Optimal Spend Rates via Backward Induction and SDP
Jan 2020 – Present
Project description
This was an attempt to try to use an "optimal control theory" technique (e.g., stochastic dynamic programming and backward induction - BI/SDP related to Bellman equations) to evaluate life-cycle spending choice (or the decumulation half, anyway). In personal finance, this method has been attempted before for life-cycle allocation choice [Irlam, G. (2014). Portfolio Size Matters. The Journal of Personal Finance. 13(2), 9-16.] but to the the best of my knowledge has not been attempted for spend rates [update: yes it has...by Irlam, G.]. Results were noisy but fairly consistent with life-cycle econ theory.
Five Retirement Processes
Jan 2019 – Present
Project description
Effort to structurally integrate four years of blogging by factoring retirement finance into what I consider the five core process and to look at them as quantitatively as I am capable:
0. Five retirement processes - Introduction
1. Return generation in multi-period time,
2. Stochastic consumption processes,
3. Portfolio longevity in its unconditional sense,
4. Human mortality and conditional survival probability,
5. Continuous management and monitoring processes
https://rivershedge.blogspot.com/p/5-processes.html
Reinforcement Learning in Personal Finance
Jan 2019 – Present
Project description
Built a rudimentary AI to teach itself optimal spend rates in decumulation using dispersion, a value function and rewards. Depending on how we frame it, the machine tended to find other known optimal solutions. May have some applicability to intractable problems or problems where solutions are not already known. RStudio and AWS. Simple, probably reductive, no other sophisticated tools.
See project Reinforcement Learning in Personal FinanceSee project
"Wealth Depletion Time" Game
Apr 2018 – Present
Project description
Jan 2019 – Present
Project description
Built a rudimentary AI to teach itself optimal spend rates in decumulation using dispersion, a value function and rewards. Depending on how we frame it, the machine tended to find other known optimal solutions. May have some applicability to intractable problems or problems where solutions are not already known. RStudio and AWS. Simple, probably reductive, no other sophisticated tools.
See project Reinforcement Learning in Personal FinanceSee project
"Wealth Depletion Time" Game
Apr 2018 – Present
Project description
After about six months of reading opaque research papers on the concept of and financial mathematics of "wealth depletion time" (the span of the planning horizon where wealth is depleted and consumption is forced to any available pensionized income and where the value function is based on relative risk utility) I decided to instantiate the concept (typically represented in continuous time math and differential equations or maybe also simulation) in a simple pedagogic model. Features include lifecycle processes for consumption, fair annuities, social security, return generation, relative risk utility, etc. The model, combined with an understanding of the analytic expressions along with simulation software that is up to the task, can be a powerful teaching tool for the risks and (utility) rewards of choices to be made within the life planning cycle. see: https://rivershedge.blogspot.com/2018/04/a-trial-run-of-wdt-game-prototype.html
Updated in early 2018 to a full simulation of WDT using random lifetime, random non-normally distributed returns, real-annuities, and custom spend plans.
Updated in early 2018 to a full simulation of WDT using random lifetime, random non-normally distributed returns, real-annuities, and custom spend plans.
See https://rivershedge.blogspot.com/2018/06/wealth-depletion-time-simulator-update.html
Stochastic Present Value of a Spend Liability for Household Balance Sheets
Jan 2018 – Present
Project description
Stochastic Present Value of a Spend Liability for Household Balance Sheets
Jan 2018 – Present
Project description
Rather than using a simulator to calculate retirement ruin probabilities by projecting (constant?) spending and randomized portfolio returns into an ersatz and unknowable future, this tool works within the context of a household balance sheet -- where asset values are (mostly) known with certainty -- to estimate the present value of a spend liability as a distribution rather than as a deterministic object. This is done by taking the current-time dollar spend amount, along with a custom-designed spend path based on expectations about forthcoming spending in the future, and then simulating that plan out by: a) randomizing the simulated lifetime duration using Gompertz math for mortality probabilities, and b) chaining spending along with randomized inflation, the planned discontinuities, and randomized spend volatility. Then the simulated series is discounted back to the present (discount rates are not yet randomized but might be) and summed. The resulting distribution of NPVs can be used to select a value for the balance sheet liability just like one would have with deterministic PV (except here we have more choices: mean, median, pth percentile, whatever). In addition, the current assets that are available to fund, if not entirely defease, the liability can be located on the dollar spend distribution in order to estimate a type of probability of success. Since discount rates are a policy choice if they not randomized into the SPV, here it is set up as an input variable designed to test ranges and sensitivities, though this may be changed later. Some posts on the SPVsim can be found at https://rivershedge.blogspot.com. A second version of the SPVsim uses the same methodology but also projects the SPV to a range of future ages by inflating the start-spend to a future age based on budgeted inflation expectations, updating the mortality probability distribution for the projection age and then running the SPVsim again.
