What it means
A simple average treats every number the same. That works when each item is equally important, but often they are not.
A fund that holds 70% of its money in one share should not give that share the same influence as a holding of 2%. To weight a calculation, you multiply each item by its weight, add the results and divide by the total of the weights.
Weights can be percentages, quantities, amounts of money or scores. The weights usually add up to 100% or to a total that is used in the division.
Weighting appears throughout finance. The weighted average cost of capital blends the cost of debt and equity according to how much of each a company uses.
Stock market indexes are weighted by the size of each company, and a weighted average cost of inventory spreads purchase costs across units bought at different prices. The choice of weights matters a great deal.
Weighting by market value gives large companies more influence, while weighting equally gives every company the same say. Two indexes built from the same shares can behave quite differently because of the weights chosen.
A frequent mistake is using a simple average when weights are needed. Averaging two interest rates of 4% and 8% gives 6%, but if 90% of the borrowing is at 4%, the true average is much lower.
Always ask what the numbers represent and how much of the total each one makes up. Weights can also be used to express judgement rather than size.
In a scorecard for choosing a supplier, a manager might give price half of the total weight because cost matters most this year. Writing the weights down before scoring begins stops the result being bent to favour a preferred choice.
In practice
Real-world examples.
Example
A company borrows $900,000 at 4% and $100,000 at 8%. The weighted average interest rate is (900,000 x 4% + 100,000 x 8%) / 1,000,000 = (36,000 + 8,000) / 1,000,000 = 4.4%. A simple average of 6% would be misleading, because most of the borrowing is at the lower rate.
Example
A retailer buys 200 units of stock at $10 and 300 units at $12. The weighted average cost per unit is (200 x 10 + 300 x 12) / 500 = (2,000 + 3,600) / 500 = $11.20. This figure is used to value the inventory and to calculate the cost of goods sold when units are sold.
Example
A manager scores three suppliers on price, quality and delivery. She gives price a weight of 50%, quality 30% and delivery 20%. The supplier with the highest weighted score wins the contract, and the scorecard is kept as a record of why.
Formula
Calculation
Weighted average = Sum of (Weight x Value) / Sum of weights
Suppose a portfolio of $100,000 is split as follows: 60% in a share fund returning 10%, 30% in a bond fund returning 4% and 10% in cash returning 2%. The weighted return is (0.60 x 10) + (0.30 x 4) + (0.10 x 2) = 6.0 + 1.2 + 0.2 = 7.4%. In dollars, the portfolio earns 100,000 x 0.074 = $7,400. A simple average of 10%, 4% and 2% would give 5.33%, which understates the result because the best performer holds the largest share.Case study
Seen in the real world.
Ferndale Home Supplies is an illustrative, fictional retailer that reported its average supplier payment time as 40 days, based on a simple average across ten suppliers. The treasurer suspected the figure hid something.
She recalculated the number weighted by the amount owed to each supplier. The two largest suppliers, which accounted for 70% of purchases, were paid in 25 days, while many smaller ones were paid very late.
In this illustrative story the weighted figure was 31 days and showed that the company was paying its biggest suppliers faster than the headline suggested. The lesson is that weights reveal where the money really is, and the right measure depends on the question being asked.
Watch out
Common mistakes.
- Using a simple average when the items have different sizes, which can give a misleading result.
- Choosing weights that do not add up to the right total, so the answer is too high or too low.
- Forgetting that different weighting methods can give different answers, and failing to state which one was used.
Questions
People also ask.
What is a weight?
It is a number, often a percentage, that shows how much influence an item has in a calculation.
Does a weighted average always differ from a simple average?
Only when the weights are unequal or the values differ, since equal weights give the same result as a simple average.
Where are weights used in finance?
They appear in portfolio returns, cost of capital, stock indexes, inventory costing, credit scoring and supplier evaluation.
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