What is a Weighted Average?
A weighted average is a type of average where each observation in the data set is multiplied by a predetermined weight before calculation. In calculating a simple average (arithmetic mean) all observations are treated equally and assigned equal weight. A weighted average assigns weights that determine the relative importance of each data point. Weightings are the equivalent of having that many like items with the same value involved in the average.
Understanding Weighted Averages
A weighted average is most often computed with respect to the frequency of the values in a data set. One can calculate a weighted average in different ways. However, certain values in a data set are given more importance for reasons other than frequency of occurrence. Each data point value is multiplied by the assigned weight which is then summed and divided by the number of data points.
A weighted average is extremely useful in that it allows the final average number to reflect the relative importance of each observation and is thus more descriptive than a simple average. It also has the effect of smoothing out data thereby enhancing accuracy.
|Data Point||Data Point Value||Assigned Weight||Data Point Weighted Value|
- Takes into account relative importance of data points when calculating an average thereby making it more descriptive than a simple average.
- Smooths out data which improves accuracy.
- Often used in finance to calculate cost basis of stock portfolios, inventory accounting and valuation.
Calculation of a Weighted Average of a Stock Portfolio
Investors often build a position in a stock over several years. Stock prices change daily, so it's tough to keep track of the cost basis on those shares accumulated over a period of years. If an investor wants to calculate a weighted average of the share price he or she paid for the shares, he or she must multiply the number of shares acquired at each price by that price, add those values and then divide the total value by the total number of shares.
For example, say an investor acquires 100 shares of a company in year one at $10, and 50 shares of the same company in year two at $40. To get the weighted average of the price paid, the investor multiplies 100 shares by $10 for year one, 50 shares by $40 for year two, and then adds the results to get a total value of $3,000. The investor divides the total amount paid for the shares, $3,000 in this case, by the number of shares acquired over both years, 150, to get the weighted average price paid of $20. This average is weighted with respect to the number of shares acquired at each price, and not just the absolute price.
Examples of Weighted Averages
Weighted averages show up in many areas of finance besides the purchase price of shares, including portfolio returns, inventory accounting and valuation. When a fund, which holds multiple securities, is up 10 percent on the year, that 10 percent represents a weighted average of returns for the fund with respect to the value of each position in the fund. For inventory accounting, the weighted average value of inventory accounts for fluctuations in commodity prices, for example, while LIFO (Last In First Out) or FIFO (First In First Out) methods give more importance to time than value. When evaluating companies to discern whether their shares are correctly priced, investors use the weighted average cost of capital (WACC) to discount a company's cash flows. WACC is weighted based on the market value of debt and equity in a company's capital structure.