Flexible Ruin Estimation Tool (FRET)
Oct 2017 – Present
Project description
Flexible Ruin Estimation Tool (FRET)
Oct 2017 – Present
Project description
Created a tractable, transparent, simple, and fast solution for estimating lifetime risk of ruin. The results map well to the solutions from a Kolmogorov partial differential equation (PDE) that evaluates the same underlying processes. My tool directly addresses P[T>=L] (probability that a lifetime process is longer than portfolio longevity in years) which also satisfies the partial differential equation. The average difference between the two (using finite differences schemes for the PDE) in terms of estimated outcomes is zero with some minor variation due to the use of simulation for one of the terms. The advantage with the sim-approximation, in addition to general transparency, is that the density and difficulty of partial differential equations are avoided while tractability in using non-normal return distributions is gained. The estimator integrates two probability distributions: one for the chance of still being alive in n years (using a Gompertz mortality model tuned to the SOA annuitant mortality table) and the other for the chance of a net-wealth-process fail within the years of that lifetime (based on a brownian motion mini-sim using Kolmogorov's coefficient for a net wealth process). This approach models the underlying processes simply but with clarity. It also enhances the ability to visualize lifetime ruin risk for a given age, return distribution assumptions, and spend rate. Prototyped in Excel; written in R October 2017.
Combined "Perfect Withdrawal Rate" Concept with Stochastic Duration (longevity)
Sep 2017 – Present
Project description
Combined "Perfect Withdrawal Rate" Concept with Stochastic Duration (longevity)
Sep 2017 – Present
Project description
I adapted a formula seen in several sources (several academic retirement papers and one web site) designed as an analytic solution to safe withdrawal rates and then added an additional feature that I don't think is being done anywhere else: a stochastic duration of periods that fits a Gompertz model for human longevity. This was a challenge suggested in one of the papers that I couldn't pass up. The base equation is "the maximum withdrawal rate possible over a fixed period of time if one had perfect foresight of investment returns" (i.e., a "perfect withdrawal rate"). As a standalone analytic solution it is both powerful and elegant. It also enables one to visualize sequence of returns risk both when looking at the composition of the equation directly and also by looking at the distribution of withdrawal rates that result from it. To this foundation I added the following: a) I iterate it x,000 times to breath some random volatility into it by using a sampled distribution of returns, and b) in each iteration I solve the equation for a randomly varying number of periods that are fitted to Gompertz distribution with Mode = M and dispersion = b. The analysis made possible from the resulting distribution of PWRs compares well to both Monte Carlo simulation and a Kolmogorov partial differential equation. Start here for more info: https://rivershedge.blogspot.com/2017/09/prelim-study-of-pwrs-and-stochastic.html
Re-coded a Kolmogorov PDE for Lifetime Probability of Ruin into R
Sep 2017 – Present
Project description
Re-coded a Kolmogorov PDE for Lifetime Probability of Ruin into R
Sep 2017 – Present
Project description
Took VBA code doing a finite-differences solution/approximation to a Kolmogorov partial differential equation (the equation is used to evaluate the lifetime probability of ruin) and re-wrote it in R. While PDEs mostly escape me, I did this recode to help me understand how the equation works in practice and to enhance my understanding of the mathematics of retirement, especially since this equation is a gem of distillation of the retirement problem. The FD approximation when run through its paces shows that it is in close proximity to Monte Carlo Simulation as well as "perfect withdrawal rates" (analytic solution to withdrawal rates assuming a known sequence of returns over time) when run in a dynamic simulation.
