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 www.csss.gov

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

$0

$1

$10

$100

$1,000

$10,000

1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

$1775.34

$59.70

$10.09

Large Company Stocks

Long-TermGovernment Bonds

Inflation

$17.48

T-Bills

The distribution of monthly nominal S&P 500 total returns vs. normal distribution: 1926 - 2002

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0.05

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0.42

0.44

Distribution of Monthly Nominal S&P 500 Returns

Monthly: Annual:Geometric Mean: 0.81% 10.2%Arithmetic Mean: 0.97% 12.3%Standard Deviation: 5.65 19.56

The distribution of monthly nominal long-term government bonds total returns vs. normal distribution: 1926 - 2002

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Distribution of Monthly Long Term Gov. Bonds Returns

Monthly: Annual:Geometric Mean: 0.44% 5.4%Arithmetic Mean: 0.46% 5.7%Standard Deviation: 2.21 7.65

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

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0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1925 1927 1929 1931 1933 1935 1937 1939 1941 1943 1945 1947 1949 1951 1953 1955 1957 1959 1961

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

0

5000

10000

15000

20000

25000

1925 1927 1929 1931 1933 1935 1937 1939 1941 1943 1945 1947 1949 1951 1953 1955 1957 1959 1961

monthly contributions invested at the generation's geometric mean rate of growth and monthly contributions invested at the generation's specific term structure of 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

0

5000

10000

15000

20000

25000

30000

35000

1925 1927 1928 1930 1931 1933 1934 1935 1937 1938 1940 1941 1942 1944 1945 1947 1948 1950 1951 1952 1954 1955 1957 1958 1959 1961 1962

First generation begins Dec 31, 1925 and ends Dec 31, 1965; last generation begins Dec 31, 1962 and ends Dec 31, 2002 ( 37 years x 12 months = 444 generations )

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

0

2000

4000

6000

8000

10000

12000

14000

16000

1925 1927 1929 1931 1933 1935 1936 1938 1940 1942 1944 1946 1947 1949 1951 1953 1955 1957 1958 1960 1962 1964 1966 1968 1969 1971

First generation begins Dec 31, 1925 and ends Dec 31, 1955; last generation begins Dec 31, 1972 and ends Dec 31, 2002 ( 47 years x 12 months = 564 generations )

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

Graph 6

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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

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$13,

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$13,

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$14,

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$14,

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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

Table 4. Assuming a 40-year investment horizon and a 20-year retirement period, this Table lists the probability that certain percentage of annual contribution will be sufficient to finance a percent of final pay

Percent of income contributed1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

50% 0.0% 0.0% 12.2% 24.8% 52.7% 67.3% 80.0% 93.0% 99.1% 99.8%55% 0.0% 0.0% 8.6% 16.7% 38.1% 60.1% 69.8% 85.1% 94.4% 99.3%

Percent 60% 0.0% 0.0% 6.1% 14.9% 27.3% 52.7% 66.4% 75.0% 87.8% 96.2%of final pay 65% 0.0% 0.0% 3.4% 12.4% 20.5% 40.3% 59.5% 67.6% 79.1% 91.0%

70% 0.0% 0.0% 0.7% 10.1% 16.0% 29.7% 52.7% 64.6% 71.2% 82.9%75% 0.0% 0.0% 0.0% 8.1% 14.9% 24.8% 41.9% 58.6% 67.3% 75.0%80% 0.0% 0.0% 0.0% 6.1% 12.8% 17.8% 31.5% 52.7% 64.0% 68.7%85% 0.0% 0.0% 0.0% 4.5% 11.5% 15.8% 26.1% 43.5% 57.7% 66.4%90% 0.0% 0.0% 0.0% 1.6% 9.2% 14.9% 22.3% 34.0% 52.7% 62.2%95% 0.0% 0.0% 0.0% 0.2% 7.7% 13.1% 17.3% 28.4% 44.4% 57.2%100% 0.0% 0.0% 0.0% 0.0% 6.1% 12.2% 15.5% 24.8% 36.0% 52.7%

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)

Table 5. Assuming a 30-year investment horizon and a 20-year retirement period, this Table lists the probability that certain percentage of annual contribution will be sufficient to finance a percent of final pay

Percent of income contributed1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

50% 0.0% 0.0% 0.0% 6.6% 11.7% 23.4% 42.2% 56.7% 63.7% 68.3%55% 0.0% 0.0% 0.0% 4.4% 9.8% 13.3% 30.3% 45.9% 58.3% 64.5%

