CPPI$^{\dagger}$ is a risk management tactic that can be applied to any investment portfolio. The approach entails banking a percentage of profits whenever a new all time high wealth is achieved, thereby ensuring that a portfolio’s drawdown never goes below some maximum percentage. Here, I review CPPI and then consider the mean growth rate of a CPPI portfolio. I find that in a certain, common limit, this mean growth is given by a universal formula, (\ref{cppi_asymptotic_growth}) below. This universal result does not depend in detail on the statistics of the investment in question, but instead only on its mean return and standard deviation. I illustrate the formula’s accuracy with a simulation in python.

$\dagger$ CPPI = “Constant Proportion Portfolio Insurance”
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We consider the equilibrium drawdown distribution for a biased random walk — in the context of a repeated investment game, the drawdown at a given time is how much has been lost relative to the maximum capital held up to that time. We show that in the tail, this is exponential. Further, when mean drift is small, this has an exponent that is universal in form, depending only on the mean and standard deviation of the step distribution. We give simulation examples in python consistent with the results.

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Here, we highlight one of the most important benefits of tax protected accounts (eg Traditional and Roth IRAs and 401ks). Specifically, we review the fact that not having to pay taxes on any investment growth that occurs while the money is held in the account results in compounding / exponential growth with a larger exponent than would be obtained in a traditional account.

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