Estimating pension discount
rates
David McCarthy
Outline
•
•
•
•
•
Motivation
Valuing risky cash flows
Approach adopted
Results
Conclusions
Motivation
• Pension wealth different from other
types of wealth (e.g. financial wealth)
•
•
•
•
Liquidity
Unhedgeable risks (mortality, wages)
Taxation
Annuitisation
Motivation
• Estimating pension wealth in the context
of household portfolios
• Traditionally, discount expected benefits at
risk free rate
Motivation
• Assessing the effects of pension design
parameters on valuation of pensions
• Designing pensions that people want
• Implications of changes in pension scheme
design on desireablility of pensions and on
individual welfare
Motivation
• Public policy towards pensions
• Taxation
• Mandatory annuitisation
• Wider “scheme design” issues
• Is the fact that contributions to DC plans are
lower a problem??
Valuing risky cash flows
• Complete markets
• All sources of risk are hedgeable
• We can change probabilities assigned to
different events and discount risky cash flows
at risk-free rate
EQ[ X ]
P
1  rf
• Ensures price prevents arbitrage
Valuing risky cash flows
• Complete markets
• Not applicable to pensions
• Taxation
• Unhedgeable risks (wage risk, mortality risk, job
change risk)
• Portfolio restrictions
• Liquidity constraints
Valuing risky cash flows
• Take a pure expected value and
discount at risk free rate
E[ X ]
P
1  rf
• Ignores undiversified risks that individuals
are exposed to in cash flow
• Ignores possibilities of arbitrage (where
these exist)
Valuing risky cash flows
• Take a pure expected value and discount
at risky rate
E[ X ]
P
1  rf  
• Risk premium takes account of risks
individuals are exposed to in cash flow
Valuing risky cash flows
• Estimating risk premium
• CAPM?
• APT?
• Portfolio of replicating assets?
Risk premia and pensions
E[ X ]
P
1  rf  
What is a “price” for
pensions?
Easy to estimate for
pensions using MonteCarlo simulation or
otherwise
A price for pensions?
• Wage sacrifice of pensions
• In simple equilibrium models of labour
market, workers should sacrifice wages for
pensions
• Could be estimated empirically
• Often estimated to be negative!! (i.e. workers
with pensions earn more)
– Efficiency wages
– Unobserved variable bias
– Productivity
Empirical estimates of wage-pension tradeoff
A price for pensions?
• Assume a model of preferences and
calculate compensating variation of
pensions
• That amount of cash which would perfectly
compensate worker in utility terms for loss
of pension
Compensating variation as price
• Advantages
• Can calculate this
• Can take account of worker characteristics
• Can disaggregate risk premium into
different sources (e.g. tax, illiquidity,
annuitisation, mortality protection)
• Consistent with other work (e.g. Hall &
Murphy, 2000, Stock options; Kahl, Liu &
Longstaff, 2003, Illiquid Stock)
Compensating variation as price
• Disadvantages
• Need to assume worker preferences
• Can use canonical model
• Need to assume that workers value
pensions rationally
• Any other options?
Worker preferences (based on work for
DWP)
• Stochastic DP life-cycle model (65
periods, 4 state variables plus time)
•
•
•
•
Unhedgeable wage risk
Unhedgeable mortality shock at retirement
Unhedgeable job change risk
Access to private annuity market at
retirement
• Liquidity constraints
• Taxation
• CRRA time-separable utility
Worker Preferences
• Pre-retirement state variables
• Private wealth (£000’s)
• Current wage (logged, relative to profile)
• DB pension related to current job (propn of
salary)
• DB pensions from past jobs and (state
pension) (£000’s)
Worker Preferences
• Post-retirement state variables
• Private wealth (£000’s)
• DB and state pension (£000’s)
• Private annuity income (£000’s), included
because taxed differently
• Mortality shock
Worker preferences
• Calibrated to UK
•
•
•
•
•
•
Wage profile / shocks
Taxation
Asset returns / shocks
Mortality / shocks
Job change
Simplified state pension (no other benefits)
Model of employee preferences: asset returns
Model of employee preferences: income taxes
• Annuity capital and equity capital gains deemed to be tax free
Model of employee preferences: mortality shock
Model of employee preferences: wages
Model of employee preferences: wage risk
Model of employee preferences: job change
Final salary pension
• Pays a pension which is a constant
fraction of final wage at 65 or the date of
leaving current job, whichever occurs
first (assume no pension in next jobs)
• No tax-free lump sum or commutation of
pension
• No default risk on pension
Estimating risk premia
• Calculate compensating variation of
pension in cash terms (after tax)
• Calculate expected (after-tax) payments
from pension, conditional on worker’s
current age, wage and financial wealth
(use Monte-Carlo simulation if needed)
• Calculate IRR on pension
Pension risk premia
• Assume IRR is constant over time (not
true as risk characteristics change over
time: there is a term structure here!)
• Could alternatively present results as
ratio of CV to present value of expected
payments discounted at risk-free rate
45-year old pension discount rates
Pension discount rates
• Wealth effect
• Replacement rate effect
Disaggregating pension discount rates
• Remove one feature of pension at a
time
•
•
•
•
•
Tax
Annuitisation
Wage Link
Mortality insurance
Call balance “liquidity” (other small effects,
too)
Disaggregated pension discount rates
35 y/o, W/Y = 1, DBRep = 0.05
0.05
0.04
0.03
0.02
0.01
Risk Free
Liquidity
Mortality
Wage Link
Annuitisation
Tax
Final
0
Disaggregated pension discount rates
45 y/o, W/Y = 1, DBRep = 0.05
0.05
0.04
0.03
0.02
0.01
Risk Free
Liquidity
Mortality
Wage Link
Annuitisation
Tax
Final
0
Disaggregated pension discount rates
55 y/o, W/Y = 1, DBRep = 0.05
0.05
0.04
0.03
0.02
0.01
Risk Free
Liquidity
Mortality
Wage Link
Annuitisation
Tax
Final
0
Disaggregation: changing replacement rate
35 y/o W/Y = 1
0.025
0.02
Tax
0.015
Ann
0.01
WageLink
0.005
Mort
0
-0.005
-0.01
Liqu
0
0.1
0.2
0.3
0.4
0.5
0.6
Disaggregation: changing wealth
35 y/o, DBRepRate = 0.1
0.025
0.02
Tax
0.015
Ann
0.01
WageLink
0.005
Mort
0
-0.005 0
-0.01
Liqu
0.5
1
1.5
2
2.5
3
Implications for scheme design
• Wage risk most important feature
making final salary pensions
unattractive
• Liquidity issues next most important
• Annuitisation, taxation, protection
against mortality shocks less important
Implications for scheme design
• Less wage risk exposure will improve
pension valuation dramatically
• More liquidity (e.g. permit early
withdrawals, current Pensions Act tax
treatment) will improve pension
valuation
• Other factors more important as
workers age
Implications for wealth surveys
• Discounting pension wealth at the risk
free rate inappropriate for most
individuals
• True rate depends on preferences,
wealth, income and size of pension
• Wealth effect ‘larger’ than effect of size
of pension
Further work
• Estimate IRRs on marginal pension
benefits
• Apply to different scheme designs
• Apply estimated discount rates to
produce tables which can be used in
existing surveys of pension wealth
• Discount rates for state benefits?