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?

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

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, 2003. World Population Prospects: The 2002 Revision.

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.

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.

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.

Retirement Longevity Distribution Rate Expected Returns and Volatility Portfolio Funding Profile

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 1972. Portfolio: 50% stocks, 40% bonds, 10% cash.

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%.

Retirement Longevity Distribution Rate Expected Returns and Volatility Portfolio Funding Profile

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 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

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

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) 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%

Historical Real Returns 1993-2006 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

Risk Premium versus Cash 1993-2006 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

Risk Premium versus Bonds 1993-2006 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

Historical Volatilities 1993-2006 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

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%

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%

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%

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%

Retirement Longevity Distribution Rate Expected Returns and Volatility Portfolio Funding Profile

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

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

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)

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)

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

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?

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)

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)

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)

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