### Efficient Frontier Polishes the Turd

Efficient Frontier has re-designed their website, although I’m not certain why, since the old version looked as nice and was as easy to navigate as the new one, in my opinion. They’ve made their ‘SEM Product Tour’ button more prominent, which I assume is intended to get more people to watch the video slideshow.

I’ll spare you the trouble of watching it, since there’s really only one interesting part. About 10 seconds in, a slide appears which looks like:

For those who can’t see the image, it says: “Our platform is built for the complexity of modern SEM” and “88+ Million Keywords Actively Managed”.

There’s also a graph which, though unlabeled, looks similar to the ‘Conversions vs. Cost’ graph shown elsewhere on their site.

That’s not really the interesting thing. The interesting thing is that the slide shows a few mathematical equations. Part reads:

This might look intimidating, but it’s actually not. It says that the Expected Return of a portfolio (*p*) is simply the weighted average of the Expected Return of each part of that portfolio.

So, if you have two investments to choose between (A and B) and let’s say that A is a stock that grows at 5% a year and B is a stock that grows at 10%, then the Expected Return of the portfolio depends on how much of A and B you own.

Put all of your money into A, then the ‘weight’ of A will be 100%. The weight of B will be 1 minus the weight of A, or 0%. And you will earn 5% interest, because you will own only investment A.

If the weight of B is 100%, then you will earn 10%. And if you put 50% of your money into A and 50% into B, then you will expect to earn 7.5%, because that is halfway between A’s expected return and B’s expected return.

The other equation is even more complicated, but if you don’t understand, don’t worry about it because I’ll give away Efficient Frontier’s ‘dirty little secret’ now: They don’t use this equation.

Here is what the equation says:

It tells us how much the value of the portfolio might vary over time. Let’s say that stocks A and B bounce up and down in value (as stocks tend to do). The term ‘σi^2’ is the *variance* of each individual stock and ‘σp^2’ is the variance of the entire portfolio (more properly called the *covariance* of the portfolio).

The term ‘ρij’ is the *correlation* between movements in the value of A and the value of B. So, if stocks A and B are completely uncorrelated (*i.e.*, ρij = 0), then sometimes A will be up when B is down and sometimes B will be up when A is down. Only rarely will both A and B be way up or way down at the same time. That is, the portfolio can vary in value *less* than either stock alone.

These equations won Harry Markowitz the Nobel Prize in Economics. In fact, Efficient Frontier says on their website: “Developed by a Nobel Prize winning economist, Portfolio Theory uses mathematical models to weight risk and return across numerous variables.”

Strictly speaking, this is true – the equations above *were* developed by a Nobel Prize winning economist. As I said earlier, though, Efficient Frontier does not use the ‘risk’ equation to determine the Cost of a portfolio of keywords. Instead, they simply sum up the cost for each individual keyword.

That is, Efficient Frontier implies (through the slide in their ‘SEM Product Tour’ and through the very name of their company) that they are using Markowitz’s equation to determine the ‘risk’ of a portfolio of keywords:

When in reality they are only using this equation:

The symbol that looks like a capital letter ‘E’ is the Greek letter Sigma. It just means ‘sum’. So, the equation above says: “To find the total Cost, add up the Cost of each individual keyword.”

As a quick recap, this is the Nobel Prize winning equation that Harry Markowitz developed:

And this is the equation that Efficient Frontier uses:

Believe it or not, Efficient Frontier is simply adding up the Cost for each keyword to get a Total Cost, and then implying that by doing so their technique is ‘Nobel Prize winning.’ For that, I guess they deserve a Nobel Prize in deceiving their clients.

**UPDATE, 3:23PM Pacific:** I should make it clear that by summing up a column of individual keyword Costs to obtain an overall Cost, what EF is doing is no different from any other SEM firm. All I’m claiming is that what EF and all other SEM firms are doing – adding up a column of Costs – is *not* what won Markowitz the Nobel Prize. So, *no firm* should claim that this was ‘developed by a Nobel Prize winning economist,’ EF included.

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