Value Weighted Indices

Here is a newsletter from John Mauldin (dated 6/16/06) on an interesting new way to construct indices that could produce substantially higher returns than standard market capitalization-weighted indices. Below his article, I include my comments on the idea.

When Does Your Large Stock Outperform?

Getting 2% of Alpha

How Significant is the CAPM Alpha?

Vancouver, La Jolla, and Home


This week we look at index funds, and specifically at problems that certain types of capitalization weighted index funds have. It is intuitively obvious that capitalization-weighted indexes have a larger proportion of their assets in the larger stocks. (Capitalization-weighted means that larger stocks are given more “weight” or proportion of the index or fund.) But is this what a rational investor should actually want? I think the information we look at today will surprise many.

On my way in to Las Vegas last Wednesday, I read a very interesting op-ed piece by Professor Jeremy Siegel of Wharton Business School. Basically, he says that “Fundamentally weighted indexes are the next wave of investing.” On May 13 of 2005, I highlighted new research by good friend Rob Arnott, where he laid out the intellectual and practical arguments for a new type of fundamentally weighted index. By that, I mean that he says stock indexes and the funds associated with them should be based upon the underlying fundamentals of the companies and not just the size of the company. At that time I said his work would be the basis for a revolution in investing and would become hugely successful. The last year has proven me right. And now, these ideas are becoming mainstream enough to make the Wall Street Journal.

Why should the average investor care? Because fundamental indexing (and we will go into what that means below) is going to come to a 401k or pension plan near you. As we will see, this type of index is clearly superior to your average offering in such plans, and offers 2% or more of alpha per year over regular index funds. And 2% is huge over the lifetime of a pension fund. Let’s look at what Siegel said:

“This new paradigm claims that the prices of securities are not always the best estimate of the true underlying value of the firm. It argues that prices can be influenced by speculators and momentum traders, as well as by insiders and institutions that often buy and sell stocks for reasons unrelated to fundamental value, such as for diversification, liquidity and taxes. In other words, prices of securities are subject to temporary shocks that I call ‘noise’ that obscures their true value. These temporary shocks may last for days or for years, and their unpredictability makes it difficult to design a trading strategy that consistently produces superior returns. To distinguish this paradigm from the reigning efficient market hypothesis, I call it the ‘noisy market hypothesis.’

“The noisy market hypothesis easily explains the size and value anomalies. If a stock price falls for reasons unrelated to the changes in the fundamental value, then it is likely – but not certain – that overweighting such a stock will yield better than normal returns. On the other hand, stocks that rise in price more than their fundamentals become ‘large stocks’ with high P/E ratios that are likely to underperform.

“These discrepancies are not easy to arbitrage away on a stock-by-stock basis. The noisy market hypothesis does not say that every stock that changes price does so by more than what is justified by fundamentals. Any particular stock may still be undervalued when it moves up in price or overvalued when it moves down. New research indicates that there is a simple way that investors can capture these mis-pricings and achieve returns superior to capitalization-weighted indexes. This is through a strategy called ‘fundamental indexation.’ Fundamental indexation means that each stock in a portfolio is weighted not by its market capitalization, but by some fundamental metric, such as aggregate sales or aggregate dividends. Like capitalization-weighted indexes, fundamental indexes involve no security analysis but must be rebalanced periodically by purchasing more shares of firms whose price has gone down more than a fundamental metric, such as sales, and selling shares in those firms whose price has risen more than the fundamental metric …

“With the advent of fundamental indexes, we’re at the brink of a huge paradigm shift. The chinks in the armor of the efficient market hypothesis have grown too large to be ignored. No longer can advisers claim that capitalization-weighted indexes afford investors the best risk and return tradeoff. The noisy market hypothesis, which makes the simple yet convincing claim that the prices of securities often change in ways that are unrelated to fundamentals, is a much better description of reality and offers a simple explanation for why value-based investing beats the market.”

