Valuation Rates and Portfolio Choice for DB Schemes

1. Valuation Rates and Portfolio Choice for DB Schemes Presented by: Craig Ansley - Director of Consulting Practice, AustralasiaFrank Russell Company New Zealand Society of Actuaries ConferenceRotorua 13-15 November 2002

2. Current Practice • Investment strategy based on DB scheme as separate entity • Valuation rates of interest taken as expected return on portfolio • Fund values adjusted (upwards) from market values Can’t be justified - Exley, Mehta & Smith (1997)

3. Overview • Funding using the expected return • Whose interest? • Theoretical results for idealised world • Relaxing the assumptions • Practice vs theory

4. PVs with deterministic returns

5. PVs with stochastic returns

6. PVs with stochastic returns

7. What’s the difference?

8. Does it matter? Even if risk doesn’t matter, valuing at the expected portfolio return leads to systematic underfunding over the long term.

9. Whose interest? • Net cost of benefits is a company liability • Member and company interests aligned on valuation and investment • Contrarian member position would require less investment risk, higher valuations

10. Idealised world • No taxes • No transactions costs • Completely accessible and liquid markets • Unlimited lending and borrowing at risk free rate • Rational investors

11. Theoretical results for idealised world Miller & Modigliani argument: • Asset allocation strategy irrelevant • Benefits and contributions must be valued at risk free rate • Assets must be valued at market

12. Relaxing the assumptions • Taxation • Quarantining assets and liabilities in a separate entity • No company access to surplus • Different tax rates for pension fund and company

13. Taxation • Benefits and contributions valued at risk free rate after tax • Assets valued at market Introducing taxation (same rate for fund and company) but leaving the other assumptions in place does not change the theoretical results.

14. Quarantining the fund • No company access to surplus • Different tax rates for pension fund and company Quarantining the fund does not matter per se; but changing the transaction rules or taxregime does matter.

15. No company access to surplus If the company cannot recover surplus in the fund,it is granting an option to the employees. • Value liabilities unchanged • Value of assets reduced by value of option • Risk should be reduced to minimise value of option  Invest in risk free asset

16. Differential Tax Rates(Unrestricted company access to surplus) Company Tax Rate tC Pension Fund Tax Rate tP Pre-tax Investment Return R Return on funds with company tax rate RC = (1 - tC) R Return on funds with pension fund tax rate RP = (1 - tP) R RC and RP perfectly correlated

17. Differential Tax Rates(Unrestricted company access to surplus) After-tax return on market RM After-tax return on risk-free asset RF Risk-freeincrementalreturn Systematicriskirrelevant

18. Example Expected return on bonds 6% Expected return on equities 9% Company tax rate 33% Pension fund tax rate on equities 7% Pension fund tax rate on bonds 33%

19. Example

20. Differential Tax RatesAND No Company Access to Surplus Investment in tax-exempt equities • Increases risk-free incremental return • Increases value of option against company Option value decreases with term to maturity

21. Why Not Invest 100% in Equities? • Convex tax schedule • Cost of credit increases to cover option against creditors • Agency risk • Bankruptcy costs

22. Summary • Increase in valuation rates justified by differential tax rates • Valuing at expected portfolio return not justified • Restricted company access to surplus is option against company • Portfolio risk limited by external costs of risk