## Morningstar and P/E TTM: what a wonderful world!

### Morningstar and P/E TTM: what a wonderful world!

I confess having some level of interest with valuation metrics, and a lingering question is always: going beyond the S&P 500, what is the current and historical PE10 (aka CAPE) for a given fund (e.g. Vanguard or else)? The trailing twelve month (TTM) PE, that is, not those strange forward-PE guesses that analysts are fond of.

I thought this would be an easy question to answer if only I could get the current and historical earnings (TTM) for a given fund. Then get the price (or market cap) and do the math... Simple, right? Or maybe get the P/E (TTM) for a given year, infer the "E", and then do the math for PE10.

It happened that I had a 2-weeks trial with Morningstar Direct, hence full access to their database of information. A simple Excel query, and I had historical prices, returns, dividends, market caps, number of shares, lots of stuff. But no earnings (or earning yield, or EPS). Really?

Ok, let's take the P/E TTM, then. So I did, and did a quick sanity check against Vanguard's current values (as of 07/31/16), and also S&P for the S&P 500. Hm, not quite aligned, and sometimes totally disconnected values. Huh? Then I checked the history of VFINX and S&P 500 index itself, and although the difference is often around 10%, in times of crisis, the Morningstar values are quite muted. What is going on?

I thought this would be an easy question to answer if only I could get the current and historical earnings (TTM) for a given fund. Then get the price (or market cap) and do the math... Simple, right? Or maybe get the P/E (TTM) for a given year, infer the "E", and then do the math for PE10.

It happened that I had a 2-weeks trial with Morningstar Direct, hence full access to their database of information. A simple Excel query, and I had historical prices, returns, dividends, market caps, number of shares, lots of stuff. But no earnings (or earning yield, or EPS). Really?

Ok, let's take the P/E TTM, then. So I did, and did a quick sanity check against Vanguard's current values (as of 07/31/16), and also S&P for the S&P 500. Hm, not quite aligned, and sometimes totally disconnected values. Huh? Then I checked the history of VFINX and S&P 500 index itself, and although the difference is often around 10%, in times of crisis, the Morningstar values are quite muted. What is going on?

### Re: Morningstar and P/E TTM: what a wonderful world!

I started to ask nosy questions and do some Web searches, and stumbled upon this methodology document from Morningstar, explaining that they weed out some 'outlier' values (negative PEs, PE>60) of individual stocks between aggregating in a fund-level PE. And yes, companies like Vanguard tell them what stocks are part of a given fund at one point in time. Then the document elaborates on a recent change, switching to the use of harmonic averages instead of arithmetic averages to further reduce the impact of outliers.

Ok... But... Why exactly would we ignore data points like companies in distress (e.g. negative earnings)? And why exactly is there a need to compute an average? I mean, it shouldn't be complicated to compute the PE of a fund, just add the combined market caps (in absolute $$), just add the combined earnings (in absolute $$), divide one by the other and normalize to the (fund) price per share. There is no 'averaging' in this process, nor issues with outlier values.

So I kept annoying the poor girl from trial customer support (who's been very patient and very nice, I have to say) and she finally sent me an Excel file from their data team with the most recent math for VFINX. Cool. So I checked it, found the numbers for the individual stocks (500-ish of them, of course), ad checked the formulas. Ok, I saw the logic for weeding out the outliers (<0, >60) and the harmonic kind of math.

And then I realized what was the true root cause of the issue.

Since I had the Excel file, I tweaked it, did the math in the 'classic' way, and funny, I ended up with a number much better aligned with the value computed by S&P itself. I was quite baffled to say the least, and did some further Internet research, and found this 15-years-old thread with multiple people expressing the same disbelief, and a Morningstar rep sticking to his (strange) views:

http://socialize.morningstar.com/NewSoc ... 32998.aspx

Ok... But... Why exactly would we ignore data points like companies in distress (e.g. negative earnings)? And why exactly is there a need to compute an average? I mean, it shouldn't be complicated to compute the PE of a fund, just add the combined market caps (in absolute $$), just add the combined earnings (in absolute $$), divide one by the other and normalize to the (fund) price per share. There is no 'averaging' in this process, nor issues with outlier values.

So I kept annoying the poor girl from trial customer support (who's been very patient and very nice, I have to say) and she finally sent me an Excel file from their data team with the most recent math for VFINX. Cool. So I checked it, found the numbers for the individual stocks (500-ish of them, of course), ad checked the formulas. Ok, I saw the logic for weeding out the outliers (<0, >60) and the harmonic kind of math.

