One characteristic of an arithmetic mean is that all observations have equal weight (=1/N). However, this may not always be the case. In some cases, different observations may influence the mean differently. This has special relevance in portfolios where a portfolio is made up of different stocks each having a different weight.
Let’s assume that we have a portfolio comprising three stocks, A, B and C as follows:
We have the stock returns for each stock and the weight of each stock in the portfolio. For example, if the investor has a total of $1,000 invested in the portfolio, 20% or $200 is invested in Stock A, $300 is invested in stock B, and the remaining $500 is invested in Stock C.
The weighted average mean is calculated using the following formula:
The weighted mean of our portfolio will be calculated as follows:
Note that the weighted mean is closer to the returns from Stock C because Stock C has more influence (weight) on the portfolio.