price weighted vs. unweighted index value computation

[keep_running]

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.

 

[S2000magician]

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.

 

[keep_running]

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

 

[S2000magician]

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%.

 

[keep_running]

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

 

[S2000magician]

Yup.

 

[S2000magician]

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.