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

• Ensures price prevents arbitrage

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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

• Ignores undiversified risks that individuals are exposed to in cash flow

• Ignores possibilities of arbitrage (where these exist)

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Valuing risky cash flows

• Take a pure expected value and discount at risky rate

• Risk premium takes account of risks individuals are exposed to in cash flow

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Valuing risky cash flows

• Estimating risk premium• CAPM?• APT?• Portfolio of replicating assets?

Risk premia and pensions

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Easy to estimate for pensions using Monte-Carlo simulation or otherwise

What is a “price” for pensions?

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 trade-off

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

0.01

0.02

0.03

0.04

0.05

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Disaggregated pension discount rates

45 y/o, W/Y = 1, DBRep = 0.05

0

0.01

0.02

0.03

0.04

0.05

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Disaggregated pension discount rates

55 y/o, W/Y = 1, DBRep = 0.05

0

0.01

0.02

0.03

0.04

0.05

Fin

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Disaggregation: changing replacement rate

35 y/o W/Y = 1

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 0.1 0.2 0.3 0.4 0.5 0.6

Tax

Ann

WageLink

Mort

Liqu

Disaggregation: changing wealth

35 y/o, DBRepRate = 0.1

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0 0.5 1 1.5 2 2.5 3

Tax

Ann

WageLink

Mort

Liqu

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?