A.G. MALLIARIS and MARY MALLIARIS Loyola University Chicago RISK MANAGEMENT SUMMER SCHOOL RISK AND RETURN OF INDIVIDUAL RETIREMENT ACCOUNTS June 19-28, 2006

Retirement Income Public Pension / Social Security Private Pension Personal Savings / Investments General Wealth

Key Questions How to Secure Adequate and Sustainable Public Pensions? What is the Role of Financial Markets?

Facts: Social Security in the U.S. 1935: Social Security Act - Old Age Benefits 1939:Survivor’s Benefits 1954:Disability Benefits 1965: Medicare

In U.S.A. Major Federal Outlays – % of Total Expenditures, 2003 Source: Office of Management and Budget

U.S. Social Security System A Pay – As – You – Go Pension System Versus A Fully Funded System

Prelude to a Crisis 1950: 16.5 workers for each retiree 2004: 3.31 workers for each retiree 2030: 2.17 workers for each retiree

Possible Solutions Raise Payroll tax rates –Now at 12.4% Cut Benefits Increase Retirement Age Allow for Private Retirement Accounts

Private Retirement Accounts Issues of Implementation Issues of Risks/Returns Strengthening Social Security and Creating Personal Wealth for All Americans Detailed Report to be found at

Contrast Extensive Research about long term investing and compounding Less is known about accumulations of monthly contributions

Wealth Indices of Investments in the U.S. Capital Markets Graph 1. The Long Run Perspective (Dec 31, 1925 to Dec 31, 2002) of Wealth Indices of Investments in the U.S. Capital Markets: A $1 Invested in Large Company Stocks; Long-Term Bonds, T-Bills, and Inflation Rate. Logarithmic Scale. Source: Ibbotson Associates SBBI 2003 Yearbook Graph 1

Distribution of Monthly Nominal S&P 500 Returns

Distribution of Monthly Long Term Gov. Bonds Returns

Evaluation Phenomenal results of a $1 investment due to compounding These results are not immediately relevant for private retirement accounts Two key reasons: Monthly contributions vs lump sum and uneven compounding

Our Goal Use Ibbotson monthly data Perform calculations with actual data instead of sample averages Evaluate the merit of individual retirement accounts

Methodology Consider a representative individual saving for his/her Retirement Choose an Investment Horizon of 20, 30, 40 years Choose Bonds and/or Stocks Use monthly data from 1926 to 2002

Purpose Compute accumulations for a representative retiree Judge the sufficiency of these accumulations

Average Annual Returns for 40- year Investment Horizon S&P 500 Returns Time Series of Average Annual Returns for a 40 year investment horizon beginning with Jan 1, 1926 to Dec 31, 1955; Feb 1, 1926 to Jan 31, 1956 and continuing to Jan 1, 1963 to Dec 31, 2002 Graph 3

Key Observation 40-year average returns are not very stable 30 or 20-year average returns are more volatile Contrast calculations based on 40-year average returns vs on the actual term structure of monthly returns

$1 monthly contributions over a 40-year investment horizon S&P 500 Returns Accumulated wealth of $1 monthly contributions over a 40-year investment horizon per generation (a total of 444 generations) computed two ways Graph 4

Partial Observation Accumulations based on generation averages often more volatile Use of actual term structure of monthly returns is more accurate

$1 monthly Contribution 40 years (3% Inflation and 2% Productivity Adjusted) S&P 500 Returns Accumulation of $1 monthly Contribution (3% Inflation and 2% Productivity Adjusted) for 40 years earning S&P 500 nominal return Graph 5

$1 monthly Contribution 30 years (3% Inflation and 2% Productivity Adjusted) S&P 500 Returns Accumulation of $1 monthly Contribution (3% Inflation and 2% Productivity Adjusted) for 30 years earning S&P 500 nominal return Graph 6

Distribution of $1 monthly Contribution (3% Inflation and 2% Productivity Adjusted) for 40 years earning S&P 500 nominal return Accumulations of $1 monthly Contribution for 40 years (3% Inflation and 2% Productivity Adjusted) Graph 7

Graph 8 Distribution of $1 monthly Contribution (3% Inflation and 2% Productivity Adjusted) for 30 years earning S&P 500 nominal return Distribution of $1 monthly Contribution (3% Inflation and 2% Productivity Adjusted) for 30 years S&P 500 Returns

Remarks Accumulations are generation dependent Accumulations are not normally distributed If contributions increase, old compound but are small and recent are large but have little time to compound Term structure of returns is critical

Median Incomes Introduce median incomes Choose a 20-year retirement horizon Evaluate accumulations

40-year Investment Horizon and 20-year Retirement period (Invested 100% in S&P 500)

30-year Investment Horizon and 20-year Retirement period (Invested 100% in S&P 500)

40-year Investment horizon and a 20-year Retirement period (Invested 100% Long-Term Government Bonds)

30-year Investment horizon and a 20-year Retirement period (Invested 100% Long-Term Government Bonds)

Probability that certain percentage of annual contribution will be sufficient to finance a percent of final pay

CONCLUSIONS Results presented in investment books need to be modified for individual retirement accounts Accumulations are unstable Accumulations are dependent on the term structure of returns Cannot use generation averages Compounding is constrained

CONCLUSIONS (Contd.) Remains true that stocks outperform bonds High inflation and/or productivity affect the accumulation/contribution ratio Going beyond the S&P 500 returns Investment/retirement horizons Fees and account management Shifting Risks

 Individual Retirement Accounts are an Important new innovation but we need to Moderate out expectations ! CONCLUSIONS (Contd.)