Weighted Average

A weighted average is a mathematical formula that takes into account the relative size or importance of each item in a list of financial data rather than a simple average of all of the items. Unlike an arithmetic average, which simply totals all of the numbers in a list and then divides that figure by the number of items in the list, a weighted average places additional importance, or weight, on additional factors. However, all of the weights in the list combined will equal 100%, or 1.

In investing, weighted averages are important in measuring various things, such as the true return on a portfolio of stocks. A weighted average would take into account what proportion of the portfolio is invested in individual stocks. Obviously, if 50% of the portfolio is invested in just one stock, while the rest of the portfolio is invested in five other companies, that one stock would have a disproportionate effect on the portfolio's return and would skew the average. A weighted average would take that imbalance into account.

For example, let's say an investor's portfolio totals US$100,000, with US$50,000 invested in one stock, while the remainder of the portfolio is invested equally in five other companies, or US$10,000 each. The return on the large stock holding was 5% for the year, while the return on each of the other five stocks was 10%. Using a simple average, the return on that portfolio would be 9.16%. We would get to that figure by adding each of the individual stock's returns and dividing by the number of stocks, as follows: 5%+10%+10%+10%+10%+10%= 55% divided by 6 = 9.16%.

However, to get a more accurate reading of the portfolio's return, we need to take into consideration that half of the portfolio underperformed the rest of it. So we need to place a greater weight on the stock that takes up half of the portfolio, while placing less on the other stocks, each of which accounts for only 10%.

In this case, we would calculate the weighted average using this formula: (.50 x 5%) + (.20 x 10%) + (.20 x 10%) + (.20 x 10%) + (.20 x 10%) + (.20 x 10%) = 7.5%.

As you can see, the weaker performance in the large stock holding has pulled down the return of the entire portfolio by virtue of its oversized weight.

Of course, different weights can be used to calculate a portfolio's return. We may also weigh the portfolio based on the price of the stocks in it, with the highest-priced stocks accounting for a larger share versus the lower-priced stocks. This is the basic difference between how two of the most common equity averages—the Dow Jones Industrial Average and the S&P 500—are calculated.

In addition to having a different number of stocks in each index—the DJIA has 30 stocks while the S&P 500 has 500—they are each calculated differently.

The DJIA, for instance, places a greater weight on the stocks in the index with the highest price per share, while the S&P places a greater weight on each stock's market capitalisation, that is, its total value calculated by multiplying its price per share by the number of shares outstanding.

As a result, Boeing Corp., at an example price of more than US$300 a share, has the greatest weight in the DJIA, larger even than Apple, which has a much greater market value (US$812 billion versus US$178 billion for Boeing) but whose share price in this example was about US$173.

In the S&P 500, however, Apple carries the greatest weight by virtue of its market cap, while Boeing doesn't even rank in the top 20. As a result, many investors believe the S&P 500 more accurately measures the stock market, not just because it follows more stocks.

Summary

A weighted average is a mathematical formula that takes into account the relative size or proportion of each item in a list of financial data rather than a simple average of all of the items.

A weighted average is important in measuring the performance of an investment portfolio because it takes into account how much money is invested in each item in the group, rather than a simple average of the returns on each item, with the largest holdings carrying the greatest weight.

However, investors can choose how much weight to assign to each item. For example, the DJIA places the most weight on the share price of each individual stock in the index, while the S&P 500 places the most weight on each stock's market capitalisation.