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Valuation Rates and Portfolio Choice for DB

Schemes

Presented by:Craig Ansley - Director of Consulting Practice, Australasia

Frank Russell Company

New Zealand Society of Actuaries ConferenceRotorua 13-15 November 2002

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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)

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Overview

Funding using the expected return

Whose interest?

Theoretical results for idealised world

Relaxing the assumptions

Practice vs theory

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PVs with deterministic returns

Stochastic cash flow tc

Deterministic interest rate i

Present value

tt

tt vcEcE )()(

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PVs with stochastic returns

S t o c h a s t i c c a s h f l o w tc

S t o c h a s t i c r e t u r n tr i n p e r i o d t

tc a n d tr i n d e p e n d e n t

P r e s e n t v a l u e f u n c t i o n

1

1)1( t

T

T rV

P r e s e n t v a l u e

)()()( TTTT VEcEVcE

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PVs with stochastic returns

R e t u r n s 1, tr t i n d e p e n d e n t i d e n t i c a l l y d i s t r i b u t e d s e q u e n c e

M e a n Ai ( a r i t h m e t i c m e a n = s i n g l e y e a r e x p e c t e d r e t u r n )

S t a n d a r d d e v i a t i o n ( v o l a t i l i t y )

C o e f f i c i e n t o f v a r i a t i o n o f a c c u m u l a t i o n f a c t o r tr1

)1( AiCV

W r i t e

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12

CV

ii A

T h e n

ivVE TT rateat)(

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What’s the difference?

Mean Discount Factors vsDeterministic Factors vt Evaluated at the Mean Return

HorizonMean Volatility i* 1 5 10 204.00% 1.00% 3.99% 0.9616 0.8223 0.6762 0.4572

vt: 0.9615 0.8219 0.6756 0.4564

5.00% 3.00% 4.91% 0.9532 0.7867 0.6189 0.3831

0.9524 0.7835 0.6139 0.3769

6.00% 6.00% 5.66% 0.9464 0.7593 0.5765 0.3324

0.9434 0.7473 0.5584 0.3118

7.00% 10.00% 6.07% 0.9427 0.7447 0.5545 0.3075

0.9346 0.7130 0.5083 0.2584

8.00% 14.00% 6.22% 0.9415 0.7397 0.5472 0.2994

0.9259 0.6806 0.4632 0.2145

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Does it matter?

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

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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

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Idealised world

No taxes

No transactions costs

Completely accessible and liquid markets

Unlimited lending and borrowing at risk free rate

Rational investors

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Theoretical results for idealised world

Asset allocation strategy irrelevant

Benefits and contributions must be valued at risk free rate

Assets must be valued at market

Miller & Modigliani argument:

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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

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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.

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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.

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No company access to surplus

Value liabilities unchanged

Value of assets reduced by value of option

Risk should be reduced to minimise value of option

If the company cannot recover surplus in the fund,it is granting an option to the employees.

Invest in risk free asset

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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

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Differential Tax Rates(Unrestricted company access to surplus)

After-tax return on market RM

After-tax return on risk-free asset RF

)][(][ FMFC RRERRE

CC

PP R

t

tR

1

1

)][(*1

][ FMFC

PCFP RRER

t

ttRRE

Risk-freeincremental

return

Systematicrisk

irrelevant

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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%

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Example

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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

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Why Not Invest 100% in Equities?

Convex tax schedule

Cost of credit increases to cover option against creditors

Agency risk

Bankruptcy costs

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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