Corporate Sponsor: Walter Welsh UConn Goldenson Center ACLI Added Value of Incorporating Annuities in Retirement Financial Planning Corporate Sponsor: Walter Welsh Presenter: Justin Xu

Outline Part 1 Part 2 Part 3 Part 4 Abstract Motivation Methodology Modeling Results Conclusion Part 3 Next Steps Future Research Part 4

Part 1 Abstract & Motivation 01

Abstract & Motivation Business Applications Maximize withdrawal level from an investment portfolio Portfolio volatility, uncertainty of health condition, randomness of death The traditional algorithmic approach of financial planning Monte Carlo (MC) simulation (fixed ending age, extremely time consuming) Actuarial method (fixed ending age, normal approximation) Academic Research Quantile optimization is a stochastic process (risk tolerance) Customer Experience User-friendly Easy to understand

Abstract & Motivation Markov Chain Monte Carlo Spending Ruin Bequest Strategy Maximizing annual spending Controlling the probability of ruin under risk tolerance Achieving a given level of ending assets at death Allocating funds in order to achieve the optimization criteria

Pure investment strategy Abstract & Motivation B To allocate funds between investment options and annuities (SPIA) Combined investment strategy Financial Planning A To allocate funds between investment options (without annuities) Pure investment strategy

02 01 04 03 Abstract & Motivation Optimal strategy? Female (65) Average health Divorced No kids 01 02 Total assets at retirement age $ 2M Target Ruin = 5% 03 Optimal strategy? 04 Asset Class Mean SD Asset 01 2.82% 5.11% Asset 02 6.97% 18.3% 10,000 social security No pension No infusion of capital SPIA 4.32% 0%

Methodology & Modeling Part 2 Methodology & Modeling 02

Methodology & Modeling Investment portfolio Insurance products Probability P(AV < 0) E(AV | AV <= 0) CTE - Positive ending assets E(AV | AV > 0) CTE + Premature death Longevity risk Annual Spending Ruin Bequest Future Lifetime

Formulating MCMC and R Application Methodology & Modeling Combined investment strategy Objective function Max(RIN) Constraints Comb.Ruin <= Pure.Ruin Comb.CTE- <= Pure.CTE- Comb.CTE+>= Pure.CTE+ Pure investment strategy Monte Carlo simulation of yields and deaths Formulating MCMC process MaxRIN (random ending age) Formulating MCMC and R Application Target Ruin = 5% Fixed Ending Age Random death Age Num. of Iterations 1,000 1,000,000 Run time 1.11 Sec 10.60 Sec 04 03 02 01 Benchmark MaxRIN Target ruin Degree of ruin (CTE –) Bequest assets (CTE +) Comparison of comb.inve.strategy Better strategy MaxRIN ↑ Target ruin ↓ Degree of Ruin (CTE –) ↓ Bequest assets (CTE +) ↑

Methodology & Modeling Pure Investment Strategy Pre-determined allocation of assets Pure Investment Strategy Optimal allocation of assets Combined Investment Strategy Pre-determined allocation of assets Combined Investment Strategy Optimal allocation of assets Pure Pure Combined Combined Formulating MCMC process R application Objective function Max(RIN) Constraints Simulated Ruin = Target Ruin Adjusted Lagrange method Objective function Max(RIN) Constraints Comb.Ruin <= Pure.Ruin Comb.CTE- <= Pure.CTE- Comb.CTE+>= Pure.CTE+ Trial and error Future research

Part 3 Results & Conclusion 03

Results & Conclusion Allo. SPIA 0% 10% 20% 30% 40% 50% USAggBonds 74% 70% 66% 62% 58% 52% REITs 26% 34% 38% 42% 48% MaxRIN 60,516 60,677 60,696 60,727 60,713 60,580 Ruin 0.05 CTE- -262,000 -248,000 -232,000 -216,000 -192,000 -175,000 CTE+ 1,821,215 1,863,504 1,892,534 1,892,795 1,866,869 1,893,519

Results & Conclusion Combined investment strategy with annuities can improve individual’s financial situation Annual spending ↑ Probability of ruin ↓ Degree of ruin ↓ Bequest assets↑ In order to get the optimal financial planning solution, a conservative investment strategy should be moved into an aggressive investment strategy Trade-off between safety income and volatility The optimal allocation of annuities is non-trivial under a reasonable range of payout ratios Allo. SPIA 0% 30% Asset 01 74% 62% Asset 02 26% 38% MaxRIN 60,516 60,727 Ruin 0.05 CTE- -262,000 -216,000 CTE+ 1,821,215 1,892,795

Next Steps & Future Research Part 4 Next Steps & Future Research 04

Next Steps & Future Research More insurance products DIA (Deferred Income Annuity) 1 2 Whole life Term life … SPIA’s and Deferred Immediate Annuities (DIA’s) with different payout ratio 3 Algorithm improvement 4 MCMC improvement Closed form solution of the optimal allocation of assets in combined investment strategy Incorporate the impact of different health conditions on annual living needs

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