The notion of optimal f is not merely a method of determining an optimal point in a risk profile. Done right, it can provide the foundation of a superior portfolio model than what's being used today. This approach, as it is applied to the multiple component case, is called the Leverage Space Model.
The most common portfolio model in use today is called Modern Portfolio Theory (MPT). it relies on the mean variance of returns to measure risk. One difference between MPT and the Leverage Space Model is the latter defines risk as drawdown, not return variance.
MPT, because it depends on the variance in the returns of its components as a major parameter, assumes the distribution of returns is statistically normal. The Leverage Space Model, however, does not; it assumes that various components have different distributions of returns. So, while MPT, due to its normal assumption, is computationally ill-equipped to deal with, say, fat-tailed distributions, the Leverage Space Model has no trouble with these more realistic situations.
Let's return to our coin-toss game from the first installment.
To review, if the coin comes up tails, we lose $1. If it comes up heads, we gain $2. There are two bins, two scenarios, and each has a 0.5 probability of occurring. In short, over time, this positive expectation game does not result in what we expect. The multiple we made on our stake, on average, after each play drops significantly. Now, let's expand this to include two such games going on at once.
With two games, we have a surface, a terrain in N + 1 dimensional, or 3D, space.
The good news is everything about the single case, discussed in Part I of this series, pertains here. What we know about drawdowns, the danger of being to the right of the peak, reducing drawdowns arithmetically while reducing returns geometrically, is still valid. If we had a portfolio comprised of 100 components, 99 of which were optimal, we could still lose money if only one …