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Author: TMFShadowDragon Big red star, 1000 posts Old School Fool Home Fool CAPS All Star Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 19164  
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 12:20 PM
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Some mathematics - for those with math-phobia - will help to illustrate the difference in the two approaches:

1) Simple PE average weight by % of total portfolio value:

Say for stock "i", the price is p(i) and the earnings are e(i). The PE for stock "i", PE(i), is p(i)/e(i). According to the simple weighted averaging approach the weight for the PE of stock "i", p(i)/ total portfolio value which is the sum of the price for all stocks which I will represent as sum(p). So, the contribution of each stock to the average is:

Contribution to PE Average = PE(i) * (pi/sum(p))

or, expanding term PE(i) which = p(i)/e(i), we get:

Contribution to PE Average = (p(i)/e(i)) * pi / sum(p) = (p(i)^2 / e(i))/sum(p)

Overall average PE = (1/(sum(p)) X sum over all stocks of (p(i)^2 / e(i)).

This approach over weights price (the "price" term is "squared"). It can sometimes work out okay since the total portfolio value, sum(p), can also have an over weighted contribution from a stock for which the price (and PE) has increased dramatically, but often this measure of average PE is easily dominated by a few high PE stocks.

2) DTM's approach is straight forward.

Overall PE = sum of price / sum of earnings = sum(p) / sum(e),

where sum(e) is the sum of earning for all stocks.

3) To see where version 2 is related to individual stock PE values, consider the inverse of PE which is earnings yield. The earnings yield for an individual stock "i" is:

yield(i) = e(i) / p(i)

If we compute the average yield of a portfolio weighted by the price contribution, p(i)/sum(p), of each stock we get:

contribution to yield = (e(i)/p(i)) * p(i) / sum(p) = e(i)/sum(p) since the p(i) terms cancel out.

The average yield of the portfolio becomes:

Portfolio Yield = sum ( e(i) / sum(p) ) for all stocks or

Portfolio Yield = sum(e) / sum(p)

Since PE is the inverse of yield, the portfolio's PE is:

Portfolio PE = sum(p) / sum(e),

which is the same as DTM's method. For the simple example of 2 stocks of the same value with respective PE's 10 and 20. The cheaper stock has 2/3 of the portfolio's total earnings yield and hence contributes that much to the total portfolio PE (the inverse of the portfolio earnings yield).

Cheers
Paul
TMFShadowDragon
Paul
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