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Which is the Optimal Portfolio in Retirement?
Van Harlow
19 May 2006
Not for sale in the U.S. or to U.S. persons.
NOT GOVENMENT INSURED  MAY LOSE VALUE  NO BANK GUARANTEE
FOR DUE DILIGENCE ATTENDEES
Retirement
Which is the optimal portfolio in retirement?
or
Given my current assets and retirement expenses,
which portfolio provides me with a reasonable
probability of funding my retirement years?
For Due Diligence purposes only. Not for distribution to the public in any form.
2
Retirement
Given my current assets and retirement expenses,
which portfolio provides me with a reasonable
probability of funding my retirement years?
The answer depends on:
• Longevity
• Distribution Rate
• Expected Returns
and Volatility
• Portfolio Funding Profile
For Due Diligence purposes only. Not for distribution to the public in any form.
3
Longevity
Life Expectancy at Birth for Selected Countries:
Circa 1950
Circa 1998
Male
Female
Male
Female
Chile*
52.9
56.8
71.0
78.0
Argentina
60.4
65.1
70.9
78.3
Brazil
49.3
52.8
59.4
69.6
Mexico
49.2
52.4
68.6
74.8
Venezuela
53.8
56.6
69.7
75.9
United States
66.0
71.7
72.9
79.6
Source: U.S. Census Bureau, International Programs Center, International Database, Gender and Aging: Mortality and Health, 1B/98-2.
*Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, 2003. World Population Prospects: The 2002 Revision.
For Due Diligence purposes only. Not for distribution to the public in any form.
4
Longevity
Life Expectancy at Birth for Selected Countries:
Males 1950 and 1988
90
80
70
60
50
Male 1950
Male 1998
40
30
20
10
y
Hu
ng
ar
Re
pu
bl
ic
ar
k
Cz
ec
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De
nm
Sp
ai
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a
an
y
G
er
m
Au
st
ri
Be
lg
iu
m
Ki
Fr
an
ce
ng
do
m
ly
No
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ay
G
re
ec
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Sw
ed
en
Ita
te
d
Un
i
Un
i
te
d
St
at
es
0
Source: U.S. Census Bureau, International Programs Center, International Database, Gender and Aging: Mortality and Health, 1B/98-2.
For Due Diligence purposes only. Not for distribution to the public in any form.
5
Longevity
Life Expectancy at Birth for Selected Countries:
Females 1950 and 1988
90
80
70
60
50
Female 1950
Female 1998
40
30
20
10
y
Hu
ng
ar
Re
pu
bl
ic
ar
k
Cz
ec
h
De
nm
Sp
ai
n
an
y
G
er
m
a
Au
st
ri
Be
lg
iu
m
Ki
Fr
an
ce
ng
do
m
ly
No
rw
ay
G
re
ec
e
Sw
ed
en
Ita
te
d
Un
i
Un
i
te
d
St
at
es
0
Source: U.S. Census Bureau, International Programs Center, International Database, Gender and Aging: Mortality and Health, 1B/98-2.
For Due Diligence purposes only. Not for distribution to the public in any form.
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Longevity
Life Spans
MALE
AGE 65
85
Age
92
88
Age
90
94
Age
85
92
100
25% chance
of living to 94
50% chance
of living to 88
COUPLES
(Both
AGE 65)
100
25% chance
of living to 92
50% chance
of living to 85
FEMALE
AGE 65
95
95
At least one person
has a 50% chance
of living to 92
97
At least one person
has a 25% chance
of living to 92
Source: Annuity 2000 Morality Table. Figures assume you are in good health.
For Due Diligence purposes only. Not for distribution to the public in any form.
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Retirement
 Longevity
 Distribution Rate
 Expected Returns and Volatility
 Portfolio Funding Profile
For Due Diligence purposes only. Not for distribution to the public in any form.
