# Fair Value Weighting Part II

Unfortunately, I don’t have much time to write in as much detail as I normally would, so let me basically use Harry Markowitz’s example of a fair-value weighting example:

Let’s assume we have a new hypothetical index with only four companies in it. Each company has \$1 of earnings, but two have growth prospects to justify a 20 times P/E (meaning the price should be \$20) and the other two have growth prospects to justify a 10 times P/E (meaning their price should be \$10). We know that the market will just guess at these values, but let’s assume these are the correct values (or the fair values).

If the market does a “pretty good” job at guessing the fair value, it might be off by 20% on average. Let’s assume that the market overprices one of the \$10 stocks and one of the \$20 stocks, and that it underprices the other \$10 stock and the other \$20 stock. Therefore we have stock prices of \$8, \$12, \$16, and \$24.

In a cap-weighted portfolio, if the prices reverted to their fair prices, you have a zero percent return – the errors cancel. If you instead had a fair-value weighted index half the portfolio would rise 25% and the other half would lose 16.7% for a net return of 4.2%.

Markowitz is quick to point out that we have no way of determining fair value, so why should we care that fair-value weighting beats cap-weighting? He answers himself: The index weighted by earnings gives you the exact same result of a 4.2% return. Each company earned \$1, so each company would be weighted equally. As long as cap-weighting has errors relative to fair value and prices revert to fair value, cap-weighting will suffer a drag relative to fair-value weighting (or a proxy of such). Any portfolio that differs from fair value weighting in a manner that is uncorrelated with the error in price will match the return of a fair-value weighted portfolio.

The specific numbers in this exercise was provided by Mr. Markowitz, but I’ll break down the calculations in the next post (after the lap of the blogs tomorrow). For those who don’t know, Harry Markowitz is a Nobel Prize winner in Economics for his contributions to CAPM, and is considered one of the fathers of Modern Portfolio Theory.

Preet Banerjee
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This is a very interesting concept. However I feel that although it has a few good things going for it, I feel it shouldn’t overlook a few of the good things in a cap-weighted index:
1. In a perfect total market cap weighting index, there should be zero turnover. You buy a fixed percentage of every company on the market and hold them all as long as you stay invested in the index. I’m light on the understanding of how these funds operate internally, but I would assume there is still some turnover due to churn as a result of new purchases and redemptions.
2. Due to the low turnover, it is hard for arbitrageurs to drive up hidden costs of the funds.
3. Also due to low turnover, these funds often have better tax characteristics if they’re held outside of a tax-sheltered account like an RRSP or TFSA.

Having said all of that, from an academic standpoint, I would agree that fair-value weighting sounds like a smarter way to invest. It sounds to me like a form of investing that would come with higher fees, and I wonder if it can outperform simpler cap-weighted funds to the extent that it can overcome the higher costs (explicit and hidden).

However, innovation and uncertainty go hand in hand, so I’d like to see some investing products utilize this concept and see how they do.

Preet, are you aware of any products that do this or can you say whether your company is working on introducing products that use this strategy?