Quantitative Modelling for Decumulation Phase

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1 Zili Zhu, Thomas Sneddon, Colin O Hare, Bernard Casey Pavel Shevchenko, Xiaolin Luo, Chenming Bao, Peter Toscas Quantitative Modelling for Decumulation Phase 5/August/2014 workshop, CSIRO-Monash Super Cluster

2 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. Analysis reports on data provided by ATO and DSS/DHS

3 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. 5. To produce pricing software for annuity products with GMDB and new features.

4 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.

5 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.

6 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. Another workshop for stakeholders to have input.

7 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 probability and fund entry/exit behaviour

8 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)

9 RECAP: Predicting retirement fund for super contribution rates: 9%, 12%, 15% 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 Average fund length (yrs) Std deviation of fund length (yrs) Starting Age Starting Salary (grows with wage inflation) $54,425 $54,425 $54,425 Contribution rate 9.00% 12.00% 15.00% Starting annual expense $42, Asset Allocation Australian Equities 35.00% International Equities 25.00% Domestic Bonds 12.00% International Bonds 8.00% Cash 20.00% Average fund length Std deviation of fund length Starting Age 25 Starting Salary $54,425 Contribution rate 9.00%

10 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 % paths with positive balances 100% 98.67% 69.17% 34.77% 17.52% 9.30% 5.64% 3.63% 2.56% $5,000, $4,500, $4,000, $3,500, $3,000, $2,500, Series1 Series2 Series3 Series4 Series5 Series6 Series7 Series8 $2,000, $1,500, $1,000, $500, $ Series9 Series10 Series11 Series12 Series13 Series14 Series paths for super fund balance across time

11 Example: combining death model with SUPA projection to show super exhausted before death for a 25-year old

12 APRA super account balances as returns from ATO Data (by age) CSIRO Mathematical & Information Sciences

13 SMSF account balances as returns from ATO Data (by age) CSIRO Mathematical & Information Sciences

14 Optimal Decisions For Better Retirement CPI Domestic Equity Idx Int Equity Idx 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 80.00% 60.00% 40.00% 20.00% 0.00% Domestic Equity Accumulated % of withdraw Int Equity

15 Possible Inclusion of: Life cycle utility modelling 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. Impact on retirees reactions to changes in pension policy Forecast future costs of the Age Pension in Australia Reproduced from J. Ding (2013)

16 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. Fixed withdrawals Fair Fees (bp) Optimal withdrawals (10% penalty) Optimal withdrawals (5% penalty) Minimum Guarantee Withdrawal Rate (%) Quarterly Payment (bp) Combined GMWB and GMDB Buying separate life insurance Minimum Guarantee Withdrawal Rate (%)

18 Example: Assuming a GMWB with 7% guarantee rate. Insurance fee (bp = basis point) Jackson National 35 b.p. Jefferson National. 35 b.p. Pacific Life 40 b.p. Sun Life (U.S.). 40 b.p. Hartford Life 50 b.p. American Skandia 35b.p. Travellers 40 b.p. 53.3bp for static withdraw case, and 97.1bp for dynamic (optimal) withdraw with 10% penalty.

19 RECAP: Impact from Specific Health Causes on Portfolio Values Calculating VaR due to different death causes (e.g. cancer) for life insurance and annuity portfolios. Estimation and uncertainty modelling of life tables and death forecasts as well as their distributions.

20 Summary Prototype SUPA model is implemented, prototype annuity pricing software is also completed for GMWB & GMDB. We can predict the probability of retirement fund outlasting individuals retirement period. Preliminary analysis is being performed on ATO data. Optimal Decisions for Better Retirement: analytics for progressively moving from equity investments into annuity type products during decumulation phase.

Risk Analytics, Real Options and Optimal Decisions

Risk Analytics, Real Options and Optimal Decisions Zili Zhu, Thomas Sneddon, Colin O Hare, Xiaolin Luo, Pavel Shevchenko, Chenming Bao, Alec Stephenson, Peter Toscas Quantitative Modelling for Decumulation Phase Decumulation Phase: Four Projects 1. ATO