which is the optimal portfolio in retirement? for due diligence attendees van harlow 19 may 2006

Which is the Optimal Portfolio in Retirement?

FOR DUE DILIGENCE ATTENDEES

Van Harlow

19 May 2006

For Due Diligence purposes only. Not for distribution to the public in any form.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?


Retirement

The answer depends on: • Longevity

• Distribution Rate

• Expected Returnsand Volatility

• Portfolio Funding Profile

Given my current assets and retirement expenses, which portfolio provides me with a reasonable

probability of funding my retirement years?


Circa 1950 Circa 1998

Longevity

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.

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

Life Expectancy at Birth for Selected Countries:


Life Expectancy at Birth for Selected Countries:Males 1950 and 1988

0

10

20

30

40

50

60

70

80

90

United S

tate

s

Sweden

Greec

e

Norway

Italy

United K

ingdom

Franc

e

Belgium

Austri

a

Germ

any

Spain

Denmar

k

Czech

Rep

ublic

Hungar

y

Male 1950

Male 1998


Longevity


Life Expectancy at Birth for Selected Countries:Females 1950 and 1988

0

10

20

30

40

50

60

70

80

90

United S

tate

s

Sweden

Greec

e

Norway

Italy

United K

ingdom

Franc

e

Belgium

Austri

a

Germ

any

Spain

Denmar

k

Czech

Rep

ublic

Hungar

y

Female 1950

Female 1998


Longevity


COUPLES(Both

AGE 65)

FEMALEAGE 65

Age 92 95

At least one personhas a 50% chance of living to 92

MALEAGE 65

Age 88 9490 100

Age 85 92 95 100

50% chanceof living to 85




At least one personhas a 25% chance of living to 92

85 97

Life Spans

Source: Annuity 2000 Morality Table. Figures assume you are in good health.

Longevity


Retirement

Longevity

Distribution Rate

Expected Returns and Volatility

Portfolio Funding Profile


$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

19

72

19

74

19

77

19

79

19

82

19

84

19

87

19

89

19

92

19

94

19

97

19

99

20

02

Distribution Rate

9% Withdrawal Rate

8% Withdrawal Rate

7% Withdrawal Rate

6% Withdrawal Rate

5% Withdrawal Rate

COUPLES(Both Age 65)

Age 85 90

Probability that at least one will be alive:

9570 75 80

83% 63% 35%

4% Withdrawal Rate

Hypothetical value of assets held in a taxable account of $500,000 invested at year-end 1972. Portfolio: 50% stocks, 40% bonds, 10% cash.


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%.

Number of years a portfolio can last in distribution

10%

9%

8%

7%

6%

5%

4%

Years

Distribution Rate


Retirement

Longevity

Distribution Rate




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


Expected Returns

Risk Premium

RPt

RRft

Inft

Risk Premium

Real risk-free return

Inflation

• 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


Expected Returns

Historical

Fundamental

Economic

Surveys

Estimating the Risk Premium


Other Approaches to Estimating the Risk Premium

• Historical evidence– 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) 2.55% - 4.32%⁃ 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) 0% - 2.4%

• Economic Estimates⁃ Mehra and Prescott (Journal of Monetary Economics, 1985) <1.0%

• Surveys⁃ Welch (Journal of Business, 2000) 4.0%⁃ Graham and Harvey (Duke University, 2001) 3.9% - 4.7%

