Quantitative Modelling for Decumulation Phase

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Quantitative Modelling for

Decumulation Phase

Zili Zhu, Thomas Sneddon, Colin O’Hare, Bernard Casey

Pavel Shevchenko, Xiaolin Luo, Chenming Bao, Peter Toscas

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The Research Project and Its Objectives



Multi-Disciplinary Team

10 people, CSIRO Sydney, Melbourne sites, Monash University,

Warwick University.



Diverse Experience

Behavioral economist, social scientist, actuaries (FIA FIAA),

statisticians, data mining specialists, financial engineers,

Operations Researchers.



Main Deliverables

• Prototype software for partners/stakeholders.

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Retirement products in Australia: limited solutions



The needs of retired individuals:

• long-term financial security: uncertainty about expenditure, longevity.

• adequate funds for emergency expenditure: health and retirement home

cost.



Main Focus of this project:

1. To establish what individuals are currently doing in retirement with their funds: SMSF and super balances, spending pattern (from ATO/DSS/DHS data).

2. To determine the probability of ruin before death given fund balances at retirement and annual withdrawal patterns. Annual death probability is also modelled.

3. To design an optimal investment strategy for meeting retirement objectives (e.g. to maximise the fund balance at a particular age with x% probability of ruin or to

minimise the probability of fund ruin before death).

4. To understand retirees behaviour and preferences for new and innovative products, such as annuity products.

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Other Focuses of this project

1. Modelling of potential solutions to increase consumer demand for annuities (e.g. compulsory purchase of immediate or deferred lifetime annuities at a particular age) and investment strategies incorporating annuity purchases (e.g. staged purchase of annuities within a portfolio).

2. To determine the % of an individual’s salary contribution to super funds in order to limit their probability of ruin.

3. The probability of ruin of an entire super fund consisting of multiple members,

regarding expected withdrawal/contribution patterns, and expected entry/exit patterns of the fund’s members.

4. Management of liquidity risk in super funds if the component of infrastructure investment is large.

5. Optimal fund investment strategy to achieve objectives regarding probability of ruin– this question may also address the optimal fund strategy given past returns within the fund and their effect upon membership levels of the fund.

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Project Progress at a Glance

1. Establish a multi-factor cascade model for future investment

returns and retirement expenditures

• SUPA (Simulation of Uncertainty for Pension Analysis) model

is completed.

2. Pricing Model for Annuity with Optimal Withdraws and GMDB

• Prototype pricing software for annuity with GMWB & GMDB

is completed.

3. Incorporate fund holder behavior and forecast ruin years

• Lee-Carter model for mortality rate

is completed.

• Impact of individual health risk factors on mortality can be analysed.

completed

• ATO and DSS (Centrelink) Data re withdrawal behavior

in progress.

• APRA Data re fund entry/exit and liquidity risk

in progress.

4. Optimal-Decisions-For-Better-Retirement

in progress

• Use Real-option methodology to construct dynamic optimal portfolios for

retirees

in progress.

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Objectives of this workshop

1. To have in-depth feedback

• Can the project output be used directly for your organisation?

• What new activities should be pursued in this project?

2. To plan for

• SUPA model and prototype pricing software for annuity products are made

available to stakeholders.

• Prototype software for Optimal-Decisions-For-Better-Retirement is made

available.

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RECAP: Using SUPA model for simulation

The SUPA model projects long-term

economic behaviour: applies

established stochastic asset model (Wilkie model)

Output from SUPA is used for

Monte Carlo simulation: any number of

paths of desired time span

Additional models extend SUPA:

models for withdrawals, death

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RECAP: answer questions through SUPA in

decumulation phase



_{Member’s questions:}

• Probability of ruin of individual’s super (before x years or before death) • $ needed in super fund at retirement (to last for x years or until death) • % of salary that should be contributed to fund to achieve some objective • Optimal investment strategies to reach $ amount or avoid ruin

• Annuity-related purchase/investment strategies



_{Fund level questions:}

• Probability of ruin of an entire group fund • $ needed in fund at given time (liquidity risk)

• % aggregate fund balance that fund should collect • Optimal investment strategy (from fund mgmt POV)

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RECAP: Predicting retirement fund for super

contribution rates: 9%, 12%, 15%

Average fund length

(yrs) 15.0992 22.1634 28.7137 Std deviation of fund

length (yrs) 7.9704 10.8315 11.7161 Starting Age 25 25 25 Starting Salary (grows

with wage inflation) $54,425 $54,425 $54,425 Contribution rate 9.00% 12.00% 15.00%

Assumptions

:

•person beginning career at 25 •starting salary of $54,425 growing

with wage inflation.

