5 th Annual CARISMA Conference MWB, Canada Square, Canary Wharf 2 nd February ialm. M A H Dempster & E A Medova. & Cambridge Systems Associates

Transcription

1 5 th Annual CARISMA Conference MWB, Canada Square, Canary Wharf 2 nd February 2010 Individual Asset Liability Management ialm M A H Dempster & E A Medova Centre for Financial i Research, University it of Cambridge & Cambridge Systems Associates

2 Outline Personal finance and individual id financial i planning Is reconciliation of theory and practice possible? DSP model for individual Asset Liability Management: ialm General discussion of objectives Drivers of undertaken risks and returns Optimization of cashflows and portfolio construction Illustrative household examples ialm Performance testing Comparison with MVO Behavioural testing Adjustments to 2009 crisis

3 Because we humanoid primates had to struggle with personal finance, we became human Joseph Schumpeter We do not prosper by income or happiness alone Samuel Brittan Is wealth the long-term spending that our portfolio can sustain? This definition is close to the truth, but it ignores purchasing power. Is wealth, then, the inflation-indexed real income that our assets could sustain over time? For most investors, this is probably the most useful definition of wealth Robert Arnott

4 Common Practice Financial planners have traditionally resisted the academic solutions based on theoretical models Asset allocation puzzle of Canner et al [J. Campbell, 2002] Common practice is based on the qualitative assessment of risk attitude tude by financial a advisers s Rule of thumb: equity fraction of one s portfolio equals 100 one s age Is Personal Finance an exact science? An immediate flat no. It is a domain full of ordinary common sense. Alas, common sense is not the same thing as good sense. Good sense in these esoteric puzzles is hard to come by. Paul Samuelson

5 In the search for good sense Modelling methodology came from Operations Research -- decision making over an uncertain future The ialm system is a decision support tool for long-term investors, which allows interactive use and re-solving with modified d data on some individual id preferences and data inputs Therefore, not one financial plan is generated for the household but many contingency plans reflecting subjective opinion regarding future life events Principal ideas are brought together from behavioural and classical finance and stochastic optimization theory in separate modules of the system in order to help individuals with longterm financial planning

6 ialm Implementation Dynamic, multi-stage optimization problem with stochastic data: simulated cashflows (inflows and outflows) of incomes, liabilities, investment returns, etc What-if scenario analysis Implementable decisions correspond to the root node of the scenario tree Periodic recalibration of the model parameters to market and personal data -- ability to modify inputs periodically or at times of significant changes in life

7 Stochastic Programming Techniques for ALM Generation of scenario trees Data process simulation time steps Decision time points: stages of the tree Implementable decisions at root node the most constrained and robust decision taking into account all generated alternative scenarios Large scale linear optimization i i problem wealth or consumption maximization at each decision time subject to constraints such as risk, budget, cash flow balance and so on at simulator time steps

8 Gather Individual and Market Data Overview of individual ALM Personal data Market data Econometric and Actuarial Modelling Events model Liabilities model Model returns on investment classes Scenario Tree Simulation Events Cash-out flows forecast Cash-in flows forecasts Optimization Model: Tailored Portfolios, Goals Spendings, Cashflow balances, etc Dynamic optimization model for assets-liabilities Objective: maximize goal spending Visualization of decisions Various Constraints

9 Software for Dynamic Stochastic Programming Input GUI parameters Simulation key processes Tree construction scenario tree derived processes StochGen Model GSPL problem formulation STOCHASTICS TM Solver StochOpt Derived assets and processes results Output GUI

10 ialm Financial Plan ialm provides optimum values for many decision variables of interest --spending, amount of savings, tax-efficient allocation between multiple portfolios, etc -- across time simultaneously for multiple scenarios of random processes representing markets returns, foreseen liabilities and life events Current ialm model includes 20 random processes that vary over the client s lifetime and around 200 mathematically formulated conditions (constraints) per node of the scenario tree Average desktop computer solving times are 3-15 minutes (Problem size over 3mln non-zero entries) An interactive process for analysing retirement and saving alternatives

11 Key Modelling Features Problem with random time horizon individual life spans Portfolio return and risk are driven by desirable consumption subject to existing and future liabilities Risk management of portfolio by constraining i the expected shortfall Overall objectives to provide sustainable spending over household lifetime Each individual goal utility function is defined over gains or losses with respect to three reference points : a piece-wise linear utility function

