Book Editing: “Making Good Decisions” – Revised Part IV – Section #51:
“Calculated Projections” with the Tools of the 21st Century (Part 9 of 10) – Testing the Multiplicative “Growth Dynamic” as a “Null Model” for the S&P500 Index
This free, public post shares the edited version of Part IV – Section #51
For readers that do not have the time to read the two-page pdf:
Part IV - Section #51: “Calculated Projections” with the Tools of the 21st Century (Part 9 of 10) – Testing the Multiplicative “Growth Dynamic” as a “Null Model” for the S&P500 Index – This section builds-up on the prior section, and applies specific estimates for μ and σ based on annual, S&P 500 index values from 1926 to 2019. It tests the hypothesis that a multiplicative “Growth Dynamic” works as a reasonable “Null Model” for the price trajectory of the S&P 500 index. To test this hypothesis, it uses the closed-form formulas for the scalars shown below, to calculate historical values shown in the middle of this left page. Finally, it compares these historical values with simulated values based on the multiplicative “Growth Dynamic”. The close fit between the historical scalars to the simulated scalars means that this stochastic model based on the multiplicative “Growth Dynamic” provides a reasonable “Null Model” for the behavior of the S&P 500 Index, as a first step toward additional simulations, and comparisons with the results of models based on other types of “Growth Dynamics”.
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“CTRI by Francois Gadenne” writes a business book, published on Substack for public peer-review, at the rate of one two-page section per day. The book connects the dots of life-enhancing practices for the next generation, free of controlling algorithms, based on the lifetime experience of a retirement age entrepreneur, and continuously updated with insights from Wealth, Health, and Statistics research performed on behalf of large companies as the co-founder of CTRI.