• Finance ,
• 15 Sep

After we have calculated our Portfolio Weights, we can determine our Portfolio Return. The idea and value of a portfolio is that we diversify your investments to reduce risk. When you diversify, you are reducing or eliminating un-systemic risk. I like to think of un-systematic risk as being unique to a company or a small slice of a bigger market picture. Diversifying will not reduce your systemic risk which is also called market risk. Continuing our example, systemic risk would be the bigger market picture. Knowing our portfolio return is crucial when you have a bunch of investments and all of them are for different investment amounts.

Portfolio Return

where

Weight 1

Return 1

Weight n times

Return N times

Return for Portfolio

Weight 1

This is the portfolio weight for our first investment. I like to keep it lower case  because this is not our main event and this is how I often see it in textbooks. The idea of a portfolio is to reduce your unsystematic risk. The ratio of each egg type to the total number of eggs is our weight.

Return 1

This is the return for each investment. We want to pair our returns and weights. We add them together

Weight n times

n is a mathematical representation of the number of occurrences. It is to complete the use of our upper case Sigma to denote that we add the first product of the weight and return for investment 1, by the weight and return for investment 2, and on and on until the break of dawn. Just kidding, but that is how I remember it because we keep repeating this until we run out of investments. n is the total number of investments in our portfolio.

Return n times

While n typically denotes Years or Periods in our equation, a more general math notation n denotes a fixed integer.  I’ve seen this used as number of iterations or counts that you see in qualitative or categorical analysis of data.

Return for Portfolio

Why we’re here! Yay we made it! Or not I guess depending on what this value is.