nJa 90
nJa 91
nJa 92
nJa 93
nJa 94
nJa 95
nJa 96
nJa 97
nJa 98
nJa 99
nJa 00
nJa 01
n02
-10.00%
24
36
48
60
72
84
96
Ja
Flip# 12
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3 Year Period
Ending
Trailing
12 Flips
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PAGE 25
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 the
goals 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
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PAGE 26
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
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PAGE 27
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?
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PAGE 28
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):
With $43k
income starting
-90% chance of exceeding $450k estate?
in 1926, they’d
-75% chance of exceeding $1.5 million estate?
have an $875K
OR…
estate
$24,000 retirement income, also 83% confidence but 2% lower
return assumption than our CMAs:
With $24k income starting
chance of exceeding $1 million?
in 1926, they’d have a
-90% chance of exceeding $1.5 million?
$2.6 million estate
Being too conservative prioritizes estate above all else!
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PAGE 29
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???
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PAGE 30
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???
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PAGE 31
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.
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PAGE 32
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.
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PAGE 33
Sample Client Confidence with 100% Large Cap as
Investment Policy:
Based upon randomizing actual historical returns from
’26-’02 1000 times
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PAGE 34
How big a difference do you think it would make if the
client were OVERWEIGHTED by 60% to Small Cap?
82%
60% Small/40% Large
Based upon randomizing actual historical returns from
’26-’02 1000 times
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PAGE 35
Shouldn’t it make a HUGE difference???
It does…so long as we are planning on coin flip odds…
82%
54%
45%
60% Small/40% Large
60% Small/40% Large
100% Large
Based upon randomizing actual historical returns from
’26-’02 1000 times
Assuming you consider 9 pts of confidence “HUGE” near the median
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PAGE 36
Measuring with a micrometer…cutting with a chain saw…
Would You Get Different Results With These Allocations?
Asset Class
#1
#2
#3
#4
Large
Large Value
Large Growth
Small
Small Value
Small Growth
40%
0%
0%
60%
0%
0%
10%
15%
15%
0%
30%
30%
0%
20%
20%
40%
10%
10%
20%
10%
10%
10%
25%
25%
SHOULD YOU?
THEY ARE ALL THE SAME!
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PAGE 37
Provided you use appropriate indices, your results would
be statistical equivalents – 10 Years Ending 2002
Would You Get Different Results With These Allocations?
Allocations:
Large
Large Value
Large Growth
Small
Small Value
Small Growth
#1
#2
#3
#4
40% 10% 0%
20%
0%
15% 20% 10%
0%
15% 20% 10%
60% 0% 40% 10%
Are we getting
0% better
30%assumptions
10% 25%by
slicing the
into more
pieces?
0%pie 30%
10%
25%
Mean
Compound
Standard Deviation
Sample Confidence
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9.46
8.22
16.59
49%
9.35
8.13
16.46
48%
9.39
8.16
16.52
48%
9.37
8.15
16.49
48%
PAGE 38
Or are we increasing our estimation error by limiting our
data set?
Since the results are statistically the
Would You Get Different
These Allocations?
sameResults
betweenWith
the allocations…
Allocation:
#1
#2
#3
#4
11 Years 2003:
Mean
Compound
Standard Deviation
Sample Confidence
10.62
9.45
16.21
64%
10.57
9.41
16.14
63%
10.63
9.46
16.20
64%
10.58
9.42
16.14
63%
10 Years 2002:
Mean
Compound
Standard Deviation
Sample Confidence
9.46
8.22
16.59
49%
9.35
8.13
16.46
48%
9.39
8.16
16.52
48%
9.37
8.15
16.49
48%
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PAGE 39
Which “Error” Reduces My OVERALL Confidence More?
Since the results are statistically the
Would You Get Different
These Allocations?
sameResults
betweenWith
the allocations…
Allocation:
25 Years 2000:
#1
#2
#3
18.13%
Sample
99%
11 YearsConfidence
2003:
11 Years 2003 Mean: 10.62 10.57 10.63 10.58
Sample Confidence
64% 63% 64%
Ignoring
10 Years 2002:
Subclasses?
Mean
9.46 9.35 9.39
Compound
8.22 8.13 8.16
Standard Deviation
16.59 16.46 16.52
Sample Confidence
49% 48% 48%
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#4
63%
9.37
8.15
16.49
48%
PAGE 40
Which “Error” Reduces My OVERALL Confidence More?
Since the results are statistically the
Would You Get Different
These Allocations?
sameResults
betweenWith
the allocations…
Allocation:
#1
#2
#3
#4
25 Year Mean 2000:
18.13%
Sample
11 YearsConfidence
2003:
11 Year 2003 Mean:
Sample Confidence
99%
Or ignoring the
of limiting
+/- 35%
10.62 10.57
10.63 effect
10.58
my sample
64% 63% 64% 63%
10 Year 2002: +/- 50%
Mean
Compound
Standard Deviation
Sample Confidence
9.46
8.22
16.59
49%
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population so I can
include SubClasses?
9.35
9.39
+/- 15%
8.13 8.16
16.46 16.52
48% 48%
9.37
8.15
16.49
48%
Ignoring Subclasses? +/- 1%
PAGE 41
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
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PAGE 42
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?!
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PAGE 43
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 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…
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PAGE 44
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…
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PAGE 45
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:
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4x=4
x=1
PAGE 46
The output is only as good as the input…
(Capital Market Assumptions)
Now, solve our simple equation but constrain x to
be < or = to .5 (just like an optimizer constraint)
If you have to constrain your optimizer to avoid “wacky” results,
YOUR INPUTS ARE WRONG!
A lesson in Algebra…
Algebra…
Solve this equation:
4x=4
x=1
OR
OR
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4x=4
If x is < or = to .5 then
xx =.5
=.5
2=4
2=4
PAGE 47
The output is only as good as the input…
(Capital Market Assumptions)
Now, solve our simple equation but constrain x to
be < or = to .5 (just like an optimizer constraint)
If you have to constrain your optimizer to avoid “wacky” results,
YOUR INPUTS ARE WRONG!
A lesson in Algebra…
Algebra…
Solve this equation:
ANY constrained
allocation is as silly as
saying 2=4!
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4x=4
x=1
OR
OR
4x=4
If x is < or = to .5 then
xx =.5
=.5
2=4
2=4
PAGE 48
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?
Worst of Median
History 10.85%
Best of
History
Long Term Nature of Market
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PAGE 49
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?
Worst of Median
History 10.85%
Best of
History
Best of history near “norm”?
Long Term Nature of Market
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PAGE 50
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?
Worst of Median
History 10.85%
Best of
History
Worst of history
near “norm”?
Effect of +/2.5%
Best of history near “norm”?
Long Term Nature of Market
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PAGE 51
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?
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PAGE 52
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?
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PAGE 53
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 data
For 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)
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PAGE 54
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 data
For 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)
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PAGE 55
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
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PAGE 56
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
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PAGE 57
Questions?
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PAGE 58