8
Distribution Rate
$1,000,000
$900,000
$800,000
$700,000
9% Withdrawal Rate
$600,000
8% Withdrawal Rate
$500,000
7% Withdrawal Rate
$400,000
6% Withdrawal Rate
5% Withdrawal Rate
$300,000
4% Withdrawal Rate
$200,000
$100,000
COUPLES
(Both Age 65)
Age
70
75
Probability that at least one
will be alive:
80
2002
1999
1997
1994
1992
1989
1987
1984
1982
1979
1977
1974
1972
$-
85
90
95
83%
63%
35%
Hypothetical value of assets held in a taxable account of $500,000 invested at year-end 1972. Portfolio: 50% stocks, 40% bonds, 10% cash.
For Due Diligence purposes only. Not for distribution to the public in any form.
9
Distribution Rate
Number of years a portfolio can last in distribution
10%
9%
8%
7%
6%
5%
4%
Years
0
10
20
30
40
50
*Hypothetical portfolio of assets held in a taxable account consists of 50% bonds and 50% stocks, assumes average annual return of 8.7%.
For Due Diligence purposes only. Not for distribution to the public in any form.
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Retirement
 Longevity
 Distribution Rate
 Expected Returns and Volatility
 Portfolio Funding Profile
For Due Diligence purposes only. Not for distribution to the public in any form.
11
Expected Returns
 Long-term view of historical returns provides the
best estimates for risks and correlations
 A risk premium approach is best for estimating
asset class returns since it provides a long-term
perspective of return expectations consistent with
the investment horizon of retirement portfolios
For Due Diligence purposes only. Not for distribution to the public in any form.
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Expected Returns
Risk Premium
• The risk premium approach to estimating
expected returns identifies the market’s
required return premium for accepting
asset class risk and adds that to the riskfree return (real risk-free return plus
inflation)
Rt = (1 + Inft) (1 + RRft) (1 + RPt) – 1
where Inft = inflation rate
RRft = real risk free rate
RPt = risk premium
For Due Diligence purposes only. Not for distribution to the public in any form.
RPt
Risk
Premium
RRft
Real riskfree return
Inft
Inflation
13
Expected Returns
Estimating the Risk Premium
 Historical
 Fundamental
 Economic
 Surveys
For Due Diligence purposes only. Not for distribution to the public in any form.
14
Other Approaches to Estimating the Risk
Premium
Literature Review
•
•
•
•
US Equity
Historical evidence
Risk Premium Estimates
– Ibbotson Associates (US Markets, 2004)
8.0%
– Jorian and Guetzmann (Journal of Finance, 1999)
4.3%
– Siegel (Financial Analysts Journal, 1992)
0.6% - 5.9%
– Dimson, Marsh and Stanton (Business Strategy Review, 2000)
5.8%
Fundamental Estimates
⁃ Fama and French (University of Chicago, 2000)
⁃ Ibbotson and Chen (Financial Analysts Journal, 2003)
⁃ Claus and Thomas (Journal of Finance, 2001)
⁃ Arnott and Bernstein (Financial Analysts Journal, 2002)
Economic Estimates
⁃ Mehra and Prescott (Journal of Monetary Economics, 1985)
Surveys
⁃ Welch (Journal of Business, 2000)
⁃ Graham and Harvey (Duke University, 2001)
For Due Diligence purposes only. Not for distribution to the public in any form.
2.55% - 4.32%
4.0%
3.0%
0% - 2.4%
<1.0%
4.0%
3.9% - 4.7%
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Historical Real Returns
1993-2006
25%
Equities
Bonds
20%
Annualized Volatility
15%
10%
5%
0%
-5%
Source: Global Financial Data
For Due Diligence purposes only. Not for distribution to the public in any form.
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Risk Premium versus Cash
1993-2006
20%
Equities-Cash
Bonds-Cash
Annualized Risk Premium, %
15%
10%
7.17%
5%
3.07%
0%
-5%
For Due Diligence purposes only. Not for distribution to the public in any form.
17
Risk Premium versus Bonds
1993-2006
15%
Annualized Risk Premium, %
10%
5%
4.21%
0%
-5%
For Due Diligence purposes only. Not for distribution to the public in any form.
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Historical Volatilities
1993-2006
45%
Equities
Bonds
40%
35%
Annualized Volatility
30%
25%
20%
15%
10%
5%
0%
For Due Diligence purposes only. Not for distribution to the public in any form.
