# price weighted vs. unweighted index value computation

Given three stocks valued at 10,20,60 dollars in a 3 stock portfolio, how would you compute the price weighted index value vs. the unweighted index value? I thought both index types use arithmetic mean computation for their respective values.

You can’t tell anything from only one set of prices.

Let’s add a second set: one month later the prices are, respectively, 15, 22, and 72.

Let’s also suppose that the two indices each start at 100.00.

For the price-weighted index, the divisor is 0.9 (= (10 + 20 + 60) / 100). The value of the index one month later is (15 + 22 + 72) / 0.9 = 121.11.

For the unweighted index, we need the individual stock returns: 15/10 − 1 = 50%, 22/20 − 1 = 10%, 72/60 − 1 = 20%. The average return is (50% + 10% + 20%) / 3 = 26.67%. The value of the index one month later is 100.00(1 + 26.67%) = 126.67.

I’m almost finished with an article on equity indices; I’ll post the link when it’s done.

Sounds good. So how would the unweighted index be adjusted for stock splits from one period to another?

You calculate the return on that stock as if the split never happened.

Suppose that the closing price before the 2:1 split was \$50/share, and the next closing price after the split was \$25.50. You calculate the return as (2 × \$25.50) / \$50 − 1 = 2%.

sounds good. so is the value weighted index weighs each company in the index based upon the market value for the corresponding companies?

Yup.

I’d been working on an article on equity indices (price-weighted, value-weighted, equal-weighted) for a while, and I just finished it; you can find it here: http://www.financialexamhelp123.com/equity-indices/

Full disclosure: as of 4/25 I’ve installed the subscription software on my website, so there’s a charge for viewing the articles.