Miscellaneous Self-Directed Continuing Ed
Jun 2017 – Present
Project description
Miscellaneous Self-Directed Continuing Ed
Jun 2017 – Present
Project description
2020 - Brownian Motion and Stochastic Differential Calculus (intro)
2020 - Linear Algebra
2018 - Macro econ topics, esp. "expected discounted utility of lifetime consumption"
2015-17 - misc refresher self-studies - intro calculus and multi-var, statistics
2017 - refresher self-study - continuous compound interest and e
2017 - Mini self-study - Kelly criterion, geometric returns, and optimal bet sizing
2017 - Mini self-study - intro to quantitative finance (ARPM ch 1:3) [in process]
2017 - Mini self-study - multi-per geom return analysis, geom frontiers, and portfolio choice
2017 - Mini self-study - math and methods of projecting high freq return series/vol to a horizon
2017 - Mini self-study - Markowitz, Meucci & Michaud methods for MVO and MV resampling
2017 - Mini self-study - utility functions and certainty equivalents (CRRA, power functions)
2017 - Mini self-study - statistics of longevity, mortality tables and aging
2017 - Mini self-study - backward induction and stochastic dynamic programming
2016 - Options on commodity futures - self directed, CBOE & other
2016 - Refresher MOOC tutorials in probability and statistics
2016 - Tutorials in R programming - self directed
2015 - present - Mathematics of retirement finance - synoptic - self directed [in process]
2015 - Econ 159: Game Theory - Polack - OpenYale
2015 - Econ 252: Financial Markets - Shiller - OpenYale
2015 - Econ 251: Financial Theory - Geanakoplos - OpenYale
2010 - Forex trading theory and practice - Integra Fund
Created a Retirement Variable-Percentage-Spending Rule of Thumb
Feb 2017 – Present
Project description
2020 - Linear Algebra
2018 - Macro econ topics, esp. "expected discounted utility of lifetime consumption"
2015-17 - misc refresher self-studies - intro calculus and multi-var, statistics
2017 - refresher self-study - continuous compound interest and e
2017 - Mini self-study - Kelly criterion, geometric returns, and optimal bet sizing
2017 - Mini self-study - intro to quantitative finance (ARPM ch 1:3) [in process]
2017 - Mini self-study - multi-per geom return analysis, geom frontiers, and portfolio choice
2017 - Mini self-study - math and methods of projecting high freq return series/vol to a horizon
2017 - Mini self-study - Markowitz, Meucci & Michaud methods for MVO and MV resampling
2017 - Mini self-study - utility functions and certainty equivalents (CRRA, power functions)
2017 - Mini self-study - statistics of longevity, mortality tables and aging
2017 - Mini self-study - backward induction and stochastic dynamic programming
2016 - Options on commodity futures - self directed, CBOE & other
2016 - Refresher MOOC tutorials in probability and statistics
2016 - Tutorials in R programming - self directed
2015 - present - Mathematics of retirement finance - synoptic - self directed [in process]
2015 - Econ 159: Game Theory - Polack - OpenYale
2015 - Econ 252: Financial Markets - Shiller - OpenYale
2015 - Econ 251: Financial Theory - Geanakoplos - OpenYale
2010 - Forex trading theory and practice - Integra Fund
Created a Retirement Variable-Percentage-Spending Rule of Thumb
Feb 2017 – Present
Project description
Given the immense amount of time I have put into multi-period life-cycle finance reading, research, and applied programming, I thought I'd try my hand at creating a custom rule of thumb that , among other things: 1) is easy to remember and portable with no need for tech or tables other than a simple calculator, 2) requires no input other than age, 3) generally respects the concepts of: early retirement has an amplified set of risks, longevity is variable, residual longevity and/or legacy require a non-zero terminal wealth plan, and risk aversion changes with age, 4) is a hyper-conservative starting point for an investigation of spend rates, and 5) has some plausible basis in econ theory and the real world evidence-based application of the concept. In a series of tests, the formula, though probably a little conservative, shows pretty well. Withdrawal % = Age / (40 - Age/3)
See project Created a Retirement Variable-Percentage-Spending Rule of ThumbSee project
Backward Induction Engine Using Dynamic Stochastic Programming
Jan 2017 – Present
Project description
See project Created a Retirement Variable-Percentage-Spending Rule of ThumbSee project
Backward Induction Engine Using Dynamic Stochastic Programming
Jan 2017 – Present
Project description
Built a backward induction engine using stochastic dynamic programming in R. The proximal purpose was to learn how it is done with a secondary goal to come up with an economically rigorous framework for asset allocation optimization that varies with plan year and portfolio size while also optimizing life-cycle planning with respect to both fail rates and fail magnitude when the optimization results are fed back into simulation.
