THE SOUTH AFRICAN INDEX INVESTOR 
“Greater rewards, lower costs” 
APPLYING INDEX STRATEGIES 
4. Fundamental Indexation # Download full version...
Indexing is a powerful model for equity investing. It is inexpensive to implement and absolutely transparent. The strategy has immense capacity, is highly liquid and is naturally well diversified. More importantly, there is overwhelming evidence that index investing, in the long run, outperforms active investing.
The Capital Asset Pricing Model (CAPM) — inspired originally by the meanvariance portfolio analysis of Harry Markowitz, and derived as a pricing formula by William Sharpe—is indoctrinated by business schools everywhere. CAPM suggests that a capweighted market index is an efficient equity investment. Investors cannot do better without extraordinary skill or information. This belief is largely unchallenged in the finance industry (except by the most brilliant portfolio managers and the most foolhardy speculators) and contributes significantly both to the popularity of index investing at the institutional level and the rising popularity of exchangetraded funds (ETFs) among retail investors.
Despite all of their benefits, however, traditional indexes are flawed in a very fundamental way. Almost all major indexes are based on marketcapitalization weightings. By definition, overvalued will have extra weight in the index at the expense of undervalued companies. A passive index investor is forced to allocate more of his portfolio in overvalued stocks and less of his portfolio in undervalued stocks—exactly the opposite of what common sense investing would suggest.
It can be quantitatively shown that a capweighted index will on average underperform a noncapweighted portfolio with similar risk, and the size of the underperformance is roughly equal to the noise in stock prices. Qualitatively, the noisier stock prices are —that is, the more prices fluctuate independent of changes in company fundamentals—the greater is the capweighted index underperformance.
Empirically, we observe that capweighted indexes do underperform significantly relative to noncapweighted indexes of similar risk characteristics. This underperformance is robust across time, macroeconomic cycles and countries.
Suppose there are only two stocks in the market: A and B, each with one share outstanding. Suppose the fair values (which investors do not observe) are $10 per share for each stock. Further, suppose that market prices are noisy, and that there is a 50/50 chance that a stock can be overvalued or undervalued by $2 per share. Note that the expected "mispricing" could occur in either of the two stocks, and we do not know which stock is overvalued or undervalued. In this economy, there is no simple way to take advantage of the mispricing (market inefficiency).
For simplicity, we also assume that the two stocks have the same equity market exposure, which leads to a 10 percent expected return on equity capital. Therefore, both companies are expected to increase their stock prices by $1 (10 percent increase on the $10 fair value). Note that the expected return on the overvalued stock is lower than the expected return on the undervalued stock, which is consistent with intuition. The investment objective is clearly to have more exposure to the undervalued stock and less exposure to the overvalued stock.
Observe that the capweighted market portfolio invests 60 percent in the overvalued stock and 40 percent in the undervalued stock. Had prices reflected the true values, however, the portfolio weight would have been 50 percent in each. After one period, assuming that the overvaluation and undervaluation persist—that is, the overvalued company appreciates from $12 to $13 and the undervalued company appreciates from $8 to $9—the capweighted portfolio return would be 10.0 percent. However, had the "fairvalue weights" been applied, the "fairvalue portfolio" would earn a return of 10.42 percent. The intuition for the capweighted portfolio's return drag is clear: The capweighted portfolio underperforms because it puts more weight in the overvalued stock, which will deliver less price appreciation in the future (and perhaps negative price appreciation if prices revert to fair values).
What is also interesting to note is that the return drag is related to the over and undervaluation. Suppose, in the previous example, the mispricing was $3 (30 percent) instead of $2 (20 percent); the return drag on the cap portfolio relative to the fairvalueweighted portfolio would be 0.99 percent instead of 0.42 percent. At $4 and $5 mispricings, the return drags are 1.90 percent and 3.33 percent, respectively.
Furthermore, suppose the mispricing is transient, meaning that the over and undervaluation dissipate over the course of the holding period; the predicted return drag on the capweighted portfolio becomes even more substantial. Returning to our original example, with $2 mispricing and reversion to fair value, the overpriced stock would revert from $12 back toward $10 while the underpriced stock would move from $8 toward $10, in addition to the $1 price appreciation associated with the equity market exposure. Therefore, the capweighted portfolio return would be 10.0 percent while the fairvalueweighted portfolio would return 14.6 percent. We note that the return drag on the capweighted portfolio is significantly increased when mispricing is temporary.
The question, then, is whether we can construct fairvalueweighted portfolios. Unfortunately, the answer is no. We do not and cannot observe companies' fair values. Fortunately, it is not necessary to construct fairvalueweighted portfolios in order to outperform capweighted portfolios.
That said, a wellbehaved portfolio should provide the greatest exposure to the largest companies, as this ensures broad market representation, high portfolio capacity and high liquidity. So how do we achieve the benefit of capweighting without using capitalization for weighting? To do this, we need to find alternative metrics for company size. The U.S. and international evidence illustrate powerfully that using a composite of company fundamentals such as cash flow, sales, gross dividend and book equity value leads to better indexes.
By construction fundamental indexing underweights growth companies that are not growing their fundamentals. In this regard, fundamental indexes will tend to have lower P/Es and higher dividend yields than standard capweighted indexes. Fundamental indexing, however, is far from simple value investing. Value indexes are limited in capacity and do not provide broad market participation and diversification.
One reason that the fundamental indexes outperform value indexes is because value indexes are based on capitalization, and discard (or underweight significantly) many growth companies that are growing their fundamentals equally rapidly. By contrast, fundamental indexes hold a significant portion in growth companies that are growing their fundamentals.
Fundamental indexes do have higher turnover than capweighted indexes. By construction, cap indexes do not require rebalancing. Turnover comes largely from index reconstitution—when names are added or deleted from the index constituent list. Fundamental indexes are designed to rebalance annually. This imposes rebalancing turnover, in addition to reconstitution turnover. In any event, the turnover costs would not erode the fundamental index's alpha against its cap benchmark.
We find that fundamental indexes underperform in a bubble environment. During periods of rapid and irrational P/E expansions, fundamental indexes aggressively rebalance away from stocks with large market capitalizations relative to their fundamental measurements, and into stocks with large fundamental measurements relative to their capitalization. This rebalancing hurts performance in markets that exhibit extreme momentum.
Fundamental indexing eliminates the return drag inherent in capweighted indexes. The methodology preserves the capacity, liquidity, diversification and broadmarket participation that are the chief benefits of traditional cap indexes. Empirically, we observe that fundamental indexes outperform their respective cap benchmarks significantly—two percent per annum in the U.S. and 3.5 percent globally. This outperformance is statistically significant and robust over different market environments, and also is present in the small and midsize indexes.
# Excerpts from an article: “New Frontiers In Index Investing: An examination of fundamental indexation” by Jason C. Hsu and Carmen Campollo. Journal of Indexes, January/February 2006. Available at http://www.indexuniverse.com/JOI/index.php?id=634
