Risk Analytics, Real Options and Optimal Decisions

Transcription

1 Zili Zhu, Thomas Sneddon, Colin O Hare, Xiaolin Luo, Pavel Shevchenko, Chenming Bao, Alec Stephenson, Peter Toscas Quantitative Modelling for Decumulation Phase

2 Decumulation Phase: Four Projects 1. ATO Data Analysis on SMSF and APRA Fund Holder Behaviour 2. Simulation of Uncertainty for Pension Analysis (SUPA): forecasting ruin years 3. Pricing Algorithm for New Guaranteed Investment Products: GMWB and GMDB 4. Optimal Decisions for Better Retirement: Dynamic Portfolio Analytics for Superannuation Life-Cycle.

3 1. ATO data analysis o 150,000 taxpayers o Data points: age, gender, SMSF account balance, SMSF contributions, SMSFearnings earnings, SMSFwithdrawals, APRAaccountbalance balance, APRA contributions o Capacity to investigate withdrawal rates, personal (non mandatory) contribution rates, account balance annual returns by category (gender, age, income quantile, fund type) o 10 year data from 2004 to 2014 o years of age o 27% SMSF only, 39% APRA only, and 34% both SMSF&APRA 440K, 48K SMSF Data APRA Data Balances F requency ^ F requency D o llars 10^3 10^4 10^ SMSF APRA

4 1. The median average values of super funds Super fund performances when member contributions are also counted: Performance rate per year: Balance changes with age: Average Logdiff SMSF APRA g bt bt 1 Average lo SMSF APRA Calendar Year

5 1. Fund performances excluding member contribution The median average: Performance rate per year: Balance moves with age: c t b t 1 Average b t SMSF APRA c t b t 1 Average b t SMSF APRA Calendar Year

6 1. Account balances change during 2006 and 2013 SMSF Balances 2006 APRA Balances 2006 Dollars Dollars SMSF Balances 2013 APRA Balances 2013 Do ollars lars Dol

7 1. SMSF & APRA Performances SMSF APRA SMSF APRA SMSF APRA bt ct bt bt c t bt bt c t bt Average b Average b Average b SMSF APRA SMSF APRA SMSF APRA Average bt ct bt Average bt ct bt Average bt ct bt t SMSF APRA Average bt ct bt SMSF APRA Average bt ct bt

8 1. SMSF Withdraw Rates For Groups SMSF Withdrawals s SMSF Withdrawals s F requency F requency Withdrawal Proportion SMSF Withdrawals s Withdrawal Proportion SMSF Withdrawals s 75+ Frequency Frequency Withdrawal Proportion Withdrawal Proportion

9 1. SMSF withdrawals according to account balances 0% 20% 40% 60% 80% 100% Medium Balance Average Withdr rawal Proportion Average Withdrawal Proportion Very Low Balance High Balance Average Withdrawal Proportion Average Withdrawal Proportion Low Balance Very High Balance Averag ge Withdrawal Proportion Averag ge Withdrawal Proportion

10 1. The Closure Rates of SMSF & APRA Funds SMSF Closure Data (SMSF Only) APRA Closure Data (APRA Only) Proportion Proportion SMSF Closure Data (Both Only) APRA Closure Data (Both Only) Proportion Proportion

11 1. The Next Step Negotiation with DHS/DSS for more comprehensive data o o Assets andbankaccountsoffull/part accounts of full/part pensionmembers Medical expenses via Medicare Moredetailed data from ATO and address concerns ondata confidentiality.

12 2. Decumulation Phase: 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: i l any number of paths of desired time span Additional models extend SUPA: models for withdrawals, death probability and fund entry/exit behaviour

13 2. SUPA can answer questions 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 ofruin ofanentire groupfund $ needed in fund at given time (liquidity risk) % aggregate fund balance that fund should collect Optimal investment strategy (from fund mgmt POV)

14 2. Progress on SUPA since last meeting 1. Addition of capacity to have different asset allocations for pre retirement asopposed to post retirement 2. Addition of variable retirement age = can alter retirement age andimmediatelysee the effect thishas has on retirement outcomes 3. Year upon year variability of mandatory contribution rate = can alter the rate to immediately see the effect of this, can have a different rate for each year into the future rather than a set rate 4. Addition of taxation arrangements investment earnings tax and contributions tax 5. Addition of age pension income = can determine when super fund balance exhausted in presence of pension income

