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Author: pauleckler Big funky green star, 20000 posts Top Favorite Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 19423  
Subject: What is your Avg Portfolio PE? Date: 2/9/2013 4:18 PM
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It is possible to calculate the average PE for a portfolio as follows--

Stock	PE	Value	% of total	PE Fraction
				
Stock A	6	5000	58.82	3.53
Stock B	200	500	5.88	11.76
Stock C	18	2000	23.53	4.24
Stock D	45	1000	11.76	5.29
				
		8500	100.00	24.82

The PE average is the sum of the PE fractions or in this case 24.82.

Stocks with very high PEs or no earnings must be dealt with.  I use a 
dummy value of 200.

A value investor should have low average PE of say 10 or less.
A growth investor might have a PE as high as say 50.
A blue chip investor or a balanced investor should have a PE near the 
S&P average of 16.

If your average is much above 50, I would say you are into speculation.

This is an easy way to check that your portfolio is consistent with 
your strategy.
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Author: DrtThrwingMonkey Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13452 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/9/2013 4:43 PM
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Stock PE Value % of total PE Fraction

Stock A 6 5000 58.82 3.53
Stock B 200 500 5.88 11.76
Stock C 18 2000 23.53 4.24
Stock D 45 1000 11.76 5.29

8500 100.00 24.82

The PE average is the sum of the PE fractions or in this case 24.82.

Stocks with very high PEs or no earnings must be dealt with. I use a
dummy value of 200.



Fraction arithmetic doesn't actually work this way, and this is shown by your calculation which obtains the wrong result. Stock A has a low PE (6), and constitutes almost 2/3 of your 4-stock portfolio, so even if the 3 other stocks had zero earnings, your PE should be just over 10. If the other 3 stocks have any earnings at all, the real average would be under 10.

It would be methodologically better to add a column, 'Earnings', so that for chart becomes:

Stock PE Value Earnings % of total PE Fraction

Stock A 6 5000 833.3 58.82 3.53
Stock B 200 500 2.5 5.88 11.76
Stock C 18 2000 111.1 23.53 4.24
Stock D 45 1000 22.2 11.76 5.29

Total 8500 969.16 100.00 24.82



Your average P/E is now just the sum of the Value (price) divided by the sume of the E (earnings), in other words, 8500/969.17 = 8.77.

This method handles high or negative ratios without the need for any dummy value, and in fact you don't need your last 2 columns either. Your actual results might be a little different, since Stock B's earnings are maybe not 2.5, if that 200 multiple was a dummy.

Regards, DTM

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Author: TMFHockeypop Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13454 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/9/2013 8:57 PM
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I'm no DTM but I figure ave is 17 PE for eight individual stocks. HP

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Author: RaptorD2 Big gold star, 5000 posts Top Favorite Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13459 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 3:08 AM
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Weight adjusted, mine average 28.8 due to some large positions with P/E's in the mid- to upper- 90's. Some of my higher CAGR's, however, are from stocks with single-digit P/E's.

< GULP >

(I use several of Microsoft's StockQuote functions in my portfolio spreadsheet and P/E is shown for all holdings.)

Dan

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Author: Carpian Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13464 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 9:21 AM
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OK, this is officially making my head spin. Let's simplify the calculation, and suppose you are holding equal values of 2 stocks, one with a PE of 10 and one with a PE of 20. Shouldn't your average PE be 15? That is what Paul's method produces.

DTM's method produces an average PE of 13. Why should the stock with the PE of 10 contribute more heavily to your "average PE" than the equal value of stock with a PE of 20?

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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: 13466 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 11:11 AM
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Hi Carpian

The two calculations estimate two different things. The PE fraction method provides a simple average, weighted by price, across a population of stocks. DTM's method is the overall PE of the portfolio. Your PE 10 stock contributes more because it contributes more (i.e., 2/3) of the earnings of the portfolio.

The "simple average, weighted by price" is about the worst way to estimate the PE of a basked of equities to determine if it is over or under priced.

Take a basket of 20 stocks of equal value in a portfolio. Nineteen (19) have a PE of 10 and one (1) has a PE of 1000. The simple average approach provides an overall PE of 59.5 while the total price / total earnings has an overall PE of 10.52. Even replacing the PE of 1000 with the arbitrary PE value of 200 still gives an overall PE of 10.5.

Which do you think better reflects the "price to earnings" of the basket of equities? Even using the mode (PE of 10 in this case) is a better approach. All of which shows that a highly valued market using a simple average weighted by market capitalization can mask a considerable number of low priced equities.

