1 / 11

Optimal Retirement Financial Planning Model

Optimal Retirement Financial Planning Model. J ustin Xu, Zhiguo Wang. September 9, 2016. Background. About 4 million people retire every year In 20 years, about 80 million people are expected to retire (By reference.com) 22.4% of seniors saved 300,000 and more (By time.com 2016)

pickett
Download Presentation

Optimal Retirement Financial Planning Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Optimal Retirement Financial Planning Model Justin Xu, Zhiguo Wang September 9, 2016

  2. Background • About 4 million people retire every year • In 20 years, about 80 million people are expected to retire (By reference.com) • 22.4% of seniors saved 300,000 and more (By time.com 2016) • $1 million can roughly yield $40,000 per year until age 95 without proper retirement investment.

  3. Strategy Comparison • What is the maximum likelihood of having at least $1 at age 95? • What is the maximum annual spending with 95% likelihood of having at least $1 at age 95?

  4. Complexity Modeling Variations Real life Cash flows Rules of withdrawing from accounts Spending curve: inflation and taper Tax variation upon account type, asset type, withdrawing source Ordinary income tax Capital gain tax Federal tax • Over 500 inputs • 5 Accounts: • Non Qualified • Qualified - Client & Spouse • ROTH IRA - Client & Spouse • Up to 10 investment assets • Flexible assets’ allocations • Infusion of capital • Annuities (SPIA & DIA) • …

  5. Case Study • Male (65), average health. Divorced, no kids • Has saved $2M (Non-qualified account: $1.2M, Qualified account: $ 800K) • $30K of social security (start from 70), no pension • Moderate allocation • Retiring this year; wants to know the maximum safe income level • Targeting a 95% confidence of having at least a dollar of assets when he is 95

  6. Modeling • Discrete optimization problem • Maximize • Subject to • Notations x: the vector of annual retirement living needs Actually, we are maximizing the initial retirement living needs 𝑔(𝑥,r): the ending value of the individual’s account at time n. It is a random variable and it depends on the annual retirement living needs () and the returns of portfolios ().

  7. Modeling Objective Function Equality Constraint The equality constraint is a probability equation The ending value of account is a stochastic process of cash flows, which is driven by the random returns of portfolios Use Monte Carlo method to simulate the distribution of • To maximize the initial retirement living needs (IRLN) • The sequence of annual retirement living needs depends on IRLN, inflation and taper

  8. Monte Carlo method • Simulate yields curves • Case study • Iteration number: 2000 • Period: 95 – 65 = 30 • The number of assets: 6 • After we get these matrices of expected returns, for a given IRLN (), we can get the distribution of by running the cash flow model

  9. Methodology Try and Error Method Formula-based Method Do not try it, just solve it Incorporate the rules into recursive formulas Derive the general form of for each scenario from recursive formulas Solve = 0 directly for each scenario and then get 2000 IRLNs Choose the quantile (1 – α%) of these 2000 IRLNs Use matrix calculation instead of loop statement • Since the cash flow model includes a lot of “rules” (i.e. the rules of calculating taxes and the rules of withdraw, in programming they are if statements), it is really time consuming to get the distribution of • 3 – 4 minutes for one trial. • If we want to satisfy the constraint (a specific ruin target) by using try and error method, it may take hours or even the whole day to get the optimal solution

  10. Summary & Next Step Summary Next Step Solve the optimal allocation of annuities Incorporate mortality and morbidity into the model Use healthy life expectancy to adjust the curve of retirement living needs • Optimization problem • Maximize the retirement living needs subject to a specific ruin probability • Monte Carlo Application • Formula method VS Try and error method • Matrix calculation VS Iterative computations

  11. Thank you！ If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. ——John von Neumann

More Related