Literature Review

US EquityRisk Premium Estimates


Historical Real Returns

Source: Global Financial Data

1993-2006

-5%

0%

5%

10%

15%

20%

25%

Austra

liaAus

tria

Belgium

Canad

a

Denmark

Finland

France

German

yIre

land

Italy

Japa

n

Netherl

ands

New Zea

land

Norway

Portug

alSpa

in

Sweden

Switzerla

nd UKUSA

Chile

Argenti

na

Greece

Israe

l

Mexico

South

Africa

Ann

ualiz

ed V

olat

ility

Equities

Bonds


Risk Premium versus Cash

-5%

0%

5%

10%

15%

20%

Austra

liaAus

tria

Belgium

Canad

a

Denmark

Finland

France

German

yIre

land

Italy

Japa

n

Netherl

ands

New Zea

land

Norway

Portug

alSpa

in

Sweden

Switzerla

nd UKUSA

Chile

Argenti

na

Greece

Israe

l

Mexico

South

Africa

Ann

ualiz

ed R

isk

Prem

ium

, %

Equities-Cash

Bonds-Cash

7.17%

3.07%

1993-2006


Risk Premium versus Bonds

-5%

0%

5%

10%

15%

Austra

liaAus

tria

Belgium

Canad

a

Denmark

Finland

France

German

y

Irelan

dIta

lyJa

pan

Netherl

ands

New Zea

land

Norway

Portug

alSpa

in

Sweden

Switzerla

nd UKUSA

Chile

Ann

ualiz

ed R

isk

Prem

ium

, %

4.21%

1993-2006


Historical Volatilities

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Austra

liaAus

tria

Belgium

Canad

a

Denmark

Finland

France

German

yIre

land

Italy

Japa

n

Netherl

ands

New Zea

land

Norway

Portug

alSpa

in

Sweden

Switzerla

nd UKUSA

Chile

Argenti

na

Greece

Israe

l

Mexico

South

Africa

Ann

ualiz

ed V

olat

ility

EquitiesBonds

1993-2006


Asset ClassRisk Premium

Risk-Free Return

Expected Nominal Return

Expected Real Return

Volatility (1-93 - 2/06)

Domestic Stocks 5.00% 6.15% 11.15% 7.64% 20.90%Developed Market 4.00% 6.15% 10.15% 6.68% 12.68%Emerging Market 5.00% 6.15% 11.15% 7.64% 20.38%Domestic Bonds 0.54% 6.15% 6.69% 3.32% 4.74%Domestic Short-Term 0.00% 0.00% 4.42% 1.12% 0.53%

Inflation 3.26%

Asset Class Assumptions

Risk and Return Assumptions

Note: 10-year CLP bond yield is 6.15%

10-year UF bond yield is 2.85%


Correlations (Unhedged Peso) 1/93 -2/06


Domestic Stocks Developed Stocks Emerging Stocks Domestic Bonds Domestic Cash

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%


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

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%



Portfolio Risks and Returns

Fund A Fund B Fund C Fund D Fund E

Expected 9.61% 8.73%Nominal Returns

Expected 6.15% 5.30%Real Returns

Volatility 12.14% 9.63%


7.95%

4.55%

7.33%

7.08%

3.70%

5.00%

6.37%

3.01%

4.08%


Retirement

Longevity

Distribution Rate




• 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


$10,000

$100,000

$1,000,000

$10,000,000

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

Tota

l Wea

lth

Portfolio in Distribution

Fund C with Constant Real Peso Withdrawal (6% initial)



• 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

$10,000

$100,000

$1,000,000

$10,000,000

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

Tota

l Wea

lth

0%

25%

50%

75%

100%

90% 50%



Solid end points = Average Market Conditions (50% Confidence)

Transparent end points = Extended Down Markets (90% Confidence)

2%

4%

6%

8%

10%

12%

0 10 20 30 40 50 60

Years Survived

Infla

tion-

Adj

uste

d W

ithdr

awal

Rat

e

Fund EFund DFund CFund BFund A

60+ years

The Impact of Withdrawal Rates on Portfolio Longevity inExtended Down Markets and Average Markets

Note: Fund E is never optimal to hold

50%

Mo

rta

lity

75%

Mo

rta

lity



Solid end points = Average Market Conditions (50% Confidence)Transparent end points = Extended Down Markets (90% Confidence)

3%

4%

5%

6%

7%

8%

0 10 20 30 40 50 60

Years Survived

Infla

tion-

Adj

uste

d W

ithdr

awal

Rat

e


60+ years

83


Note: A 5% initial inflation-adjusted withdrawal is probably the maximum distribution

Note: Funds B, C & D are attractive portfolios for a range of withdrawal rates



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

Observations



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?

Sensitivity Analysis




2%

4%

6%

8%

10%

12%

0 10 20 30 40 50 60

Years Survived

Infla

tion-

Adj

uste

d W

ithdr

awal

Rat

e


60+ years85

4% Chilean Equity Risk Premium


Note: Results similar tobase case


2%

4%

6%

8%

10%

12%

0 10 20 30 40 50 60

Years Survived

Infla

tion-

Adj

uste

d W

ithdr

awal

Rat

e



67

Equity Volatilities 20% Higher than Base Case



Note: Fund D is an attractiveportfolio


2%

4%

6%

8%

10%

12%

0 10 20 30 40 50 60

Years Survived

Infla

tion-

Adj

uste

d W

ithdr

awal

Rat

e



6598

Equity Risk Premiums Lower than Base Case



Note: Funds C and D areattractive for all withdrawal rates


Conclusions

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

Which is the Optimal Portfolio in Retirement?

which is the optimal portfolio in retirement? for due diligence attendees van harlow 19 may 2006

Documents

diligence purposes

longevity slide

chance of living

withdrawal rate couples

retirement years

retirement expenses

longevity source

international database