*This is a very basic article explaining why unweighted arithmetic average is not suitable when portfolio is not equally weighted. See more about When to Use Arithmetic Average and When Not.*

## 3 stock portfolio example

Let’s say you have 1 million dollars and you want to invest it in stocks. You construct a fairly concentrated portfolio – you particularly like stock ABC. At the beginning of the year **you have invested 1 million dollars in 3 stocks:**

- Stock ABC: 80% of portfolio = USD 800,000
- Stock DEF: 10% of portfolio = USD 100,000
- Stock GHI: 10% of portfolio = USD 100,000

The important factor for illustrating the point of this article is that **the positions have different weights** in the portfolio: 80%, 10%, and 10%.

## Performance of individual stocks

One year later, you are looking at your portfolio’s performance. The 3 stocks performed like this:

- Stock ABC -20%
- Stock DEF +10%
- Stock GHI +40%

## Arithmetic average of the stocks’ returns

What is the arithmetic average? The sum of -20%, +10% and +40% equals +30%. Divided by 3, the **arithmetic average of the stocks’ returns in the last year is +10%.** (See How to Calculate Arithmetic Average: The Very Basics).

## Percentage return and P/L of total portfolio

How much money have you made?

- In stock ABC you have lost 20% of 800,000 = USD 160,000
- In stock DEF you have made 10% of 100,000 = USD 10,000
- In stock GHI you have made 40% of 100,000 = USD 40,000

The whole portfolio P/L is negative 160,000 plus 10,000 plus 40,000, which equals a loss of USD 110,000. **On percentage basis, you have lost 11% of your initial investment.**

## Why is arithmetic average not working?

Though 2 of the 3 stocks have risen and arithmetic average of the 3 stocks’ returns is +10%, your portfolio has lost money, as your **biggest (and losing) position in stock ABC has outbalanced the two smaller positions**. Had your portfolio been equally weighted (each stock 33.3%), its return would have been +10%. But you were unlucky to allocate more to ABC, the one stock that has lost in the end.

## Weighted average is better for calculating total portfolio return

For **calculating average return of a portfolio or basket of stocks**, arithmetic average is only suitable when all stocks have equal weights in the portfolio, which is rarely the case. **When the weights are different**, you need to take it into account and use **weighted average** instead.