•post-retirement withdrawal

requirement of $42,254 growing with price inflation.

•fund allocation set in accordance

with APRA average asset allocation 2009 data (bottom-right table)

Input variables:

•commencement age •starting salary

•withdrawal requirement •fund allocation

Starting annual expense $42,254.00

Asset Allocation Australian Equities 35.00% International Equities 25.00% Domestic Bonds 12.00% International Bonds 8.00% Cash 20.00%

Average fund length 24.0725

Std deviation of fund length 11.85156064

Starting Age 25

Starting Salary $54,425

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RECAP: Probability Distribution of Super Fund Balances

250 paths are shown in

the graph.

SUPA model can project:

oRuin age.

oSuper fund balance by age.

Age 65 70 75 80 85 90 95 100 105

% paths with positive balances 100% 98.67% 69.17% 34.77% 17.52% 9.30% 5.64% 3.63% 2.56%

250 paths for super fund balance across time

$0.00 $500,000.00 $1,000,000.00 $1,500,000.00 $2,000,000.00 $2,500,000.00 $3,000,000.00 $3,500,000.00 $4,000,000.00 $4,500,000.00 $5,000,000.00 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 ₁₀1 ₁₀5 ₁₀9 Series1 Series2 Series3 Series4 Series5 Series6 Series7 Series8 Series9 Series10 Series11 Series12 Series13 Series14 Series15

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Example: combining death model with SUPA projection to

show super exhausted before death for a 25-year old

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APRA super account balances as “returns”

from ATO Data (by age)

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SMSF account balances as “returns” from ATO

Data (by age)

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Optimal Decisions For Better Retirement

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 65 70 75 80 85 90 95

CPI Domestic Equity Idx Int Equity Idx

0.00% 20.00% 40.00% 60.00% 80.00% 100.00% 65 70 75 80 85 90

Domestic Equity Int Equity Accumulated % of withdraw

Left: 30 year economic scenario generated by SUPA model (each standardised to 0.15 at t=0)

oRed = Domestic equity index value

oGreen = International equity index value

oBlue = Consumer price index value

 Dynamic optimal withdrawal/investment decision for portfolio of domestic /international equities given the above scenario.

oRed = Allocation to domestic equities

oGreen = Allocation to international equities

oBlue = Accumulation of withdrawal proportion

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Possible Inclusion of: Life cycle utility modelling

Re pr oduc ed fr om J. Di ng (2 01 3)

•Impact on retirees’ reactions to changes

in pension policy

•Forecast future costs of the Age Pension

in Australia

•Reference: Paper by Jie Ding of Macquarie University

•Based on utility parameters estimated from empirical data to gauge

retirees’ preference for bequest, housing, luxury consumption.

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RECAP: Pricing Variable Annuities

Prototype pricing software has been completed

o to price Variable Annuities with Guaranteed Minimum Withdraw

Benefit (GMWB) and Guaranteed Minimum Death Benefit (GMDB)

Fast numerical evaluation of Variable Annuities

owith different guarantee features and policyholder behaviors

(passive and optimal behaviors)

Pricing model can be distributed to design new annuity

products.

10 60 110 160 210 260 310 4 6 8 10 12 14 16 Fa ir F ees (b p)

Minimum Guarantee Withdrawal Rate (%)

Fixed withdrawals

Optimal withdrawals (10% penalty) Optimal withdrawals (5% penalty)

15 20 25 30 35 40 45 50 4 6 8 10 12 14 16 Q ua rt er ly P ay m en t ( bp)