Public Pension Finance Symposium May Session 4: New Ideas for the Future The Case for Stochastic Present Values.

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1 Public Pension Finance Symposium May 2009 Session 4: New Ideas for the Future The Case for Stochastic Present Values Dimitry Mindlin

2 The Case for Stochastic Present Values Dimitry Mindlin, ASA, MAAA, PhD President May 18,

3 Risk and Risk Premium Risk premium is one of the central concepts of finance. Risk premium does not exist without risk. 2

4 Present Values in Two Camps Traditionalists : Use risk premium without risk. Financial Economists : Ignore risk premium. 3

5 Key Assumption Present Value of Pension Commitment is a A. Number B. Random Variable 4

6 Investment Return FV - Future Value (asset value in the future) PV Present Value (asset value at the present) R P Investment Return for portfolio P R P FV PV PV 5

7 Future and Present Values CONVENTIONAL INVESTOR: given investment return R P and present value PV, future value FV is calculated as FV PV R 1 P RETIREMENT INVESTOR: given investment return R P and future value FV, present value PV is calculated as PV FV R 1 P 6

8 Uncertain Return Uncertain PV PV FV R 1 P If portfolio P contains risky assets, then return R P is uncertain and present value PV is uncertain as well. 7

9 Pension Commitment Pension Commitment is a series of benefit payments to plan participants. 8

10 Present Value {B k } benefit payments (pension commitment) {R k } portfolio returns RA (Required Assets) present value of the pension commitment RA N 1 R 1 R k 1 1 B k k 9

11 Policy Portfolio Valuation Asset Class Allocation US Equities 45% International Equities 15% Bonds 40% Geometric Return 7.10% Arithmetic Return 7.55% Return St Dev 9.86% 10

12 Marked-To-Market Valuation Market Value of Assets 1,000 Marked-to-Market Liability 1,375 Ratio 73% 1,375 11

13 Asset-Liability Valuation MVA 1,000 RA Mean 1,055 RA Median 1,002 RA St Dev 321 Shortfall Probability 50% Shortfall Size 295 Shortfall St Dev

14 Shortfall Probability 13

15 The Goal of Retirement Investing I Fischer Black (1995): a plan sponsor may want to choose an investment strategy to minimize the present value of future contributions to the plan. Black, Fischer. The Plan Sponsor s Goal, Financial Analysts Journal, July-August

16 Mean-Variance Analysis Commitment-Driven Investing Mean-Variance Portfolio Optimization (H. Markowitz) Object of Analysis Required Assets (RA) Portfolio Return (R) Object Desired Low High Equation A = E X + ts X U = E X - ts X Optimization Problems X policy portfolio E X RA mean S X RA st dev t risk aversion factor Given A, maximize t Given t, minimize A X policy portfolio E X return mean S X return st dev t risk aversion factor Given U, maximize t Given t, maximize U 15

17 The Goal of Retirement Investing II Peter Bernstein (2003): the policy is to provide the investor with the highest probability of being able to pay for the groceries when the time comes. Bernstein, Peter. Which Policy Do You Mean? Economics and Portfolio Strategy, August 15,

18 Safety First Analysis Commitment-Driven Investing Safety-First (A. Roy) Object of Analysis Required Assets (RA) Portfolio Return (R) Object Desired Low High Equation p = Pr(RA < A) p = Pr(R < r) Optimization Problems A disastrous cost Given A, maximize p Given p, minimize A r disastrous return Given r, minimize p Given p, maximize r 17

19 The Time Diversification Problem One of the most fascinating unresolved problems in finance that has been debated for decades. Some classic models (P. Samuelson, R. Merton) demonstrate that rational investors should expect to have the same portfolio regardless of time horizon. Target date funds invest against the recommendations of these models. Initial applications of the concept of stochastic present values have demonstrated the rationality of evolving portfolios. 18

20 The Cost of Running a Pension Plan THE COST OF RUNNING A PENSION PLAN IS UNCERTAIN 19

Glide Path 2.0, or Why Is Paris Upside Down? Dimitry Mindlin, ASA, MAAA, Ph.D. President CDI Advisors LLC

Glide Path 2.0, or Why Is Paris Upside Down? Dimitry Mindlin, ASA, MAAA, Ph.D. President CDI Advisors LLC CDI ADVISORS LLC Dimitry Mindlin, president of CDI Advisors LLC, is an actuary and investment consultant.