This is a question about a mathematical concept, but I think I will be able to ask the question better with a little bit of background first.

Warren Buffett famously provided 2 rules to investing:

> 
> Rule No. 1: Never lose money. Rule No. 2: Never forget rule No. 1.
> 
> 
> 

I initially took this quote as tongue-in-cheek. Duh, of course you don't want to lose money. But after better educating myself in the world of investing I see this quote more as words from the wise sensei of investing. It means more than just be careful, or be conservative. Losing money can destroy a portfolio because there is a mathematical disadvantage.

Consider two hedge fund managers: Mr. Turtle and Mr. Hare.

Mr. Turtle is steady, he doesn't have high returns, but he also doesn't lose money. Mr. Hare is aggressive, getting huge returns, but occasionally losing money. Here are their returns over the past 5 years

[![enter image description here](https://i.stack.imgur.com/6wiLJ.png)](https://i.stack.imgur.com/6wiLJ.png)

Mr. Hare has a higher average rate of return. Further, he has made (significantly) more money in 4 out of the 5 years. Mr. Turtle, however, has made his clients more money overall in the same timeframe.

This seems counter-intuitive. I would think you would want to maximize your average rate of return at all costs, but it's not that simple.

**Why?**

Why does one negative input have such a significant impact on an exponential growth function?

Why doesn't the average rate of growth always lead to the largest possible result?

How does one explain this (hopefully in layman's terms)?