Variance: The Reason Why Rich Get Richer And Poor Get Poorer

The math and psychology behind long term gains and losses!

Rich vs. Poor Seesaw: Illustrative art created by the author

Variance is not the first word that comes to mind when you think about why the rich get richer and the poor get poorer. But in this essay, we will not only see why this is the case, but also find out what expected utility theory has to say about this phenomenon as well.

We will start by pondering upon a hypothetical betting game. Following this, we will see what expected value theory has to say about this hypothetical bet. Next, we will cover what expected utility theory has to say and how variance slots into all of this.

By the end of this essay, you would be able to appreciate some of the mathematics and psychological implications behind financial decisions and financial gains/losses from stock markets, retirement funds, indices, options, etc.

The Hypothetical Betting Game

Let us say that you are presented with a fair bet (50% chance of winning) — something like a fair coin toss. If you win, you get two million dollars. If you lose, you lose one million dollars. A simple Game, right?

Would you play this game? That decision is not necessarily simple. We will eventually see why. But first, let us see…