Workshop on Non-Financial Defined Contribution Schemes:

1. Rate of return in the Hungarian pension system:An application of the Swedish automatic balance mechanism Workshop on Non-Financial Defined Contribution Schemes: The New Revolution for Reforming National Pension Schemes? Budapest, September 19, 2012 Róbert I. Gál(gal@tarki.hu)

2. Structure of thepresentation: Interpretation of the period rate of return in a PAYG scheme Stocks from flows The Hungarian case This presentation is based on Gál, Gergely and Medgyesi (2011) and Gál and Simonovits (2012)

3. An interpretation of the period rate of return (PRR) in a PAYG system Why is such an interpretation needed? PAYG pensions are based on past investments in contribution paying capacities.Returns of such investments can be measured. Here the PRR is the rate with which the value of individual accounts (individual eligibilities) can be raised without net pension liabilities exceeding the value of contribution asset. This definition (offering a proxy to returns in a PAYG scheme) derives annual returns from long-term sustainability: annual returns are the maximum growth of the value of eligibilities affordable under contribution constraints. In order to calculate the PRR we have to know the net pension liabilities and the contribution asset.

4. Stocks from flows The accumulating contribution asset can be assessed from current contributions and age profiles (Settergren and Mikula 2006): CA ≈ C*TD, where CA: is contribution asset, the present value of future net contribution flows C: aggregate contributions in year t TD: turnover duration, Ap – Ac(money-weighted average age of pensioners and contributors, respectively) TD is standing for the time contributions (eligibilities) spend in the pension system before they are translated into pensions. TD and ETD The relationship was first established by Willis (1988) and Lee (1994) for general wealth-accumulation under conditions of the golden rule. Bommier and Lee (2003) later generalized the theorem to a less restrictive environment.

5. Stocks from flows Annual return (period RR, PRR): changes in CA projected on net pension liabilities. It can be decomposed to changes inCAdue to the changesinETD and C. where C: current contributions, ETD: expectedturnover duration, PL: net pension liabilities, F: capital fund of the pension system; in the Hungarian case the capital accumulated in the mandatory private funds, r: the market interest rate on capital.

6. The Hungarian case Expected turnover duration, 1992-2008, years

7. The Hungarian case Contribution asset, 1992-2008

8. The Hungarian case Net pension liabilities (implicit pension debt 2), 1992-2008

9. The Hungarian case Period rate of return, 1992-2008

10. The Hungarian case Some conclusions: Not only funded schemes produce negative returns PRR is a proxy measure for returns in a PAYG scheme There are limits of the applicability/interpretation of the PRR as a return concept: • What if PL is not equal to CA in t0? • What if PL has independent changes?

11. The Hungarian case The CA/PL ratio, 1992-2008