1. Which is the Optimal Portfolio in Retirement?
Van Harlow
19 May 2006
Not for sale in the U.S. or to U.S. persons.
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FOR DUE DILIGENCE ATTENDEES

2. 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?

3. 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

4. Longevity Life Expectancy at Birth for Selected Countries: Circa 1950
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
Chile and Mexico in 20 years
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, World Population Prospects: The 2002 Revision.

5. Life Expectancy at Birth for Selected Countries: Males 1950 and 1988
Longevity
Life Expectancy at Birth for Selected Countries: Males 1950 and 1988
Source: U.S. Census Bureau, International Programs Center, International Database, Gender and Aging: Mortality and Health, 1B/98-2.

6. Life Expectancy at Birth for Selected Countries: Females 1950 and 1988
Longevity
Life Expectancy at Birth for Selected Countries: Females 1950 and 1988
Source: U.S. Census Bureau, International Programs Center, International Database, Gender and Aging: Mortality and Health, 1B/98-2.

7. Longevity Life Spans 85 92 95 100 88 94 90 100 92 97 85 95 MALE Age
25% chance
of living to 92
50% chance
of living to 85 88 94
FEMALE
AGE 65
Age 90
100
50% chance
of living to 88
25% chance
of living to 94
From 2000 mortality tables
Explain
Interesting to note that in 1940, for 65 year olds,
Male life expectancy 77
Female life expectancy 78
In 1900, for newborns,
Male life expectancy 48
Female life expectancy 51 92 97
COUPLES
(Both AGE 65)
Age 85 95
At least one person
has a 50% chance
of living to 92
At least one person
has a 25% chance
of living to 92
Source: Annuity 2000 Morality Table. Figures assume you are in good health.

8. Retirement Longevity Distribution Rate Expected Returns and Volatility
Portfolio Funding Profile

9. Distribution Rate Age 70 75 80 85 90 95 COUPLES (Both Age 65)
9% Withdrawal Rate
8% Withdrawal Rate
7% Withdrawal Rate
6% Withdrawal Rate
5% Withdrawal Rate
4% Withdrawal Rate
You and your spouse retire in 1972 with $500,000
50% stock / 50% bond portfolio
Withdrawal rates:
9%  $45,000 in first year
3% inflation  $46,350 in second year
Run out of money in 1981 (9 years)
5%  Run out of money in 22 years (age 87)
Still > 2/3 chance that at least one of your would still be alive
1/3 chance that one of your would still be alive 8 years later
Assumes no transactions costs or taxes
Age 70 75 80 85 90 95
COUPLES (Both Age 65)
Probability that at least one will be alive:
83%
63%
35%
Hypothetical value of assets held in a taxable account of $500,000 invested at year-end Portfolio: 50% stocks, 40% bonds, 10% cash.

10. Number of years a portfolio can last in distribution
Distribution Rate
Number of years a portfolio can last in distribution 10 20 30 40 50
10% 9% 8% 7% 6% 5%
Here is a different perspective on distribution rates
Monte Carlo simulations of a 50% stock /50% bond portfolio
Portfolio fails when the chance of going broke exceeds 10%
Asset allocation of 50% to 70% equity at the beginning of retirement turns out to be optimal in most cases
I will provide some intuition in a moment 4%
Years
*Hypothetical portfolio of assets held in a taxable account consists of 50% bonds and 50% stocks, assumes average annual return of 8.7%.

11. Retirement Longevity Distribution Rate Expected Returns and Volatility
Portfolio Funding Profile

12. 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

13. 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 risk- free 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
RPt
Risk Premium
RRft
Real risk-free return
Inft
Inflation

14. Estimating the Risk Premium
Expected Returns
Estimating the Risk Premium
Historical
Fundamental
Economic
Surveys

15. Other Approaches to Estimating the Risk Premium
Literature Review
US Equity Risk Premium Estimates
Historical evidence
Ibbotson Associates (US Markets, 2004) 8.0%
Jorian and Guetzmann (Journal of Finance, 1999) 4.3%
Siegel (Financial Analysts Journal, 1992) % - 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) 4.0%
Claus and Thomas (Journal of Finance, 2001) 3.0%
Arnott and Bernstein (Financial Analysts Journal, 2002) % - 2.4%
Economic Estimates
Mehra and Prescott (Journal of Monetary Economics, 1985) <1.0%
Surveys
Welch (Journal of Business, 2000) %
Graham and Harvey (Duke University, 2001) % - 4.7%

16. Historical Real Returns
25%
Equities
Bonds
20%
15%
Annualized Volatility
10% 5% 0%
-5%
Austria
Finland
France
Ireland
Italy
Australia
Belgium
Canada
Denmark
Germany
Japan
Norway
Portugal
Spain UK
USA
Sweden
Chile
Greece
Israel
Mexico
Netherlands
New Zealand
Switzerland
Argentina
South Africa
Source: Global Financial Data

17. Risk Premium versus Cash
20%
Equities-Cash
Bonds-Cash
15%
10%
Annualized Risk Premium, %
7.17% 5%
3.07% 0%
-5%
Australia
Austria
Italy
Belgium
Canada
Denmark
Finland
France
Germany
Ireland
Japan UK
Norway
Portugal
Spain
Sweden
USA
Chile
Argentina
Greece
Israel
Mexico
Netherlands
New Zealand
Switzerland
South Africa