Siegel gave credit to my good friend Rob Arnott for the basic research. Rob challenged the conventional thinking with an explosive new study published last year (and highlighted here) in the Financial Analyst Journal. He also summarized it in a speech at my Accredited Investor Strategic Investment Conference last year. We’re going to look again at a part of that speech today.

As usual, whenever Arnott’s involved you have to have your thinking cap on. You will want to pay attention to this article, as Rob is going to show us how to get an extra 2% of alpha on our stock portfolios. So put up your tray tables and put on your seatbelts.

Today’s letter will be a little bit different than my usual format in that almost the entire content will be directly quoting Arnott’s speech. When the word “I” is used, it is Rob. So in place of the usual quotes, readers should assume that the content and intellectual property is essentially Rob’s. If I want to get in a clarifying or personal side note, I will simply put it in brackets [like this].

By way of introduction, Rob serves as Editor of the Financial Analyst Journal. He has authored over sixty articles for journals such as the Financial Analyst Journal, the Journal of Portfolio Management and the Harvard Business Review. He is Chairman of Research Associates and is sub-advisor for the Pimco All Asset Fund, which now has over $6 billion. Rob is one of those guys who by walking into any given room is one of the smartest guys in the room, if not the smartest.

Rob starts out with the point that most of the financial world revolves around the use of various economic theories [Now to Rob]:

Any given economic theory will perfectly describe the world as long as you agree with the underlying assumptions. More often than not, however, the underlying assumptions take us from the real world into a world of, well, theory.

One of the most famous theories is the capital-asset pricing model (or CAPM). It is the basis for a number of index models, especially capitalization-weighted indexes like the S&P 500.

Now, for most of us, our biggest bet is in equities. Is theory leading us astray here? Let’s suppose we have a perfect crystal ball. It can’t tell us the share prices of every asset a year from now, or two years from now, but it can tell us the cash flows into the future on every investment we could make. The crystal ball lets us calculate the true fair value of every asset in the market. If we know the true fair value, then the market value will match that, the capital-asset pricing model will be correct, and the index will be perfectly efficient, in the sense that there is no way to boost returns without boosting risk.

Now let’s suppose our crystal ball is just a little bit cloudy and we can’t see the future precisely. Then what winds up happening is that every asset is trading above or below true fair value. We can’t know what true fair value is. But we can know that every stock, every asset, every bond is going to be trading above or below what its ultimate true fair value is. Even the most ardent fans of the efficient markets hypothesis would say, “That’s reasonable. That’s reality.”

Now if every asset is trading above or below its true fair value, then any index that is capitalization-weighted (price-weighted or valuation-weighted) is automatically going to have us overexposed to every single asset that’s trading above its true fair value and underexposed to every single asset that’s trading below its true fair value.

[Read that again. This is one of the reasons why value investing beats indexing over the long term.]

So this is the first time we’ve circled back to some concrete implications for the market. It means that the capitalization-weighted indexes on which our entire industry relies are fundamentally, structurally flawed and will inherently overweight every stock that’s above fair value and underweight every stock that’s below fair value.

Now let’s look at what that does to returns. If you put most of your money in assets that are above fair value, you have proportionately too little in assets that are below fair value, and you’re getting a return drag. The cap-weighted indexes are producing returns that are below what they should be, below what would be available in a valuation-indifferent index.

If you construct an index that is valuation-indifferent, that doesn’t care what the PE ratios are, that doesn’t care what the market capitalization is, then return drag disappears – and you can quantify it. It’s about two to four percent per year. And how many managers out there reliably add two to four percent per year in the very long run? Darn few of them.

[Other studies show that about 80% of mutual funds underperform the market.]

