ITA Wealth Management

In the forward of Robert Arnott’s new book, “The Fundamental Index: A Better Way to Invest,” Harry Markowitz poses this argument.

“Suppose we have four companies, each with $1 in reported earnings. Suppose two of these have ample future growth prospect that would justify a price 20 times the current profits, or $20, and the other two have less impressive prospects and fully deserve $10 — 10 times the current earnings. But, no one can have a clear view of the future prospects of our companies, so the market merely guesses at these fair values. Suppose the market does a pretty good job, but misjudges those prospects by 20 percent in each of the four cases, with one growth stock priced 20 percent too high and one 20 percent too low, and likewise for the value stocks. So, we have two stocks with a true value of $20 each, priced at $24 and $16, and two stocks with a true value of $10, priced at $12 and $8.”

This is not hard to follow so far. Markowitz goes on to make the argument as to why value portfolios perform better than cap-weighted portfolios.

“Suppose prices revert to fair value in the next year. The “cap-weighted” portfolio produces zero return; since the prices are symmetric around value, the errors cancel. If we could construct a fair-value-weighted portfolio, few would disagree that it should be better than capitalization weighting. It is. Half of our portfolio rises 25 percent in value, and half loses 16.7%, for an average of 4.2 percent return. Why? Because the fair value portfolio puts equal amounts in over- and undervalued stocks, while capitalization weighting put 60 percent of our money in the overvalued and 40 percent in the undervalued companies.”

“Since we have no idea what the fair value is for each company, and so there’s no way for us to construct this fair-value-weighted portfolio, why should we care that fair value weighting beats capitalization weighting? What of the other construction methods? The portfolios weighted equally and by company profits (efficiency -weighted), which lead to the same weighting in this example, produce a return of 4.2 percent also, identically the same as the fair-value-weighted portfolio!”

Take time to pencil out the Markowitz argument above.

Lowell Herr

Photograph: Lightening over Portland, OR — Image by David Vernier