In my view the simple average weighted by market capitalization / portfolio value is a nearly meaningless statistic.

Cheers

Paul
TMFShadowDragon

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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: 13470 of 19423
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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Author: DrtThrwingMonkey Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13471 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 1:48 PM
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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).



ShadowDragon's reasoning is correct.

The average of two PE's of 10 and 20 is not 15, even if that would seem logical at first glance. This is sort of akin to the common mathematical problem of paddling downstream at 10 km/h and back upstream at 20 km/h, and not having an average speed of 15 km/h, despite the same (false) intuition you would have with your 2 P/E ratios.

In both cases, you have fractions, X/Y, with X/Y behaving properly and Y/X not behaving properly. So for instance it is true that the average of 2 and 4 is 3, but it is not true that the average of 1/2 and 1/4 is 1/3.

With your P/E's of 10 and 20, it is the same thing, except that the 'well-behaved' fraction is not P/E, it is E/P, aka earnings yield. It is better to think of your stocks trading at 10 and 20 times earnings as giving you yields of 10% and 5%, respectively, with an average yield of, yes, 7.5%. If you turn that earnings yield of 7.5% on its head, you get 13.3, the correct answer.

Maybe you are not quite convinced yet. "The average of 10 and 20 is 15, I'm not going to be persuaded to abandon the obviously correct answer and say that the average of 10 and 20 is 13.333!", you might reasonably say. In the same way, you might say that the canoeist's average speed is 15, calculations be damned. And in a way, you would be right: you had two speeds during your return trip, and the average of those two speeds was 15. It's just that you spent 2/3 of your time going at 10, and only 1/3 of the time going at 20, so it would make more sense for you to weight your speeds by time, NOT weight by distance. In the same way, you should weight your P/E's by earnings, not by price.

In the end, you can do it any way you want, but doing it my way will give you a more sensible answer, the same answer you would get by just adding all the earnings and all the prices and calculating the ratio of the sums, as in Dragon's calculation.

Regards, DTM

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Author: pauleckler Big funky green star, 20000 posts Top Favorite Fools Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13472 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 1:55 PM
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Thanks to all for their input. It's remarkable what you can learn on Motley Fool's discussion boards.

FWIW, I calculate the PE of essentially my CAPs portfolio at 16.04. That is remarkably low compared to where I thought I might be.

Looks like I am being reasonably conservative in spite of a few high fliers.

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Author: 38Packard Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13474 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 5:49 PM
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JNJ = PE of 24.75
PG = PE of 24.51
Weighted PE = 24.67
Much higher than I thought - but JNJ and PG have both been on a roll lately.

'38Packard

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Author: stillwater9999 Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13475 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 7:36 PM
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13.2

But still have plenty of stocks with huge potential.

You do not have to pay high multiples.

sw

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Author: BenHacker Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13477 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 8:00 PM
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For everyone who is having trouble averaging "PEs" after the (excellent) summaries by DTM, just switch to earnings yields or "EPs" and you're going to find yourself in a much more logical place.

Two stocks at 10x and 20x (PEs) become 10% and 5% respectively when looking at EPs.

The "average" of 10% and 5% is 7.5%, or a 13.33 PE. Probably more intuitive for most of us.

Ben

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Author: Carpian Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13481 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/10/2013 9:23 PM
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Thanks for the responses and clarifications! I think I'm getting it now.

Interestingly enough, the weighted average of PE ratios by value of holding seems to be the method used by Morningstar in computing the PE ratio for mutual funds. But it may not be the best look at the picture.

http://www.morningstar.com/InvGlossary/price_earnings_ratio....

The (P/E) ratio of a fund is the weighted average of the price/earnings ratios of the stocks in a fund's portfolio. The P/E ratio of a company, which is a comparison of the cost of the company's stock and its trailing 12-month earnings per share, is calculated by dividing these two figures.

At Morningstar, in computing the average, each portfolio holding is weighted by the percentage of equity assets it represents, so that larger positions have proportionately greater influence on the fund's final P/E.


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Author: physdude One star, 50 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 13485 of 19423
Subject: Re: What is your Avg Portfolio PE? Date: 2/11/2013 12:38 AM
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One option common in academic circles is to use the log of the ratio as this is agnostic to the directionality of the fractions. It always leads to somewhat sensible results (though geometric averages might be more difficult to intuitively get).

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