Weighting

Recently, I talked about volume weighting stock prices, where prices associated with high volume were more significant. That was fun! Then Donald W. pointed out these weighting schemes for ETFs. ** That reminded me of the days when I dabbled in various schemes for calculating "weighted averages". Like evaluating a basket of stocks: Creating Indexes Equal-weighted Indexes Comparing Active & Passive performances Then there's weighting when it comes to looking at historical performances ... like weighted moving averages: Exponential Moving Average A host of other averages Mamma mia! That, too, was great fun! Mebbe, when people say: "The average was ..." we should respond: "Average? What average?"   ** Although it's not clear (at first), by "equal weighting" the author means equal dollar amounts invested in each, not equal shares. Here's an interesting fact: Had you bought 1 share in each of the 30 DOW stocks, one year ago, your gain would be 43%. That'd be equal-share-weight, eh? (The DOW Index has this weighting. More dollars are invested in stocks with higher prices.) Aah, but had you bought $1.00 in each of the 30 DOW stocks, one year ago, your gain would be 49%. That'd be equal-dollar-weight, eh? Before we get too excited about doing MUCH better, consider the previous year. Equal-share-weighting would have given us -37% whereas equal-dollar-weighting would have given us -36%. Here's a pretty picture (using the current 30 DOW stocks): For reasons I don't understand, the equal-shares weighting should be the same as the actual DOW. I reckon the DOW components have changed over the past year, eh? After all, GM was dumped ... and wasn't CISCO added?