15 2. Front page of SUPA Model Output

16 2. Example: Impact of altered mandatory contribution rate schedule (September 2014) Assumptions: Starting annual expense $42, Asset Allocation (constant) To right Mandatory contribution rate Australian Equities International Equities 35.00% 25.00% schedule for comparison is pre- Domestic Bonds 12.00% International Bonds 8.00% September schedule vs new Cash 20.00% schedule (see below) Starting 25 Starting Salary $54,425 YEAR Pre % 10% 10.5% 11% 11.5% 12% 12% 12% 12% 12% 12% 12% New 9.5% 9.5% 9.5% 9.5% 9.5% 9.5% 9.5% 10% 10.5% 11% 11.5% 12%

17 2. Example: Impact of altered mandatory contribution tib ti rate schedule (September 2014) Statistic Old CR structure New CR structure Difference Comments: Can readily alter CR schedule to immediately see Standard deviation of fund length post- retirement impact Can also alter retirement age to immediately see impact Results align with recent literature surrounding impact of CR changes Average fund length post-retirement (years) Probability of super funds ruin before death 23.49% 26.00% +2.51% Expected number of years between ruin and death Fund balance at retirement at 65 (current $) $781, $749, $32, Fund balance at retirement at 65 (nominal $) $2,160, $2,071, $89, Fund balance at mid (current $) $87, $77, $10, Fund balance at mid (nominal $) $115, $102, $13,892.20

18 2. Next steps for SUPA Additional features: Salary inflation based upon cohort salary inflation experience (rather than wage index) Withdrawals based upon % of super fund balance (variable with age) and income replacement rate (in addition to ASFA retirement standard d level) l) Capacity to alter asset allocation on an annual basis Deliverables: 2 papers p in final draft process: o SUPA model as a new approach for retirement income assessment o Applications of the SUPA model in retirement income assessment Current version of model available for cluster stakeholders

19 3. Products with Protected Capital, Income and Death Benefit Variable annuities with guarantees (GMWB, GLWB, ) also marketed as various wealth protection/guarantee retirement products Guarantee to return the entire initial investment through cash withdrawals during contract or guarantee of income (even for market downturns when investment account depleted) Returns remaining portfolio at maturity (gain from market ktupside) Withdrawals can be fixed or flexible subject to penalty if contract rate is exceeded or contract is terminated earlier Fixed term or lifetime contract duration Death D hbenefit can be added d for extra fee but cheaper than separate life insurance Sales of Variable ibl Annuities ii in USA, Source: Milliman Q3 2014

20 3. Market for advanced products and challenges USA, Japan and UK: significant market for variable annuities (e.g. $150b in US 2013) In I July 2014, Forethought htlaunched dforeretirement tfoundation VA: GLWB with fees increase/decrease based on 10 year Treasure rate. Australia market early stage: e.g. MLC protected wealth and protected income products; AMP North Protected Retirement guarantee. Pricing sophisticated products with equity risk, interest rate risk, systematic mortality risk and human behaviour is a difficult numerical/mathematical problem especially in the case of flexible/dynamic withdrawals. Existing products are limited by numerical difficulties; e.g. industry practice is to use Monte Carlo forward simulation while correct pricing for flexible withdrawals requires backward solution for optimal control problem. Quoted academic literature computing time is hours per price in the case of flexible withdrawals. Also, over simplistic stochastic ti models dl( (e.g. lognormal lwalk) are used. Some industry approaches restrict product features, underestimate risks or overpricing. E.g. assumption of pre determined withdrawals, Normal distribution for risky asset returns, deterministic interest rate, constant volatility, mortality from simple life table (ignoring systemic mortality risk)