And then I realized what was the true root cause of the issue.

**Morningstar computes a weighted average of the individual stocks PE (TTM)**. Say what? Think about it for a second. They don't add the market cap, then add up the earnings, no, they make an average of the individual P/Es. Which is of course NOT mathematically equivalent to the regular way of doing things, and of course gets them in trouble when "E" values get negative or null or very small. And then they added the harmonic logic to make it 'prettier'. Oh, and they do the same kind of trick for Price/Sales, Price/Book, etc.Since I had the Excel file, I tweaked it, did the math in the 'classic' way, and funny, I ended up with a number much better aligned with the value computed by S&P itself. I was quite baffled to say the least, and did some further Internet research, and found this 15-years-old thread with multiple people expressing the same disbelief, and a Morningstar rep sticking to his (strange) views:

http://socialize.morningstar.com/NewSoc ... 32998.aspx

### Re: Morningstar and P/E TTM: what a wonderful world!

Now what are the consequences of this 'creative' approach? Well, first, this is pretty confusing. Next, you just cannot compare the PE TTM computed by Morningstar with the PE TTM from other sources (say Yahoo or Vanguard or Prof. Shiller).

Furthermore, since Morningstar doesn't provide access to the earnings themselves, there is no way one can reconstruct the 'classic' PE (or infer PE10). And for those of you who use 1/PE (or 1/PE10) as an expected returns model, well, be VERY careful to the source you're using.

So... either you like the Morningstar methodology (I don't!) and you stay in their world, or... you stick to the Vanguard current value (hence no history), or... Well, I don't know. Where else can we find reliable historical earnings (and sales, and book value) for funds?

Side note #1: I think we may want to add a bit to the P/E wiki page, and provide more details on the various ways used by various sources to do their respective math.

Side note #2: Morningstar Direct is a costly subscription (and I'll pass). One can find the Morningstar PE TTM on the YCharts Web page though (e.g. here is an example). YCharts is clearly aware of the issue, and relabeled the data point as "Weighted Average PE Ratio", which is indeed a much better characterization of what Morningstar does. Oh, and the P/E displayed on the regular Morningstar pages is a forward-PE (the guesswork from analysts), not a trailing PE.

Furthermore, since Morningstar doesn't provide access to the earnings themselves, there is no way one can reconstruct the 'classic' PE (or infer PE10). And for those of you who use 1/PE (or 1/PE10) as an expected returns model, well, be VERY careful to the source you're using.

So... either you like the Morningstar methodology (I don't!) and you stay in their world, or... you stick to the Vanguard current value (hence no history), or... Well, I don't know. Where else can we find reliable historical earnings (and sales, and book value) for funds?

Side note #1: I think we may want to add a bit to the P/E wiki page, and provide more details on the various ways used by various sources to do their respective math.

Side note #2: Morningstar Direct is a costly subscription (and I'll pass). One can find the Morningstar PE TTM on the YCharts Web page though (e.g. here is an example). YCharts is clearly aware of the issue, and relabeled the data point as "Weighted Average PE Ratio", which is indeed a much better characterization of what Morningstar does. Oh, and the P/E displayed on the regular Morningstar pages is a forward-PE (the guesswork from analysts), not a trailing PE.

### Re: Morningstar and P/E TTM: what a wonderful world!

Forgive me if I missed it, but what was the ttm p/e you found after going through the data?

### Re: Morningstar and P/E TTM: what a wonderful world!

FWIW, we've had several other threads where it's been pointed out that mutual funds, and indexes use different methodologies to calculate the fund vs the indexes P/E ratio.

You can find the historic P/E ratio of Vanguard's index funds by going through their historic annual reports in the SEC database

https://www.sec.gov/edgar/searchedgar/mutualsearch.html

(Look for the N-CSR filings for more recent annual reports, or the N-30D filing for some older ones pre 2003)

https://www.sec.gov/cgi-bin/browse-edga ... cd=filings

https://www.sec.gov/cgi-bin/browse-edga ... cd=filings

(The valuation data is usually listed in the report under the heading "Portfolio Characteristics")