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Risk and Return Assumptions
Asset Class Assumptions
Asset Class
Domestic
Stocks
Developed
Market
Emerging
Market
Domestic
Bonds
Domestic
Short-Term
Risk Premium
Risk-Free
Return
Expected Nominal
Return
Expected Real
Return
Volatility
(1-93 - 2/06)
5.00%
6.15%
11.15%
7.64%
20.90%
4.00%
6.15%
10.15%
6.68%
12.68%
5.00%
6.15%
11.15%
7.64%
20.38%
0.54%
6.15%
6.69%
3.32%
4.74%
0.00%
0.00%
4.42%
1.12%
0.53%
Inflation
3.26%
Note: 10-year CLP bond yield is 6.15%
10-year UF bond yield is 2.85%
For Due Diligence purposes only. Not for distribution to the public in any form.
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Risk and Return Assumptions
Correlations (Unhedged Peso) 1/93 -2/06
Domestic Bonds Domestic Stocks Domestic Cash Developed Stocks Emerging Stocks
Domestic Stocks
Developed Stocks
100.0%
35.3%
67.1%
18.3%
-0.2%
100.0%
62.3%
5.1%
6.3%
100.0%
23.5%
5.2%
100.0%
20.7%
Emerging Stocks
Domestic Bonds
Domestic Cash
For Due Diligence purposes only. Not for distribution to the public in any form.
100.0%
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Risk and Return Assumptions
Portfolio Allocations
Fund A
Fund B
Fund C
Fund D
Fund E
Stocks Domestic
18.2%
20.2%
18.4%
12.6%
0.0%
Stocks
Developed
27.2%
18.9%
11.5%
5.6%
0.0%
Stocks
Emerging Markets
33.4%
21.8%
13.0%
6.2%
0.0%
Bonds
7.8%
19.1%
34.7%
48.4%
86.0%
Cash
13.3%
20.0%
22.3%
27.2%
14.0%
For Due Diligence purposes only. Not for distribution to the public in any form.
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Risk and Return Assumptions
Portfolio Risks and Returns
Fund A
Fund B
Fund C
Fund D
Fund E
Expected
Nominal Returns
9.61%
8.73%
7.95%
7.08%
6.37%
Expected
Real Returns
6.15%
5.30%
4.55%
3.70%
3.01%
Volatility
12.14%
9.63%
7.33%
5.00%
4.08%
For Due Diligence purposes only. Not for distribution to the public in any form.
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Retirement
 Longevity
 Distribution Rate
 Expected Returns and Volatility
 Portfolio Funding Profile
For Due Diligence purposes only. Not for distribution to the public in any form.
24
Portfolio Funding Profile
$10,000,000
Portfolio in Distribution
Fund C with Constant Real Peso Withdrawal (6% initial)
Total Wealth
$1,000,000
$100,000
$10,000
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Horizon
• The Profile is determined using historical simulations to understand a portfolio’s ability to
fund a retirement horizon of varying lengths and with differing degrees of confidence
For Due Diligence purposes only. Not for distribution to the public in any form.
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Portfolio Funding Profile
$10,000,000
100%
75%
Total Wealth
$1,000,000
50%
$100,000
25%
90%
50%
$10,000
0%
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Horizon
• A Funding Profile reflects the number of retirement years that a particular portfolio might be expected to
support expenses in retirement as a function of inflation-adjusted withdrawal rates
• Consistent with Fidelity’s retirement approach, the number of funding years are indicated at the 50% and
90% confidence level, reflecting portfolio longevity in average and extended down markets
For Due Diligence purposes only. Not for distribution to the public in any form.
26
Portfolio Funding Profile
The Impact of Withdrawal Rates on Portfolio Longevity in
Extended Down Markets and Average Markets
Inflation-Adjusted Withdrawal Rate
10%
Fund E
Fund D
Fund C
Fund B
Fund A
75% Mortality
50% Mortality
12%
Note: Fund E is never
optimal to hold
8%
6%
60+ years
4%
2%
0
10
Solid end points = Average Market Conditions (50% Confidence)
Transparent end points = Extended Down Markets (90% Confidence)
20
30
40
50
60
Years Survived
For Due Diligence purposes only. Not for distribution to the public in any form.
