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Investment Return Nested Inertia - a research proposal

Updated: Oct 5, 2023

The lead researcher seeks assistance to develop VBA macros or related code to implement this simulation proposal. A starting spreadsheet will be provided to build the code set. In return for code writing, the researcher will provide personal finance insight, co-authorship, and an hourly stipend. The final results will be promoted on social media and the TCV website. Please contact Jeff Hulett at to express your interest and qualifications.

About the lead researcher: Jeff Hulett is a career banker, data scientist, behavioral economist, and choice architect. Jeff has held banking and consulting leadership roles at Wells Fargo, Citibank, KPMG, and IBM. Today, Jeff is an executive with the Definitive Companies. He teaches personal finance at James Madison University and provides personal finance seminars. Check out his new book -- Making Choices, Making Money: Your Guide to Making Confident Financial Decisions -- at


This research proposal explores the impact of volatility on long-term investment returns. A finance foundation is that the Future Value transformation function is convex to time.

Convexity implies that over time a) returns will increase at an increasing rate and b) investment return volatility is less negative to the downside and more positive to the upside. This model seeks to validate that under a series of Monte Carlo simulations, the convexity implication is validated. (cite Hulett, Math intuition)

The future value function is a convex transformer. It transforms the baseline inputs of time and savings into the output of future wealth. The transformation process includes the 2 "what is convexity" characteristics. (cite Hulett, Math intuition)

The simulation model approach relates to evolutionary biology and physics. The model emulates the impact of the investment environment's nature (long term 'normal' volatility), as well as, the random impact of how multiple market participants are nurtured within the environment. (subject to short term inertia) (cite Hulett, Ergodicity)

Investment returns on diverse funds are notoriously volatile. Investment return volatility has been demonstrated to be stochastic or random. The random nature of volatility tends to have memory or inertia. (add citations) The extent of the inertia is generally related to unexpected market disruptions creating inertial momentum. The financial crisis is a good example.

  • On July 11, 2008 - IndyMac Bank failed.

  • On September 7, 2008 - Fannie Mae and Freddie Mac were taken over by the U.S. Government.

  • On September 15, 2008 - Lehman Brothers went bankrupt

  • On September 26, 2008 - Washington Mutual went bankrupt.

(cite U.S. Congress, Financial Crisis Inquiry Report)

These disruptions created significant market turmoil and downward market inertia. From September 1, 2008 to December 3, 2008, the S&P 500 dropped 1300 to 870, or a drop of 33%. In that time period, 7 out of 10 days were down days for the S&P 500.

This suggests while returns may be stochastic, there is also inertia. The intensity of market disruption is likely to create inertia within the stochastic nature of the markets. In terms of the standard statistical moments, the 1st and 2nd moment of mean and variance may resemble that of a normal distribution, however, the 3rd and 4th moments of skewness and kurtosis are a dead give away the distribution is anything but normal. (cite Hulett, Numbers Don't Lie) This means that only using the typical normal distribution is not an appropriate manner to understand investment return volatility, especially within shorter time periods. This also suggests visually inspecting a distribution is often more revealing than relying on its calculated moments.

Model Approach:

This model seeks to both integrate:

a) Nature -> stochastic variations for longer-term normal stochastic volatility, as well as

b) Nurture -> inertia associated with shorter-term disruptions.

The (a) longer-term normal stochastic volatility is based on long-term investment return averages and standard deviations from the normal distribution. Over a long enough time period, typical normal distribution measures are appropriate. A 40-year time period is used to apply standard variations observed from the 10-year Treasury

In (b) shorter time periods, an investment return nested inertia approach is used.

The nesting occurs over 3 time frames using 10 even interval time frames.

  • The highest level or level 1 is 40 years long and divided into 10 4-year intervals.

  • Level 2 is 4 years (or 48 months) divided into 10 4.8 months (or 144 days) intervals.

  • Level 3 is 4.8 months (or 144 days) divided into 10 14.4-day intervals.

For the target investment returns a historically observed high volatility investment fund return (IR) of 10% is utilized, along with a 2.5 standard deviation (SD). The baseline standard deviation occurs from the actual 10-year Treasury Bond history.

Level 1 uses the high volatility IR and 2.5 SDs, randomly applied using a random number generator.

Level 2 uses all intervals within each level 1 interval. The level 2 return is seeded from the randomly assigned level 1 return. Then, a level 2 return is calculated using the randomly seeded higher-level return and the associated SD.

Level 3 uses all intervals within each level 2 interval. The level 3 return is seeded from the randomly assigned level 2 return. Then, a level 3 return is calculated using the randomly seeded higher-level return and the associated SD.

The model implies that randomly occurring nested cycles may occur in

  • 10 4-year periods over 40 years

  • 10 4-month periods over 4 years, and

  • 10 2-week periods over 4 months.

Nature and nurture:

The purpose of the random nesting inertia is for the higher-level seeded IR to provide the starting point for the inertia-impacted lower-level stochastic returns. It is like saying the parent is providing the development environment for the child, but different children may vary in terms of how they develop within that environment. This approach recognizes the inertia of the environment impacts an investor's outcome resulting from the environment AND that many investors may have random variations within the same inertia-impacted environment.

The model is a Monte Carlo simulation using the seeded and historically observed long-term return expectation. A series of nested loops occur from a programming standpoint. Random variations occur at the lower level environment and are seeded by the higher level environment.

Model outcome:

As suggested in the background section, diversified investment pools are convex to time. In the case of this model - high-volatility, high-return investments are utilized. Convexity is a feature of the Future Value function available to transform savings and time into wealth. (cite Hulett, Math intuition) The question becomes -- what is the impact of inertia-impacted volatility on the Future Value transformer?

This model is expected to show the impact of an array of simulated outcomes using this IR nested inertia construct. The expected output of the model is:

  • 100 simulation runs for the 40 year time period.

  • Graphics showing the boundaries and concentrations of those 100, 40 year simulations.

  • Observations and recommendations owing to the outcome.

The assertion of the 2 "what is convexity" characteristics mentioned earlier are being tested. The intent is to encourage people with multi-decade investment time horizons to invest in well-diversified, high IR, and highly volatile investment funds.

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