18. Risk Premium versus Bonds
15%
10%
Annualized Risk Premium, % 5%
4.21% 0%
-5% UK
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Ireland
Italy
Japan
Norway
Portugal
Spain
Sweden
USA
Chile
Netherlands
New Zealand
Switzerland

19. Historical Volatilities
45%
Equities
Bonds
40%
35%
30%
25%
Annualized Volatility
20%
15%
10% 5% 0%
Austria
Finland
France
Ireland
Italy
Japan
Spain UK
Norway
USA
Australia
Belgium
Canada
Chile
Israel
Denmark
Germany
Portugal
Sweden
Netherlands
New Zealand
Switzerland
Argentina
Greece
Mexico
South Africa

20. Asset Class Assumptions
Risk and Return Assumptions
Asset Class Assumptions
Note: 10-year CLP bond yield is 6.15%
10-year UF bond yield is 2.85%

21. Correlations (Unhedged Peso) 1/93 -2/06
Risk and Return Assumptions
Correlations (Unhedged Peso) 1/93 -2/06
Domestic Bonds
Domestic Stocks
Domestic Cash
Developed Stocks
Emerging Stocks
Domestic Stocks
100.0%
35.3%
67.1%
18.3%
-0.2%
Developed Stocks
100.0%
62.3%
5.1%
6.3%
Emerging Stocks
100.0%
23.5%
5.2%
Domestic Bonds
100.0%
20.7%
Domestic Cash
100.0%

22. Portfolio Allocations
Risk and Return Assumptions
Portfolio Allocations
Fund A
Fund B
Fund C
Fund D
Fund E
Stocks -
18.2%
20.2%
18.4%
12.6%
0.0%
Domestic
Stocks
27.2%
18.9%
11.5%
5.6%
0.0%
Developed
Efficient Frontier
Stocks
33.4%
21.8%
13.0%
6.2%
0.0%
Emerging Markets
Bonds
7.8%
19.1%
34.7%
48.4%
86.0%
Cash
13.3%
20.0%
22.3%
27.2%
14.0%

23. Portfolio Risks and Returns
Risk and Return Assumptions
Portfolio Risks and Returns
Fund A
Fund B
Fund C
Fund D
Fund E
Expected
9.61%
8.73%
7.95%
7.08%
6.37%
Nominal Returns
Expected
6.15%
5.30%
4.55%
3.70%
3.01%
Real Returns
Efficient Frontier
Volatility
12.14%
9.63%
7.33%
5.00%
4.08%

24. Retirement Longevity Distribution Rate Expected Returns and Volatility
Portfolio Funding Profile

25. Portfolio Funding Profile
Portfolio in Distribution Fund C with Constant Real Peso Withdrawal (6% initial)
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

26. Portfolio Funding Profile
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

27. Portfolio Funding Profile
The Impact of Withdrawal Rates on Portfolio Longevity in Extended Down Markets and Average Markets 2% 4% 6% 8%
10%
12% 10 20 30 40 50 60
Years Survived
Inflation-Adjusted Withdrawal Rate
Fund E
Fund D
Fund C
Fund B
Fund A
60+ years
50% Mortality
75% Mortality
Note: Fund E is never optimal to hold
Solid end points = Average Market Conditions (50% Confidence)
Transparent end points = Extended Down Markets (90% Confidence)

28. 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 7%
Fund A
Note: A 5% initial inflation-adjusted withdrawal is probably the maximum distribution 6%
Inflation-Adjusted Withdrawal Rate 83 5%
60+ years 4%
Note: Funds B, C & D are attractive portfolios for a range of withdrawal rates 3% 10 20 30 40 50 60
Solid end points = Average Market Conditions (50% Confidence)
Years Survived
Transparent end points = Extended Down Markets (90% Confidence)

29. 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

30. 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?

31. Portfolio Funding Profile
The Impact of Withdrawal Rates on Portfolio Longevity in Extended Down Markets and Average Markets 2% 4% 6% 8%
10%
12% 10 20 30 40 50 60
Years Survived
Inflation-Adjusted Withdrawal Rate
Fund E
Fund D
Fund C
Fund B
Fund A
60+ years 85
4% Chilean Equity Risk Premium
Note: Results similar to base case
Solid end points = Average Market Conditions (50% Confidence)
Transparent end points = Extended Down Markets (90% Confidence)

32. Portfolio Funding Profile
The Impact of Withdrawal Rates on Portfolio Longevity in Extended Down Markets and Average Markets
12%
Equity Volatilities 20% Higher than Base Case
Fund E
Fund D
Fund C
Fund B
Fund A
10%
Note: Fund D is an attractive portfolio 8%
Inflation-Adjusted Withdrawal Rate 6% 4% 67 2% 10 20 30 40 50 60
Solid end points = Average Market Conditions (50% Confidence)
Years Survived
Transparent end points = Extended Down Markets (90% Confidence)

33. Portfolio Funding Profile
The Impact of Withdrawal Rates on Portfolio Longevity in Extended Down Markets and Average Markets
12%
Fund E
Equity Risk Premiums Lower than Base Case
Fund D
Fund C
Fund B
Fund A
10%
Note: Funds C and D are attractive for all withdrawal rates 8%
Inflation-Adjusted Withdrawal Rate 6% 98 4% 65 2% 10 20 30 40 50 60
Years Survived
Solid end points = Average Market Conditions (50% Confidence)
Transparent end points = Extended Down Markets (90% Confidence)

34. Which is the Optimal Portfolio in Retirement?
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