This is a deceptive example.  It’s easy to construct exceptions, but only if we cannot divide the universe in two equal halves by fair value.  In this case, the cap-weighted investor has 60% invested in the undervalued stock … which represents 67% of the fair value of the market.  The overvalued half of the fair value portfolio consists of $7.5 billion in fair value:  Company B plus one-fourth of Company A.   The undervalued half of this universe consists of $7.5 billion in fair value:  the remaining three-fourths of Company A.  The cap-weighted investor has $8.25 billion invested in the overvalued former portfolio and $6.75 billion in the undervalued latter portfolio. 

It is mathematically impossible to construct a counterexample, as I’m sure Edesess would concede, if the market is ranked by relative valuation and then partitioned in half by fair value.

The statement is imperfectly worded, but not in any way that is important in the real world.  The two-company counterargument is deceptive in ways that (I think) are important.

Take Edesess’s example one step further.  Assume that Company A has a fair value of $10 billion and a market value of $9 billion and Company B has a fair value of zero with a market value of $1 billion.  In this case, the cap-weighted portfolio would invest 90% in the undervalued Company A and 10% in the overvalued Company B; over half of our money is in an overvalued company.  But this is pretty meaningless, because all of the true value of the market is in Company A.  This is the Achilles heel in the Edesess “counterexample”:  his example is specifically structured so you cannot divide the universe in half by fair value. 

Let’s construct a dividing line at the midpoint of the fair value of all companies, when they are first ranked by their relative valuation.   These two-company examples have a huge company straddling that dividing line.  In the real world, the company that straddles that dividing line would typically be too small to matter.

In my counterexample, if you start with the more undervalued companies and work your way down, the halfway point of the cap-weighted portfolio is $7.5 billion and the halfway point of the fair value portfolio is $7.5 billion.  The simple fact is that most of the cap-weighted investor’s money is in the overvalued portion of the market portfolio.

As an aside, I have a draft article that is scheduled to appear in the Journal of Portfolio Management on “clairvoyant” value.  We went back historically and asked “what were the fair values in the market, and how did the market perform relative to these fair values?”  Two important findings emerged.  First, there is an awesome correlation between whether the market values of companies were above or below their economic footprint and the future growth of these companies.  The market does a really good job distinguishing fast and slow growing companies.  Second, we found that the market routinely pays a premium of two-times the valuation premium that these fast-growing companies deserve. 

This is a mathematical truism: if the correlation between pricing error and fair value is zero, then the correlation between pricing error and price must be negative (except in the trivial cases of zero standard deviation of error or of infinite standard deviation of error).  This was glossed over by Andre Perold in his paper, as Harry Markowitz and I pointed out. 

The interesting thing is that much of the controversy hinges on one’s frame of reference.  In a cap-weighted world, prices are correct, the market is the market, and you will perceive anything that increases your exposure to value stocks and lowers your exposure to growth stocks as value-tilting.  From that frame of reference, you would be absolutely correct. 

But from an economic frame of reference, where one owns businesses and not stocks, the market prices react to constantly shifting expectations, fads, bubbles, and crashes.  From this perspective, the market is making an active bet, with a growth bias.  Growth stocks are trading at premium multiples, and are therefore accorded more weight in the market portfolio than in the economy are not necessarily better investments. 

Both views are right from their own frame of reference.  Both views are predicated on a widely respected and accepted frame of reference.  But the concept of an economic frame of reference is not radical; it’s merely fallen out of favor.  Graham and Dodd, and John Burr Williams, whose work dates back 75 years, wrote that you do not invest in stocks; you invest in companies.