 # DJIA Price Weighted Index

In the CFAI text, it states that the Price-Weighted Index calculation used by the DJIA has a downward bias due to the sample being weighted on price. As a result, when a stock splits, the value of that stock is lower and therefor brings the average down. However, the text also states that the average is adjusted for changes in the makeup of the index or when a stock splits. If this is the case, wouldn’t a stock split not have an effect on the average? Can someone help me upderstand what I am missing? Thanks! TheChad

Look at an example for this Day*** Stock A***Stock B***Stock C 1*****10******35********100 2*****11******33********104 Divisor of average = 1.5 Day 1 Average = (10 + 35 + 100 ) / 1.5 = 96.67 Day 2: (11+33+104) / 1.5 = 98.67 % change in average = 98.67 / 96.67 - 1 = 2.07% So clearly the increase is driven by the price of the highest stock C. If C had changed to 98 – the Day 2 average would have been lower. (Not doing the calc here). Originally divisor = # of stocks in the average. Over time the divisor changes due to splits and addition / subtraction of companies whose stocks are owned on the average. When a stock split occurs, the divisor is adjusted downwards to hold the market average constant, even though the numerator which is the sum of the prices declines on the average. Say stock C had a 2:1 split – the divisor would be adjusted downwards so the index was the same before and after the split. Day 2 : Average before split = 98.67 Day 2: Average after split = (11 + 33 + 52 ) / New Divisor = 98.67 New Divisor = .9729 As you say above – the average before and after the split are kept the same. (Day 2 average). The price increase of Stock C moved the average upwards – which explained Statement 1:Price-Weighted Index calculation used by the DJIA has a downward bias due to the sample being weighted on price Statement 2: is the mechanics by which the Statement 1 is achieved. I hope I am not confusing the issue further. CP

Thank you for the explanation. I think I am on the right track, but something just isn’t clicking. Using a simple example assuming prices stay the same except for StockC which is reduced due to a split: *******StockA******StockB*******StockC Day1****10**********20**********100 Day2****10**********20***********50 (After StockC splits) The way I am thinking about it, the average in both cases would be: Day1: (10+20+100)/3 = 43.33 Day2: (10+20+50)/1.846 = 43.33 **Where 1.846 is the adjusted divisor to account fo the change in price due to the stock split What factor would be driving the price of this index down that I am not taking into account? Thanks again for your help TheChad

If you had not adjusted the divisor downwards, I think the text is trying to say that the lower price, would have resulted in a lower index as in 80 / 3 = 26.67 instead of 43.33 that you had before. CP