21 ir fee (bp) Fa 3. pricing engine for advanced retirement products Pricing combined death and minimum withdrawal guarantees with flexible withdrawals engine capability: pricing accurately and in real time; can be used to develop new wealth retirement products, portfolio risk management and hedging/trading strategies for competitive advantage Pricing different guarantee features mathematics is similar to pricing exotic options: exotic pricing ii engine Rdit Reditus for FX exotics showcase application static/fixed withdrawal optimal withdrawal (10% penalty) optimal withdrawal (5% penalty) 0 5% 7% 9% 11% 13% 15% minimum guaranteed withdrawal rate (%) Australia data: life table and interest rate curve, male 60 years old, 20% volatility t (bp) benefit payment Quarterly death GMWDB, male separate life insurance, male 0 5% 7% 9% 11% 13% 15% minimum guaranteed withdrawal rate (%)

22 3. prototype software: GMWB and GMDB

23 3. Extensions of current pricing algorithm Adding features of existing products on the market and comparing with market prices Mortality risk factor models to account for mortality systematic (undiversified) risk: model estimation and use for annuity pricing Pricing annuity type products with many underlying stochastic variables (interest rate, volatility, mortality) Hedging annuity products and portfolio management

24 4. Dynamic Portfolio Analytics for Superannuation Life Cycle Objectives: Link the empirical research findings to strategic financial a planning; Generic/flexible multi-period dynamic portfolio optimization engine: o Simulation based & data driven; o Asset/liability model free; o Provide recommendation of fund management decisions.

25 4. Portfolio Engine Design

26 4. Prototype Software: RiskLab

27 4. Example: investment in five assets o A global equity portfolio Invested in 5 equity markets: AU, US, UK, JP and EM Investment returns accounted using AU Dollar(home currency). 10 years investment period with rebalancing annually. 50bps proportional transaction cost rate charged on absolute turnover of the portfolio at every portfolio rebalancing time. Investors might have different risk preferences. o Objective: find optimal strategy to maximise the total expected utility function for the investor.

28 4. Result: multi period vs CAPM Blueline line: interpolated efficient frontier of a CAPM style investment Red line: multi period optimization

29 4. Example: Visualization of Dynamic Decisions Dynamic solution display through motion plots; Interactive for decision makers; Intuitive illustration of future investment decisions in an uncertain ti environment.

30 4. Example: hedge inflation for post retirement phase o An post retirement client: Invested in 2 equity markets: domestic & international; A dynamicwithdraw pattern subject to CPI; Some income protection products to hedge the risks, for example, an CPI linked annuity product. o Objective: find optimal strategy to maximise the total expected utility function for the investor.

31 4. Dynamic Portfolio Decisions Simulation scenarios: Optimal strategies:

32 Deliverables 1. Prototype quantitative models 2. Publications o o o o ATO Data Analysis Simulation of Uncertainty t for Pension Analysis (SUPA) New Pricing Algorithms for Innovative Guaranteed Investment Products Dynamic and Optimal Decisions in Superannuation Life-Cycle.

33 Publications White papers pp Zili Zhu and Thomas Sneddon: The impact on superannuation fund balances from the new compulsory superannuation Digital Flagship, e Publish: EP147667, 11 September Journal papers pp Thomas Sneddon, Zili Zhu and Colin O Hare (2014).Methodology of modelling retirement outcomes. Preprint. Submitted to Mathematical Population Studies: An International Journal of Mathematical Demography Xiaolin Luo, and PV P.V. Shevchenko (2014). Fast Numerical Method for Pricing of Variable Annuities with Guaranteed Minimum Withdrawal Benefit under Optimal Withdrawal Strategy. Preprint. Submitted to Risks Xiaolin Luo, and P.V. Shevchenko (2014). Valuation of Variable Annuities with Guaranteed Minimum Withdrawal and Death Benefits via Stochastic Control Optimization. Preprint. Submitted to Insurance: Mathematics and Economics. Technical reports P. Shevchenko and Xiaolin Luo (2014). Pricing Variable Annuities Under the Optimal Withdrawal Strategy using Gauss Hermite Quadrature on a Cubic Spline Interpolation. technical report EP P. Shevchenko and Xiaolin Luo (2013). Valuation of variable Annuities with Guaranteed Minimum Withdrawal Benefits via Finite Difference Method. technical report EP Thomas Sneddon, Zili Zhu and, Colin O Hare (2014). The SUPA (Simulation of Uncertainty for Pension Analysis) Model: Technical Report. technical report. Thomas Sneddon, Zili Zhu and Colin O Hare (2014). Applications of the SUPA Model: Technical Report. technical report.