Weighted earnings: they don’t add up… and you may get burned

This post looks at why index earnings are derived by summing earnings of index constituents without first weighting the earnings by index weight (cap-weight or otherwise). While earnings are probably the most widely followed fundamental item, this explanation is applicable to a data point of one’s choice – operating earnings, cash flow, etc. An easy way to understand this kind of fundamental index data is to think of an index, such as the S&P 500, as a hypothetical portfolio.

Consider a theoretical example in which we hold 1,000 shares in each of two stocks, ABC and XYZ. ABC is quite profitable, while XYZ is operating at a loss.

Despite the fact that 95% of the portfolio is invested in a stock with a PE of 13.3 ($40/$3), the portfolio as a whole has a claim to $1,600 in total earnings. We can’t ignore the losses generated by XYZ simply because we wish to – we hold 1,000 shares and each one is losing $1.40.

Dividing portfolio value by portfolio earnings claims gives a ratio of 26.25 – the price to earnings ratio (PE) of the portfolio. PE, calculated on this basis, has the useful property of indicating how long it takes to “earn” back our investment under current conditions – in this case, 26 ¼ years.

Conversely, if we were to weigh earnings claims by portfolio weights we would get the following:

Table B