You can get the earnings for the S&P500

WSJ: The S&P Gets Its Earnings Wrong

WSJ: The Inexact Business of Valuing ETFs

You can find the historic P/E ratio of Vanguard's index funds by going through their historic annual reports in the SEC database

https://www.sec.gov/edgar/searchedgar/mutualsearch.html

(Look for the N-CSR filings for more recent annual reports, or the N-30D filing for some older ones pre 2003)

https://www.sec.gov/cgi-bin/browse-edga ... cd=filings

https://www.sec.gov/cgi-bin/browse-edga ... cd=filings

(The valuation data is usually listed in the report under the heading "Portfolio Characteristics")

You can get the earnings for the S&P500

*Index*from S&P ( http://us.spindices.com/documents/addit ... s-est.xlsx ), but one should be aware that this data at times will conflict with how a mutual fund comes up with the P/E for it's portfolio of individual stocks. A mutual fund will often weight the individual company P/E's, and possibly throw out the extremes that would cause the math to fall a part, whereas the index itself typically adds all the earnings of all the companies together as if it was one big pool of earnings and then puts the total index price over that... which may sound reasonable at first, but it does cause some extreme abnormalities that aren't quite right in situations like 2008/2009 when there were losses by just a small number of companies by weight that were big enough to offset all of the earnings by the majority of the index, despite the fact that any liability caused by the other companies doesn't necessarily flow over to be the liability of some other company.WSJ: The S&P Gets Its Earnings Wrong

WSJ: The Inexact Business of Valuing ETFs

"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

### Re: Morningstar and P/E TTM: what a wonderful world!

Thanks a lot for the background, JoMoney. I had no idea that I had stumbled on an old Siegel vs S&P dispute, that is funny. For reference, here is the short (and in my humble opinion very much to the point) answer from S&P: S&P Does the Earnings Correctly. And a longer rebuttal from Seeking Alpha. And here is some background from S&P itself on how it does the math.JoMoney wrote:You can get the earnings for the S&P500Indexfrom S&P ( http://us.spindices.com/documents/addit ... s-est.xlsx ), but one should be aware that this data at times will conflict with how a mutual fund comes up with the P/E for it's portfolio of individual stocks. [...]

WSJ: The S&P Gets Its Earnings Wrong

Ok, so we established that Morningstar and Prof. Siegel support a cap-weighted computation of the P/E ratio. While S&P and Prof. Shiller support a simple process of adding up market caps and earnings (which are usually proportional to the size of the company, if I may say).

Do you know what exact procedure Vanguard uses? Because while I was looking at the issue, it did seem that their numbers didn't align with either Morningstar or S&P for VFINX...

Last edited by siamond on Mon Sep 19, 2016 4:27 pm, edited 1 time in total.

### Re: Morningstar and P/E TTM: what a wonderful world!

Most mutual funds use a weighted average of the individual stock P/E in their portfolio, and they treat index mutual funds the same way they do their other portfolios. But some of them do different things (like throw out, or discount the weighting) on extreme P/E's like negative earnings or P/E over 60 or over 100 or some other threshold.

The other WSJ article I linked had Vanguard saying they use a "harmonic mean" of the P/E ratios, which essentially means they weight them as they are int he portfolio, but I'm not sure if they do anything 'funny' with the outlier/immeasurable PE's

The other WSJ article I linked had Vanguard saying they use a "harmonic mean" of the P/E ratios, which essentially means they weight them as they are int he portfolio, but I'm not sure if they do anything 'funny' with the outlier/immeasurable PE's

"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

### Re: Morningstar and P/E TTM: what a wonderful world!

Ah, thank you, I was struggling with the WSJ firewall and only read the 2nd article one minute ago. Sheesh, this is disappointing, so Vanguard do something similar to Morningstar then (well, clearly with some twists in the process as their numbers do NOT match Morningstar, as I previously explained, and by a mile when it comes to VEA and VWO). Here is another old thread from 2000 which might help understand the Vanguard procedure, assuming it didn't change. Note that Morningstar did change their procedure since then, as I explained in my intro.JoMoney wrote:The other WSJ article I linked had Vanguard saying they use a "harmonic mean" of the P/E ratios, which essentially means they weight them as they are int he portfolio, but I'm not sure if they do anything 'funny' with the outlier/immeasurable PE's

I have to say I fail to understand the logic of doing a weighted average of individual P/Es... If two companies merge, to begin with (barring speculative forces), their market caps will be additive, and their earnings will be additive. A $ is a $. And yet neither the arithmetic nor the harmonic mean of the PEs will provide the same result before and after merger... Seems to me Prof. Shiller and S&P are correct. But the argument must be more complicated than that...