12 Prospect Theory Value Function

13 Individual Goal Utility For each individual goal the level of spending y is in the range between acceptable (s) and desirable (g) subject to existing and foreseen liabilities, i.e. minimum (h) spending. These values specify the shape of the utility function for each goal Objective to maximize goal spending: piecewise linear utility functions for goal spending with priorities u (utility) g 1 α g 1 α s h α h s g y (spending) 1

14 Overall Objective The objective is to maximize the expected present value (over all scenarios) of life time consumption, i.e. spending on goals T E 1{any alive, t} ut t= 1 1 where u = u, z + I φ xs xs τi τ ( π + π I ) t g t t t g G t xs τ Here z is excess borrowing, I is total tax payment and φ is the inflation index at t t t t Consumption refers to all elective spending on chosen goals alive d m alive C =, s, (, +, ) + ˆ t αg t φ Fg t Fg t α gt g, t φg, ty g, t g G m g g G\ G m

15 Wealth Generation ialm objectives are achieved through optimum resource allocation over a network of cashflows Together with the stream of labour and other income the income from portfolio returns provides optimal spending on goals at minimal risk Fundamental constraints of portfolio allocation subproblem Initial holding Portfolio cashflow Asset inventory balance Investment limits, position limits Portfolio drawdown etc Optimal allocation between different types of account Two types of portfolio: taxable and savings portfolios such as 401K (USA) or SIPP and ISA (UK)

16 Cashflow Constraints Net wealth x r + x r tx+ tx + a a a a Transaction costs Returns Coupons and dividends Interest on bank deposits Regular income Employer pension contributions Qualified coupons and dividends Qualified returns I C I + I z ρ r D + cash t 1 t 1 I p + I qc P o qe 401 k q 401 k + + I qd Portfolio ( ) x a P qualified contributions q+ P P + asset purchases asset sales s P Qualified account ( 0 ) asset sales x q a q 401 k+ z P q qnr+ loan repaym yment x Margin cash m mr ( + r ) borrowing ( m m ) m new margin loans ma Cash holding + ( z ) q + a P q qualified withdraw wal asset purchases Qualified portfolio q ( ) x a argin loan repayment m excess borrowing at t + C goa oal spending Excess borrowing repayment xs z t income loan repa payment incom me borrowing Goal Equity (see below) L asset loan repayment asset borrowing z xs xs z t + r (1 ) 1 Excess borrowing xs z I, t z (1 + r + r ) cash s I, t 1 t 1 I Income borrowing z I Loans secured on assets x r z I + F τ τ av r P qp q τ cash s I, t 1 r t 1 + r I + ( ) z r xs xs t 1 1 x r q tx+ q tx a a a a Interest charges on margin loans Interest on goal loans Goal consumption (non capital) Liabilities Taxation Unauthorized qualified withdrawal penalty Interest charges on secured borrowing Interest charges on income loans Interest charges on excess borrowing Transaction costs (qualified portfolio)

17 Household Data FT weekly supplement Money Family member describes their financial position and goals and asks expert financial advisers for recommendations on investment, savings and appropriate spending Quantity and quality of data provided by household may vary significantly Adviser s opinions may differ significantly Example -- Pimlott household

18

19 Model Illustration: Pimlott Household

20

21

22

23

24

25 2007

26 2009

27 2007

28 2009

29

30 Performance of ialm Testing on real profiles of UK and US investors and comparison with recommendations of financial advisors Comparison with MVO based methodology Backtesting performance over 10 years: for US model Behavioural aspects tested using ability to analyse relationship between current wealth, earnings, savings and desirable consumption

31 Visual Summary of Profile Goals Getting an Overview Cash Flows Portfolio Wealth

32 Helping households become involved in managing their investments Linking Strategic and Tactical Decisions ialm decision tool takes a long term view of individual circumstances and recommends strategic allocations in market indices This gives a dynamic view of asset management over household lifetime which requires an implementation of the current year optimal portfolio Tactical allocation exploits financial advisors knowledge at the level of individual fund characteristics adding alpha without increasing beta and use the expertise of the financial adviser Both levels must consider the legal and institutional framework Taxation Pension regulations

33 References Dempster et al. (2006). Managing guarantees. Journal of Portfolio Management Dempster et al. (2009). Risk profiling defined benefit pension schemes. Journal of Portfolio Management Medova et al. (2008). Individual asset-liability management. Quantitative Finance Dempster &Medova (2010). Asset liability management for individual households. British Actuarial Journal. To be presented to a Sessional Meeting of the Institute of Actuaries, London