While browsing around on the web today I encountered an article from early 2009 that argued that most/many claims that are made in favor of fundamentally weighted indices are flawed. Before continuing reading this post, I would suggest reading the article. It’s just three pages in a large font, and I don’t want to repeat the complete argument :).
Intuitively the argument for fundamentally weighted indices is compelling. If the market is not efficient then stocks that are overvalued have a bigger market cap than they should have and stocks that are undervalued have a smaller market cap than they should have. If you now buy this market you must by definition underperform compared to the case where every security is fairly valued, right? Or perhaps wrong? Can you argue with the example below?
Consider a two-company world. Company A has a fair value of $10 billion with a market value of $9 billion, and Company B has a fair value of $5 billion with a market value of $6 billion. If we have a $150,000 market-capweighted portfolio, it will have $90,000 in Company A, the undervalued company, and $60,000 in Company B, the overvalued company. It will not have most of its money in companies that are above fair value—it will have most of its money in the company that is below fair value.
He is absolutely right that you have more money in the undervalued company in this example than in the overvalued company! But what is important to note that the undervalued company is less undervalued than the overvalued company is overvalued. The result is that the total market value of both companies remains equal and, as a result, both market efficiencies offset each other. If you would buy the complete market it would cost you $15 billion in both cases and in both cases you get company A and company B. Doesn’t matter if you overpay $1 billion for company B and underpay $1 billion for company A. The net result is exactly the same!
So when we add as a constraint that if the market as a whole is fairly valued the conclusion that the author draws is inescapable: there is no hidden performance drag by buying a market cap weighted portfolio. If you don’t overpay for the market as a whole it doesn’t matter that for some individual securities you overpay and underpay for others.
But this is of course only true if the market as a whole is correctly valued. Whether or not this is true depends on how market inefficiencies manifest themselves. Let’s take a look at a market with two companies, but to make things even simpler both companies have a $10 billion fair value. Let’s say that on a single day there is a 50/50 probability that a company drifts 1% away from fair value, either up or down. After one day the market is expected to look as following:
|Fair value||Move||Market cap|
|Company A||$10 billion||+1%||$10.1 billion|
|Company B||$10 billion||-1%||$9.9 billion|
| Total||$20 billion||$20 billion|
So it seems like everything is still well for the argument that market inefficiencies – represented by random movements away from fair value – don’t make a market cap weighted portfolio inferior compared to buying the stocks at intrinsic value. If you would buy the whole market you still get the same two companies at the same price!
While this model appears to be reasonable there is one major flaw, and that is the fact that these returns introduce a bias when we start compounding across multiple periods. A plus 1% return followed by a minus 1% returns doesn’t net out to zero. If we would alternate a long series of +1% returns and -1% returns the market cap of both companies would converge to zero. That wouldn’t make sense! To remove the bias from the expected returns we need to combine random movements of plus 1% with minus 0.9901%:
- $10.0 billion * 1.01 = $10.1 billion
- $10.1 billion * 0.990099 = $10.0 billion
What we are basically saying that market prices are log-normally distributed around fair value. The log-normal distribution is asymmetrical, as it should be because asset prices can’t go below zero. I think that by now you can guess what the impact will be if we redo our table:
|Fair value||Move||Market cap|
|Company A||$10 billion||+1.00%||$10.1 billion|
|Company B||$10 billion||-0.9901%||$9.90099 billion|
| Total||$20 billion||$20.00099 billion|
Because of the small difference in the up- and down move we lose the result that the market as a whole remains fairly valued, and as a result, a market-cap weighted approach will be at a disadvantage compared to a fundamentally weighted approach. Buying these two companies at fair value is better than buying them at their combined market cap.
Is this a reasonable result? Small-caps stocks are known to outperform large-cap stocks. The traditional academic view is that the difference in performance is the result of differences in risk between small and large stocks, and to some extent that is probably true. But a part of the performance differential could also be caused by the fact that undervalued companies have a smaller market cap than overvalued companies when they have an identical intrinsic value.
So, to summarize: I think that the intuitive idea that a fundamentally weighted index should outperform a market cap weighted index is actually correct. Whether or not it works in practice depends on how inefficient the market is compared to the added trading costs that will be incurred by a fundamental weighting.