This post illustrates a couple of things that I learned this year with an application in finance. I learned about the simplex when I was researching amino acids. I learned some nitty-gritty about portfolio theory. These combined with my pre-existing knowledge about game theory and mixed strategy solutions.
Specifically, I learned a way of visualizing all possible probabilities of portfolio outcomes. This post narrowly focuses on 3 so that I can draw a picture. But the idea generalizes to many probabilities.
Say that I can choose to hold some combination of 3 assets (A, B, & C), each with unique returns of 0%, 20%, and 10%. Obviously, I can maximize my portfolio return by investing all of my value in asset B. But, of course, we rarely know our returns ex ante. So, we take a shot and create the portfolio reflected in the below table. Our ex post performance turns out to…