### Re: Morningstar and P/E TTM: what a wonderful world!

Morningstar gets their holdings information from regulatory filings so it is often sparse and extremely delayed. If you want accurate and comparable numbers you basically need to do it yourself. You also really have to watch how negative P/Es get treated.

Price can be used as a denominator to avoid this problem and for consistency (earnings yield, dividend yield, etc...).

As you have learned, there are numerous ways of calculating even basic portfolio statistics. Just wait until you try to reproduce a 3-year daily standard deviation calculation.

Price can be used as a denominator to avoid this problem and for consistency (earnings yield, dividend yield, etc...).

As you have learned, there are numerous ways of calculating even basic portfolio statistics. Just wait until you try to reproduce a 3-year daily standard deviation calculation.

### Re: Morningstar and P/E TTM: what a wonderful world!

It would be great to summarise some of the issues you and JoMoney discuss on the wiki for future generationssiamond wrote:Side note #1: I think we may want to add a bit to the P/E wiki page, and provide more details on the various ways used by various sources to do their respective math.

This feels like yet another indicator of the shaky foundation that any backtesting house of cards is built upon -- whether it is used for trading strategies, retirement planning, or barroom bets. Not that we have any real alternatives....

Some other similar things off the top of my head

- Ibbotson's historical bond data methodology

- The Cowles Commission throwing out 1/6th of US stocks for the period 1871-1937 (which is what Shiller uses; the Dimson-Marsh-Staunton database includes these, however).

- Until very recently, there was no source for Over The Counter stocks (i.e. NASDAQ) before 1972; Global Financial Data just added these 9,000 stocks to their database.

- And, of course, all the global data which is only now slowly becoming available.

### Re: Morningstar and P/E TTM: what a wonderful world!

Yes, thank you, that is indeed a (rather painstaking!) way to get historical information. Sadly, if I am not mistaken, Vanguard doesn't report the cumulative earnings of the companies held in a given fund in such reports. They do report the cumulative market cap, and the list of companies, but not the corresponding cumulative earnings. Same issue as Morningstar. And then Vanguard has its own P/E math, which they succinctly describe in the reports as:JoMoney wrote:You can find the historic P/E ratio of Vanguard's index funds by going through their historic annual reports in the SEC database

*Price/Earnings Ratio. The ratio of a stock’s current price to its per-share earnings over the past year. For a fund, the weighted average P/E of the stocks it holds.*

Which severely lacks specifics (what type of average? what happens to negative or null or very small earnings? etc). And I can't find a detailed methodology document on their Web site. Which is a bit hard to swallow, if one decides to do their own 'special' math for such a well-known quantity, and deviate from the way S&P does it for its indexes, then they'd better clearly document it... Did I miss something?

---------------------

Unrelated PS for my own reference: here is a good 2013 thread pointing to a video from Prof. Siegel explaining his views on the matter; and including eloquently articulated counter views from Nisiprius - which I totally agree with.

---------------------

EDIT: Quote from the 2006 WSJ article: The Inexact Business of Valuing ETFs

*Joseph Brennan, a Vanguard executive, says the company uses what mathematicians call the "harmonic mean" in calculating an average earnings figure for its funds' P/E ratios. He adds that there are various ways to calculate a P/E, and investors shouldn't be using one number to compare funds. "Buyers need to understand the statistics they are looking at," he says.*

Last edited by siamond on Tue Sep 20, 2016 11:21 pm, edited 1 time in total.

### Re: Morningstar and P/E TTM: what a wonderful world!

Aiming at an extension of the Wiki page, here is my understanding so far of PE TTM methodologies when used for funds:AlohaJoe wrote:It would be great to summarise some of the issues you and JoMoney discuss on the wiki for future generations

S&P (and Prof. Shiller): price-per-share / aggregate-earnings (simple sum of individual earnings) per share

=> FACTUAL

Morningstar/YCharts: weighted harmonic average of individual P/Es, filtering companies with negative earnings, capping individual P/Es to 60, weights according to individual market cap vs aggregate market cap of selected companies

=> FACTUAL (since 2015, weighted arithmetic average of filtered P/Es was used before)

Vanguard: weighted harmonic average of individual P/Es, with no filtering (negative earnings are fine)

=> MY CURRENT UNDERSTANDING, WOULD LIKE A HARD CONFIRMATION & REFERENCE

Yahoo: PE TTM not provided for funds

iShares: excludes negative P/Es (see fact sheet description), not sure how averaging is performed

Research Affiliates and Star Capital (International PE/CAPE): don't know

**Any further information and/or correction would be appreciated.**

### Re: Morningstar and P/E TTM: what a wonderful world!

I got confirmation from the Vanguard support people that the description in my previous post was correct. There is no externally visible document documenting this fact though. Here is a short summary.