Retirement Finance Blog
Jan 2016 – Present
Project description
Retirement Finance Blog
Jan 2016 – Present
Project description
Started a retirement finance blog with original content and links to such topics as:
- Retirement Finance and Planning
- Markets, the Economy and Investing
- Alternative Risk
- Society and Capital
rivershedge.blogspot.com
Custom Monte Carlo Simulator, A Retirement Finance Research Tool
2016 – Present
Project description
- Retirement Finance and Planning
- Markets, the Economy and Investing
- Alternative Risk
- Society and Capital
rivershedge.blogspot.com
Custom Monte Carlo Simulator, A Retirement Finance Research Tool
2016 – Present
Project description
This tool includes some features not currently found in free products in an integrated way although many of the features (not all) show up here and there. For my version, I include things like: stochastic longevity, stock-bond dependent return correlation, a correct total return bond formula, "regime" suppression of returns, historical return suppression, random spending variance and trends as well as large spending shocks, a customizable spending path, rudimentary but customizable tax and fee variables, output history retention, etc. Rewritten in late 2016 in R. 2017: added custom mortality distribution options, sampling methods, alternative custom return distributions, back-end analytics, rudimentary utility analysis of terminal wealth, and dynamic asset allocation based on the table output from a backward induction exercise.
Proprietary Trading
2009 – Present [note: over in 2020]
Project description
Proprietary Trading
2009 – Present [note: over in 2020]
Project description
Starting in 2009, Silkwood Capital developed and now operates several successful proprietary trading programs designed to produce absolute returns and to hedge multi-family capital at risk. Strategies employed seek conservative equity-like returns with low, asymmetric, bond-like volatility that pushes an efficient frontier up and left. The current focus is on a systematic rules-based alt-risk approach that includes, in layers, an enhanced-risk collateral yield management program, alternative fixed income positions, momentum-traded diversified credit, a short volatility-risk-premium strategy, plus other macro and alt-risk strategies as the opportunity arises. ~40 month Sharpe (2017) is > 1.3 and R/R has been generally well outside a benchmark EF in backward-looking mean-variance space. Omega ratio shows consistent positive asymmetry in up/down risk though the results are highly dependent on the baseline return expectation. Depending on the benchmark, have bettered hedge fund benchmarks 4 of 5 last years (granted this has been a low bar lately) as well as a passive asset allocation index also used as a benchmark.
Private Placements - Specialty
2005 – Present [over 2020]
Project description
Private Placements - Specialty
2005 – Present [over 2020]
Project description
Silkwood will periodically make private placements that meet selected criteria related to long term financial or non-financial goals. For example:
Peer-to-Business Asset Based Lending -- crowdfunding model is applied to business lending and the asset-secured working capital of small and medium businesses. Offers growing companies competitively priced working capital while supporting job-creating small and medium businesses.
Peer-to-peer micro loans -- directly fund the micro-notes of hundreds to thousands of prime retail borrowers without the terms of, or inter-mediation by, traditional financial institutions. Since 2008.
Impaired International Credit -- private placement into de-levered, or non-core financial assets that enter global supply through legislation (Dodd-Frank, Basel III, Solvency III,etc.), tighter standards, or destabilizing macro events.
Private Placements - Ventures and Venture Development
2004 – Present [over 2020]
Project description
Peer-to-Business Asset Based Lending -- crowdfunding model is applied to business lending and the asset-secured working capital of small and medium businesses. Offers growing companies competitively priced working capital while supporting job-creating small and medium businesses.
Peer-to-peer micro loans -- directly fund the micro-notes of hundreds to thousands of prime retail borrowers without the terms of, or inter-mediation by, traditional financial institutions. Since 2008.
Impaired International Credit -- private placement into de-levered, or non-core financial assets that enter global supply through legislation (Dodd-Frank, Basel III, Solvency III,etc.), tighter standards, or destabilizing macro events.
Private Placements - Ventures and Venture Development
2004 – Present [over 2020]
Project description
Since 2004, Silkwood Capital has invested in, and supported the development of, a number of seed to mid stage ventures. Participation has been in the form of debt placements, preferred and common sub-S and C corp shares, LLC member units, founder's shares, partnership agreements, royalty agreements, warrants, and in some cases direct hands-on development support. Examples include:
Integra Capital Management -- private placement into a seed-stage macro discretionary foreign exchange hedge fund paired with venture development support designed to enhance the success potential of the placement.
MyNextLeap -- Idea-stage venture focused on an emerging nexus between wellness and workforce optimization. Placement plus venture development support.