27
Portfolio Funding Profile
The Impact of Withdrawal Rates on Portfolio Longevity in
Extended Down Markets and Average Markets
8%
Fund E
Fund D
Fund C
Fund B
Fund A
Inflation-Adjusted Withdrawal Rate
7%
Note: A 5% initial inflation-adjusted
withdrawal is probably the maximum
distribution
6%
83
5%
60+ years
4%
Note: Funds B, C & D are attractive
portfolios for a range of withdrawal rates
3%
0
10
Solid end points = Average Market Conditions (50% Confidence)
Transparent end points = Extended Down Markets (90% Confidence)
20
30
40
50
60
Years Survived
For Due Diligence purposes only. Not for distribution to the public in any form.
28
Portfolio Funding Profile
Observations
 Fund E does not appear to be attractive to hold
 A 5% initial inflation-adjusted withdrawal rate is probably
the maximum distribution to fund a retirement beginning
at age 65
 Funds B, C and D are attractive portfolios for a broad
range of withdrawal rates
For Due Diligence purposes only. Not for distribution to the public in any form.
29
Portfolio Funding Profile
Sensitivity Analysis
 What if the Chilean equity risk premium is 4% instead of
5%?
 With if equity volatilities were 20% higher than assumed
in the base case?
 What if all equity risk premiums were lower than
assumed in the base case?
For Due Diligence purposes only. Not for distribution to the public in any form.
30
Portfolio Funding Profile
The Impact of Withdrawal Rates on Portfolio Longevity in
Extended Down Markets and Average Markets
12%
Fund E
Fund D
Fund C
Fund B
Fund A
4% Chilean Equity Risk Premium
Inflation-Adjusted Withdrawal Rate
10%
Note: Results similar to
base case
8%
6%
60+ years
85
4%
2%
0
10
Solid end points = Average Market Conditions (50% Confidence)
Transparent end points = Extended Down Markets (90% Confidence)
20
30
40
50
60
Years Survived
For Due Diligence purposes only. Not for distribution to the public in any form.
31
Portfolio Funding Profile
The Impact of Withdrawal Rates on Portfolio Longevity in
Extended Down Markets and Average Markets
12%
Fund E
Fund D
Fund C
Fund B
Fund A
Equity Volatilities 20% Higher than Base Case
Inflation-Adjusted Withdrawal Rate
10%
Note: Fund D is an attractive
portfolio
8%
6%
4%
67
2%
0
10
20
Solid end points = Average Market Conditions (50% Confidence)
Transparent end points = Extended Down Markets (90% Confidence)
30
40
50
60
Years Survived
For Due Diligence purposes only. Not for distribution to the public in any form.
32
Portfolio Funding Profile
The Impact of Withdrawal Rates on Portfolio Longevity in
Extended Down Markets and Average Markets
12%
Fund E
Fund D
Fund C
Fund B
Fund A
Equity Risk Premiums Lower than Base Case
Inflation-Adjusted Withdrawal Rate
10%
Note: Funds C and D are
attractive for all withdrawal rates
8%
6%
98
65
4%
2%
0
10
Solid end points = Average Market Conditions (50% Confidence)
Transparent end points = Extended Down Markets (90% Confidence)
20
30
40
50
60
Years Survived
For Due Diligence purposes only. Not for distribution to the public in any form.
33
Conclusions
Which is the Optimal Portfolio in Retirement?
 A 5% initial inflation-adjusted withdrawal rate is probably
the maximum distribution to fund a retirement beginning
at age 65
 In the scenarios examined, Fund E does not appear to
be attractive
 Funds B, C, and D have attractive funding profiles
under the base case assumptions
 In scenarios more favorable to bonds, not surprisingly,
Funds C and D have attractive profiles
For Due Diligence purposes only. Not for distribution to the public in any form.
34