1. S&P computes the S&P 500 P/E by dividing the current index price by the sum of the earnings (positive or negative) of all constituents.

2. Prof. Shiller uses the same methodology as S&P in his S&P 500 historical series.

3. Vanguard computes the P/E of a fund by using a weighted harmonic average of the individual P/E of all constituents (even if earnings are negative or vey low). The weights are based on market caps.

4. Morningstar also uses a weighted harmonic average, but remove all constituents with a negative P/E, and caps remaining individual P/Es to a maximum of 60 before computing the average.

I'll expand the P/E wiki page to capture those findings, and include a few pointers that were discussed in this thread.

1. S&P computes the S&P 500 P/E by dividing the current index price by the sum of the earnings (positive or negative) of all constituents.

2. Prof. Shiller uses the same methodology as S&P in his S&P 500 historical series.

3. Vanguard computes the P/E of a fund by using a weighted harmonic average of the individual P/E of all constituents (even if earnings are negative or vey low). The weights are based on market caps.

4. Morningstar also uses a weighted harmonic average, but remove all constituents with a negative P/E, and caps remaining individual P/Es to a maximum of 60 before computing the average.

I'll expand the P/E wiki page to capture those findings, and include a few pointers that were discussed in this thread.

### Re: Morningstar and P/E TTM: what a wonderful world!

Thanks siamond, this is a very interesting thread. And the link to M*s discussion was priceless.

Paul

Paul

When times are good, investors tend to forget about risk and focus on opportunity. When times are bad, investors tend to forget about opportunity and focus on risk.

### Re: Morningstar and P/E TTM: what a wonderful world!

Cap-weighted E/P makes more sense than cap-weighted P/E, right? If an index has 50% weight in two stocks, each priced at 100, and with annual earnings of $1 and $10, the average P/E is (100 + 10)/2 = 55, the average E/P is (1/100 + 1/10) = 5.5%, and aggregate earnings divided by aggregate price is 11/200, which is also 5.5%. An E/P of 5.5% equates to a P/E of 18.2, which is what should be reported, not 55.siamond wrote:Ok, so we established that Morningstar and Prof. Siegel support a cap-weighted computation of the P/E ratio. While S&P and Prof. Shiller support a simple process of adding up market caps and earnings (which are usually proportional to the size of the company, if I may say).

### Re: Morningstar and P/E TTM: what a wonderful world!

The reason you may want to set negative earnings to zero when computing aggregate earnings is because of limited liability. A loss-making company is not worth less than zero. Otherwise, if you think a fair P/E at the aggregate level is 20, adding a company with negative earnings of $1 billion to a an index reduces the fair value of the index of $20 billion. Amazon lost money for many years, but it was not worth less than zero during that time.siamond wrote:Ok... But... Why exactly would we ignore data points like companies in distress (e.g. negative earnings)? And why exactly is there a need to compute an average? I mean, it shouldn't be complicated to compute the PE of a fund, just add the combined market caps (in absolute $$), just add the combined earnings (in absolute $$), divide one by the other and normalize to the (fund) price per share. There is no 'averaging' in this process, nor issues with outlier values.

An empirical question is what has better predicted stock market returns -- a P/E computed with negative earnings set to zero or a P/E without this adjustment.

### Re: Morningstar and P/E TTM: what a wonderful world!

Following up on my previous post:

It is common to value a company at a multiple of its earnings, but this breaks down when earnings are negative or close to zero. Empirically, how does the stock market value loss-making companies? Some possibilities are as a multiple of

(1) average earnings over the last 5-10 years. This is plausible for cyclical companies

(2) estimated future earnings.

(3) book value

(4) sales

If you want to value an index from the ground up, metrics beyond earnings should be considered, especially for unprofitable companies.

It is common to value a company at a multiple of its earnings, but this breaks down when earnings are negative or close to zero. Empirically, how does the stock market value loss-making companies? Some possibilities are as a multiple of

(1) average earnings over the last 5-10 years. This is plausible for cyclical companies

(2) estimated future earnings.

(3) book value

(4) sales

If you want to value an index from the ground up, metrics beyond earnings should be considered, especially for unprofitable companies.