Now while it’s a bad index, equal weighting will outperform a cap-weighted index. [Equal weighting means that you put the same amount of money in a stock, no matter what its capitalization or share price.] A lot of folks think that equal-weighted indexes outperform mainstream capitalization indexes because they have a small-stock bias. The theory being that small companies beat large because they have a value bias, and cheap stocks outperform expensive ones. That’s not quite correct. What equal weighting does is underweight every stock that’s large, regardless of whether it’s cheap or dear, and overweight every stock that’s small, regardless whether it’s cheap or dear.

This means that from a valuation perspective every stock that’s overvalued is overweight in the cap-weighted index, and in the equal-weighted index it’s a crap shoot, 50/50. You have even odds, whether it’s overvalued or undervalued, of being over- or underweight.

Let’s look at this from the vantage point of a concrete example. Let’s suppose we have a world with two stocks. Each has a true fair value of a hundred bucks, but the marketplace doesn’t know what the true fair value is. One stock is estimated by the market to really be worth fifty bucks and the other is estimated to really be worth a hundred and fifty, but both valuations are wrong. Capitalization weighting puts 75 percent on that overvalued stock.

Now suppose over the next ten years, today’s valuation errors are corrected. Both stocks move to a hundred dollars, but a new 50-percent error is reintroduced because news has come along and people have been drawn into the hype that one company looks really good and the other looks really bad. These errors are introduced into the pricing, and you have a steady state: the size of the errors stays steady, but the old errors have been corrected. In that world, the estimated cap-weighted return is zero, and the equal-weighted return is 33 percent.

[Both stocks start at $50 and $150 for a total portfolio of $200. In ten years, both stocks are worth $100. If you cap-weighted your portfolio, you would not have made anything. If you put an equal $100 into the companies, you would have made $100 on the lower priced stock and lost $33 on the higher priced stock, for a portfolio profit of $67 on your original $200. Thus Rob’s 33% return.]

Sigma Investing Comments

This makes a lot of sense to us. Look at this interview on the PIMCO site for some more details.

Here’s what you need to believe for it to hold.

  1. The market caps don’t always reflect the true values of companies (we definitely buy this)

  2. The over-valued companies will underperform in the future (this requires that the over-valuation is “discovered” by the market) and the under-valued will outperform.

  3. These fundamental proxies (like book value, revenues, etc.) will randomly distribute the errors in valuation — they may actually correct the errors in the valuation but random distribution of the errors in terms of weighting might be all you can hope for.

These ideas seem to hold to us.

It seems like the magnitude of the positive impact is dependent on two things:

  1. The shape of the distribution of variance between market cap value and true value. If this distribution has many companies centered very close to zero, then the gain of the technique of randomizing your errors should be small. If it is more spread out, you will make most of your gains on the companies in the tails of the distribution.

  2. The second factor is how your re-weighting scheme will weight the companies in the tails of the distributions. If you randomly uniformly distribute them in terms of relative weighting, you should do better but you’ll still be making many mistakes. If you had perfect knowledge, you would flip the tails in terms of weightings. The choice of weighting scheme has value.

Thus, if there are large tails in your distribution of market cap to true value variance and you have a better than random way of re-weighting the stocks, you should do well.

The main concern that we have with this approach is how robust is this 2% estimate for increased performance. William Bernstein wrote an article about it.

It’s a bit technical but he uses this three-factor model from Fama and French which tries to explain the behavior of returns in terms of three factors (market returns, returns of value stocks, and returns of small cap stocks). It’s based on their research that value and small stocks have over-performed historically. Bernstein estimates that 2/3’s of the 2% gain is from higher weighting of value and small stocks in the re-weighted indexes and the remaining is from the new weighting methodology. But, that is a smaller alpha (about 0.7%).

We also echo Bernstein’s advice to watch out for higher fees in these indexes. Higher fees could eat up all the gains from this better performance.

So, we like the approach but it would be nice to see a couple of more studies about the improvement and we’d like know more about the fees of the funds. Note that the main study comes from the guy who has launched the index fund. The PRF ETF seems to have fees of 0.6%.