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Weighted average definition
A weighted average is an average that gives each value a different level of importance, set by a weight, before the figures are combined. It produces a single figure that leans toward the values carrying the most weight.
Each value is multiplied by its weight, the results are added together, and the total is divided by the sum of the weights. In finance the weight usually stands for size, quantity, percentage allocation, or market value, which is why it suits portfolio returns, average purchase price, index construction, and cost of capital.
A weighted average differs from a simple average. A simple average adds the values and divides by how many there are, treating each one equally. A weighted average lets larger or more important values count for more, so the two can give very different results from the same numbers.
Weighted average Example
You buy shares at two prices:
- 100 shares at USD 10 - 200 shares at USD 15
You work out the weighted average purchase price:
[(100 √ó USD 10) + (200 √ó USD 15)] √∑ 300 shares
(USD 1,000 + USD 3,000) √∑ 300 = USD 13.33
Your weighted average price is USD 13.33 per share, closer to USD 15 than USD 10 because more shares were bought at the higher price.
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