Question Regarding Percents

[Herdeman]

Hi,

I'm looking at some analysis for returns over a period of a number of years. I'm trying to calculate which set of margins would be more profitable over time:

Returning 20%, 70% of the time.

or Returning 15%, 80% of the time.

I'm not sure how to properly come to an answer, but would like to know the working for future use.

Thanks

 

[tkhunny]

The simple, and not actually all that helpful, answer would be a simple multiplication.

0.2 * 0.7 = 0.14
0.15 * 0.8 = 0.12

However, this is not meaningful. What is the return the other 30% (or 20%) of the time?

 

[Herdeman]

The simple, and not actually all that helpful, answer would be a simple multiplication.

0.2 * 0.7 = 0.14
0.15 * 0.8 = 0.12

However, this is not meaningful. What is the return the other 30% (or 20%) of the time?

In this case, let's assume it's -5% for both 30% and 20%

 

[tkhunny]

Okay, then extend the definition for the entire probability distribution.

The usual idea is \(\displaystyle E[x] = \sum x\cdot Pr(x)\)

This compiles the "Expected Value".