Weighted Mean

The weighted mean is computed by weighting each observed value according to its importance. In contrast, the arithmetic mean assigns equal weight to each value. Notice that the return of a portfolio is the weighted mean of the returns of individual assets in the portfolio. The assets are weighted on their market values relative to the market value of the portfolio. When we take a weighted average of forward-looking data, the weighted mean is calledexpected value.

Example

A year ago, a certain share had a price of $6. Six months ago, the same share had a price of $6.20. The share is now trading at $7.50. Because the most recent price is the most reliable, we decide to attach more relevance to this value. So, suppose we decide to "weight" the prices in the ratio 1:2:4, so that the current share price is twice as important as the price from six months ago, which in turn is twice as important as the price from last year.

The weighted mean would then be: (1 x 6 + 2 x 6.2 + 4 x 7.5) / (1 + 2 + 4) = $6.91. If we calculated the mean without weights, we'd get: (6 + 6.2 + 7.5) / 3 = $6.57. The fact that we've given more importance to the most recent (higher) share price inflates the weighted mean relative to the un-weighted mean.