### Re: Morningstar and P/E TTM: what a wonderful world!

Yes, I agree, and both Vanguard and Morningstar now use a harmonic average (hence cap-weighting individual E/Ps). Now it is much less clear if a harmonic average computation is better than the simple additive process used by S&P. If you had used different weights in your example, you'd find a different result between the two approaches. Your point about company liability is certainly interesting. On the other hand, if both companies suddenly merged (say without any restructuring to begin with), then earnings should be additive, market caps should be additive too, and the harmonic average approach doesn't make sense. In other words, I can appreciate that there are pros & cons in this story.Beliavsky wrote:Cap-weighted E/P makes more sense than cap-weighted P/E, right? If an index has 50% weight in two stocks, each priced at 100, and with annual earnings of $1 and $10, the average P/E is (100 + 10)/2 = 55, the average E/P is (1/100 + 1/10) = 5.5%, and aggregate earnings divided by aggregate price is 11/200, which is also 5.5%. An E/P of 5.5% equates to a P/E of 18.2, which is what should be reported, not 55.siamond wrote:Ok, so we established that Morningstar and Prof. Siegel support a cap-weighted computation of the P/E ratio. While S&P and Prof. Shiller support a simple process of adding up market caps and earnings (which are usually proportional to the size of the company, if I may say).

The upper level conclusion is that one shouldn't compare fund (or index) P/Es between Morningstar, Vanguard and S&P simply because they are not computed in the same way - which wasn't obvious to me until a few weeks ago, and is a poorly documented fact.

### Re: Morningstar and P/E TTM: what a wonderful world!

This would indeed be interesting to do. Sadly, besides Prof. Shiller database, there is little such history being kept. Morningstar did archive some P/E history, but only starting from 1999, which is definitely not enough to do such an empirical test. So I guess that one would have to come back to individual holdings, dig up related prices and earnings from CRSP, and assemble some synthetic index (S&P 500 or else) to compare the various methodologies. Sounds like a solid research project to delegate to a young grad student!Beliavsky wrote:An empirical question is what has better predicted stock market returns -- a P/E computed with negative earnings set to zero or a P/E without this adjustment.

### Re: Morningstar and P/E TTM: what a wonderful world!

Ok, I took a stab at expanding the P/E wiki page, adding a section about fund & index P/Es. Feedback welcome.

### Re: Morningstar and P/E TTM: what a wonderful world!

For archive, here is the final answer from Vanguard Support about this matter.

The following is our methodology for calculating the P/E ratio for our

funds. The calculations are completed by the Bank of New York Mellon and it

would be applied to all of the securities within a fund.

The dollar-weighted harmonic mean of individual company P/E ratios is used.

This approach first considers holdings' E/P ratios (aka Earnings yield),

which then are summed on a dollar-weighted basis across the entire

portfolio to achieve a portfolio E/P ratio. Finally the inverse of this

ratio is taken to arrive at the more familiar P/E ratio. The

dollar-weighted methodology includes cash and does not set min/max P/E

levels.

This calculation is equivalent to summing the holdings' prices and dividing

that result by the sum of the holdings' earning-per-share. Because harmonic

mean methodology is employed, negative P/E ratios actually may increase the

portfolio average. This is appropriate because, in theory, a negative P/E

ratio (which is necessarily only caused by negative earnings-per-share,

since prices cannot be less than zero) represents a very high price

relative to the earnings stream purchased.

Harmonic mean methodology is based on the E/P ratios and results in a

continuous distribution from worst to best of all companies with earnings

data, including those with negative earnings. Other approaches using the

more familiar P/E ratio do not yield a continuous distribution when

companies with negative earnings are included. Additionally, distortions

caused by companies with very small earnings relative to their prices (and

thus that have astronomical P/E ratios) are eliminated by the use of E/P.

The following example illustrates the difference between averages based on

P/Es and averages based in E/Ps (harmonic means) when one company has

negative earnings. Please note that the stocks have equal weights.

By taking the inverse of the E/P portfolio average (1/0.025) you arrive atCode: Select all

`P/E E/P Company A 10 0.10 Company B -20 -0.05 Portfolio Average P/E = -5.0 E/P = 0.025`

a P/E for the portfolio = 40.0

The straight P/E calculation results in a nonsensical -5, while the

harmonic mean (using E/Ps and then taking the inverse) results in a P/E of

40. This is exactly the same number arrived at if one were to separately

sum all prices of the stocks in the portfolio and divide that value by the

sum of all earnings.