First Trust DJ Internet Index ETF (NYSEARCA:FDN) seeks investment results that correspond generally to the price and yield (before the fund's fees and expenses) of an equity index called the Dow Jones Internet Composite Indexâ„ .

A quick look at the fund's positions shows some major positions that either carry an EXTREMELY high PE ratio, or are not profitable at all so the PE Ratio is inapplicable (names like AMZN,NFLX,CRM and LNKD appear in the top 10 holdings which comprise some 57% of the total ETF capitalization).

Yet, FDN lists on its web site a seemingly benign PE Ratio of just 23.06 as of 8/31/15 : https://www.ftportfolios.com/Retail/Etf/EtfSummary.aspx?Ticker=FDN

Looking at the numbers, any person with a sharp inquisitive mind would wonder how does First Trust comes up with such a low PE number for the entire ETF.

If we just examine the 4 positions mentioned above which account for about 23% of the entire fund's capitalization we see the following last FY PEs:

AMZN - PE NA (losses in 2014)

NFLX - 182 PE

CRM - 137 PE

LNKD - 96 PE

One might think that First Trust (NYSE:FT), a reputable organization, would apply a forward projected PE in order to account for future potential earning in this portfolio (after all, the past is the past..) - so I looked up consensus estimates for the current fiscal year and came up with the following:

AMZN - 333 PE

NFLX - 439 PE

CRM - 98 PE

LNKD - 87 PE

Doesn't help us much, does it?

Any way you slice it (and I tried, I really tried), whether you use weighted based PEs, simple average PEs, even if you just eliminate all losing companies PEs - you don't get to such a low PE of 23 - not by a long shot!

So how does FT come up with such PE, which intuitively seems wrong to any neophyte with a rudimentary understanding of the Internet Sector valuation?

Introducingâ€¦WEIGHTED HARMONIC AVERAGE PE..

FT gets its PE data from S&P CApital IQ and chose to omit any position with no PE (companies who lost money) from the equation.

They then applied the Harmonic Average (or Mean) to the remaining set of positions.

In essence the Harmonic Mean of a list of numbers tends strongly toward the least high elements of the list, it tends (compared to the arithmetic mean) to mitigate the impact of large outliers and aggravate the impact of small ones.

As such, positions with HUGE PE values , no matter what their weight in the fund, are far less important for the purpose of establishing the fund's PE than companies with much lower PE ratios.

As an aside, there is a school of thought that believes the Harmonic PE is actually the right way to express PE ratios when the population (or sample) has a few data points that are much higher than the rest (outliers), the harmonic mean is the appropriate average to use. But what happens if outliers are the norm in your sample group, when the mean is very high to begin with and there are a few very low PE outliers that get a much weightier significance, does this help the investor or masks true characteristics of the portfolio?

For a bried discussion of means in finance see the link below :

economistatlarge.com/finance/applied-finance/differences-arithmetic-geometric-harmonic-means

So for example, YHOO with a FY 2014 PE of about 20 and a weight of just 3.19% in FDN, would be infinitely more important than AMZN which carries no PE for that year (losses) and has a 11.06% weight in FDN.

As an exercise let us examine just those two positions with a 2015 projected PEs (based on consensus estimates):

AMZN - 333 PE

YHOO - 46 PE

The average of the two PEs would be 189.5

The WEIGHTED average of the two PEs (given the current weights in the FDN portfolio) would be :

(333 X 11.06 + 46 X 3.19) / 14.25 = 268.75

What would be the HARMONIC average?

1 / (0.7761 / 333 + 0.2239 / 46 ) = 138.827

As you can see, this Harmonic weighted average PE is dramatically lower than the simple weighted average PE and gives a lot more weight to low PEs than it gives to very high PEs.

FT is well within its right to use any metric it chooses but I find it very odd that they do not publish the methodology for deriving their PE number on the website, Fact Sheet or Prospectus.

I strongly suspect the vast majority of FDN holders or buyers would benefit from knowing what the weighted average of the portfolio really is and eliminating companies with no PE from the equation further distorts the picture.

While losing companies have no PE to speak of, a portfolio must somehow account for them if it publishes a PE ratio.

If I had to evaluate this portfolio, since its results would be capitalization based (different weights will affect the portfolio differently) , I would use a weighted average PE and would arbitrarily assign a PE of 100 (or the average between 100 and the current year expected PE, if one wants to rid of complete arbitrary assumptions and give some weight for future EPS for companies with no EPS during the last FY) to the companies with no PE as of last FY results.

Granted, one can choose his own arbitrary PEs for companies with no earnings based on one's own valuation preferences but I think FT method in assigning PE ratio to the FDN portfolio is lacking in many ways and masks a lot of useful data to investors.

Comments, as always are cherished.