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 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 mean-variance portfolio analysis of Harry Markowitz, and derived as a pricing formula by William Sharpe-is indoctrinated by business schools everywhere. CAPM suggests that a cap-weighted market index, like the S&P 500 or Russell 1000, 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 exchange-traded funds (ETFs) among retail investors.
A Crucial Flaw In Traditional Cap-Weighted Indexes
Despite all of their benefits, however, traditional indexes are flawed in a very fundamental way. Almost all major indexes are based on market-capitalization 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 port folio in undervalued stocks-exactly the opposite of what common sense investing would suggest.
It can be quantitatively shown that a cap-weighted index will on average underperform a non-cap-weighted portfolio with similar risk, and the size of the underperformance is roughly equal to the noise in stock prices (Hsu 2005 and Treynor 2005). Qualitatively, the noisier stock prices are -that is, the more prices fluctuate independent of changes in company fundamentals - the greater is the cap-weighted index underperformance.
Empirically, we observe that cap-weighted indexes do underperform significantly relative to non-cap-weighted indexes of similar risk characteristics (Arnott, Hsu and Moore 2005, and Tamura and Shimizu 2005). This underperformance is robust across time, across time, macroeconomic cycles and countries.
Return Drag On Cap-Weighted Portfolios
We offer a simple example in this section to highlight the return drag associated with cap-weighting, and to illustrate how the noise in stock prices relates to the size of the cap index underperformance.
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 cap-weighted 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 cap-weighted portfolio return would be 10.0 percent. However, had the "fair-value weights" been applied, the "fair-value portfolio" would earn a return of 10.42 percent. The intuition for the cap-weighted portfolio's return drag is clear: The cap-weighted 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 fair-value-weighted 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.
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