JobDig/LinkUp -- Private late stage recruitment advertising company focused on employment, recruiting and job seach. LinkUp is currently the fastest-growing job search engine on the web.
UnityWorks! Media -- Private mid-stage venture offering micro-branded online video advertising systems.
IntelAccount -- Early-stage venture; outsources the accounts payable business process for small businesses.
TV Trainer -- Seed stage venture provided culturally-based workforce training products and services using a patented optical technology. Limited development support.
MPT Mean-Variance Mapper
2016 – 2017
Project description
Integra Capital Management -- private placement into a seed-stage macro discretionary foreign exchange hedge fund paired with venture development support designed to enhance the success potential of the placement.
MyNextLeap -- Idea-stage venture focused on an emerging nexus between wellness and workforce optimization. Placement plus venture development support.
JobDig/LinkUp -- Private late stage recruitment advertising company focused on employment, recruiting and job seach. LinkUp is currently the fastest-growing job search engine on the web.
UnityWorks! Media -- Private mid-stage venture offering micro-branded online video advertising systems.
IntelAccount -- Early-stage venture; outsources the accounts payable business process for small businesses.
TV Trainer -- Seed stage venture provided culturally-based workforce training products and services using a patented optical technology. Limited development support.
MPT Mean-Variance Mapper
2016 – 2017
Project description
This tool was created to use standard Modern Portfolio Theory formulas for portfolio return and covariance in order to generate a mean variance map and efficient frontier for portfolios of two and five ETFs. A sampling technique is used to manage the large number of allocation choices possible (~4.6M combinations if allocating in 1% increments). The goal is to provide mean-variance performance context for alternative-risk trading strategies. Late 2016 - rewritten in R. 2017 switch added for multiple methods for calculating mean return and standard deviation. [Note: this was retrospective analysis not forward]
Custom Black-Scholes-Based Option Pricing and Graphing Model
2016
Project description
Custom Black-Scholes-Based Option Pricing and Graphing Model
2016
Project description
This tool is used to look at intra-tenure convexity risk and scenarios for complex option strategies. It includes features I can't yet find in a fully integrated free product:
- Long/short call/put strategy P&L chart
- Implied underlying P&L overlay
- Slider for intra-tenure P&L
- Slider for expanding and contracting volatility
- Slider for expanding and contracting price change increments
- Overlay of a delta-hedge P&L as well as the hedged intra-tenure P&L
- Scaled implied-price probability-density graph with standard deviation markers
- Manual adjustments for vol. skew
Custom Hack: Options Probability and Premium Opportunity Tool
2016
Project description
- Long/short call/put strategy P&L chart
- Implied underlying P&L overlay
- Slider for intra-tenure P&L
- Slider for expanding and contracting volatility
- Slider for expanding and contracting price change increments
- Overlay of a delta-hedge P&L as well as the hedged intra-tenure P&L
- Scaled implied-price probability-density graph with standard deviation markers
- Manual adjustments for vol. skew
Custom Hack: Options Probability and Premium Opportunity Tool
2016
Project description
The tool is used to find higher probability, lower risk short-selling opportunities in Future's Options. It generates a normal distribution, a "premium intensity" function that is a proxy for a skewed probability distribution; and a graphical premium display chart that is overlaid with a delta threshold indicator that provides a rough, simple and quick visual cue for where the lower risk / reasonable premiums are to be found on the mid-outer bounds of an estimated price distribution. Re-write in R, early 2017.
Deterministic Retirement "Risk Of Ruin" Formulas & Models
2016
Project description
Deterministic Retirement "Risk Of Ruin" Formulas & Models
2016
Project description
I used, and in some cases modified, third-party-developed formulas in order to create an integrated and "triangulated" point of view of "ruin risk" in retirement. The model comes at the retirement problem from multiple directions using multiple methods. This was done to contextualize the results of other Monte Carlo and historical simulators. In addition to tapping internet-based simulations, the other formulas and tools include: a regression formula from David Blanchett, Kolmogorov differential equations for lifetime ruin risk, Milevsky's Fibonacci formula for portfolio longevity, Inglis' divide-by-20 rule, Waring and Seigel's ARVA (annually recalculated virtual annuity) method, etc.
Rolling Market History Simulator
2016
Project description
Rolling Market History Simulator
2016
Project description
This was a one-time simulator built to model retirement and asset-class based withdrawal strategies. It was constructed as a one-off in order to confirm someone else's research results. Which it did.
[ other "projects" on LI includes past employment which is not germane here]
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