Percent 60% 0.0% 0.0% 0.0% 2.0% 7.8% 11.7% 19.9% 36.7% 49.5% 59.6%of final pay 65% 0.0% 0.0% 0.0% 0.0% 5.9% 9.9% 13.1% 26.2% 40.2% 52.5%

70% 0.0% 0.0% 0.0% 0.0% 4.1% 8.2% 11.7% 17.6% 31.9% 43.8%75% 0.0% 0.0% 0.0% 0.0% 2.0% 6.6% 10.1% 12.2% 23.4% 36.7%80% 0.0% 0.0% 0.0% 0.0% 0.2% 5.1% 8.9% 11.7% 15.8% 28.4%85% 0.0% 0.0% 0.0% 0.0% 0.0% 3.9% 7.1% 10.3% 12.2% 21.5%90% 0.0% 0.0% 0.0% 0.0% 0.0% 2.0% 5.9% 9.4% 11.7% 14.7%95% 0.0% 0.0% 0.0% 0.0% 0.0% 0.5% 4.8% 7.8% 10.3% 12.2%100% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.7% 6.6% 9.6% 11.7%

40-year Investment horizon and a 20-year Retirement period (Invested

100% Long-Term Government Bonds)

Table 6. Assuming a 40-year investment horizon and a 20-year retirement period, this Table lists the probability that certain percentage of annual contribution will be sufficient to finance a percent of final pay

(Invested 100% Long-Term Government Bonds)

Percent of income contributed1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

50% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 1.8% 17.6% 24.1% 27.9%55% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 4.1% 20.3% 24.5%

Percent 60% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.5% 7.4% 21.8%of final pay 65% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 1.1% 11.3%

70% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.2%75% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.5%80% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%85% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%90% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%95% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%100% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

Table 7. Assuming a 30-year investment horizon and a 20-year retirement period, this Table lists the probability that certain percentage of annual contribution will be sufficient to finance a percent of final pay

(Invested 100% Long-Term Government Bonds)

Percent of income contributed1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

50% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.7% 13.5%55% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 1.1%

Percent 60% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%of final pay 65% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

70% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%75% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%80% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%85% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%90% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%95% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%100% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

30-year Investment horizon and a 20-year Retirement period (Invested

100% Long-Term Government Bonds)

Table 9. Assuming a 30-year investment horizon and a 20-year retirement period(Invested 50% S&P500 and Long-Term Government Bonds)

Percent of income contributed1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

50% 0.0% 0.0% 0.0% 0.0% 0.0% 7.4% 12.8% 16.8% 21.6% 23.9%55% 0.0% 0.0% 0.0% 0.0% 0.0% 1.6% 9.8% 14.7% 17.2% 22.0%

Percent 60% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 6.6% 11.2% 15.2% 17.6%of final pay 65% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.7% 8.5% 12.6% 15.6%

70% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 5.1% 10.1% 13.8%75% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.4% 7.4% 11.2%80% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 4.1% 9.2%85% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 6.7%90% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.2%95% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%100% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

Table 8. Assuming a 40-year investment horizon and a 20-year retirement period(Invested 50% S&P500 and Long-Term Government Bonds)

Percent of income contributed1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

50% 0.0% 0.0% 0.0% 3.6% 15.8% 22.1% 29.5% 34.2% 40.3% 45.5%55% 0.0% 0.0% 0.0% 0.0% 12.6% 19.4% 24.5% 30.4% 34.5% 41.4%

Percent 60% 0.0% 0.0% 0.0% 0.0% 7.4% 15.8% 21.4% 28.2% 31.1% 34.9%of final pay 65% 0.0% 0.0% 0.0% 0.0% 0.5% 13.3% 19.1% 23.0% 29.3% 32.0%

70% 0.0% 0.0% 0.0% 0.0% 0.0% 9.0% 15.8% 20.3% 25.7% 30.2%75% 0.0% 0.0% 0.0% 0.0% 0.0% 3.6% 13.3% 18.0% 22.1% 28.2%80% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 10.1% 15.8% 19.6% 23.9%85% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 6.5% 13.5% 17.8% 21.4%90% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.7% 10.8% 15.8% 19.4%95% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 7.9% 14.0% 17.6%100% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.6% 11.9% 15.8%

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.)