Financial Model Advice - Stable Paretian Distributions and the use of Fractals
Long story short, I fell down a rabbit hole of academic papers in my free time trying to think of better risk management to include in our models since we currently use a normally distributed Monte Carlo to act as a sensitivity analysis for variables such as rent growth, vacancy, cap rates, ancillary revenues, op ex, etc.. This one paper explained Chaos Theory and the use of Fractals in Financial Modeling and the conclusion was to use a Stable Paretian Distribution instead of a normal distribution when simulating and was wondering if anyone has experience in applying this to an excel model? If anyone has advice or know the functions to use to achieve this, please let me know.
I would just use python.
Why are you even bothering with Monte Carlo, that’s simply a function of the probabilities you put into the formulas which I’m guessing you don’t have a standardized and informed way of attributing other income probabilities…
Can you link me to the Chaos Theory/Fractals academic paper? would love to have a look
It's called "Chaos Theory and the Science of Fractals in Finance" by Tania Velasquez
It's wild to me that some people actually think this type of mathematical analysis is worth your time in real estate...
If it's just a building, then why use any financial models at all right? It's simply a tool for risk management and sensitivity analysis. If anyone in any industry was 100% confident in their assumptions about 10 years from now and didn't want to look at any other possible scenarios in a sensitivity analysis, then they would be laughed at and never taken seriously.
If you look at the paper it outlines that there's a butterfly effect and enough "outlier events" that markets don't act in a linear and idealized way. In the last ~23 years we went through the ".com" bubble, great recession, 2018's downturn, initial pandemic in 2020, and now 3 years later we are headed into a recession. The paper says that we can only write off so many times as "flukes" and exceptions to the rules rather than just the rules are more complex than we originally thought. The same way scientists thought Newtonian principles were the end-all-be-all for centuries, and now know that isn't the case. So rather than use a normal distribution for randomly generated scenarios, given certain parameters that someone deems to be possible outcomes (guardrails), we could look to stable paretian distributions to account for the chaos in the markets.
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