1
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
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
Stochastic cash flow tc
Deterministic interest rate i
Present value
tt
tt vcEcE )()(
5
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
6
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
11
12
CV
ii A
T h e n
ivVE TT rateat)(
7
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
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
Asset allocation strategy irrelevant
Benefits and contributions must be valued at risk free rate
Assets must be valued at market
Miller & Modigliani argument:
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
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
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
)][(][ FMFC RRERRE
CC
PP R
t
tR
1
1
)][(*1
][ FMFC
PCFP RRER
t
ttRRE
Risk-freeincremental
return
Systematicrisk
irrelevant
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
Top Related