- Expected return is the return of an average stock plus the return due to the investor’s skill.
- Traditional indexing does not come up to the expected return of uninformed investors.
- Active managers evaluated against cap-weighted indices have to surmount the benchmark’s return drag before they can add value.
The gently satirical variety show “A Prairie Home Companion,” long running on public radio in the United States, has made the fictional town of Lake Wobegon famous. The residents of Lake Wobegon believe that in their town “all the women are strong, all the men are good looking, and all the children are above average.” But the townsfolk are outlandishly optimistic. Clearly, we recognize that everyone can’t be above average; indeed, we would generally suspect naiveté when met with such unrealistic positivity. Nonetheless, when it comes to investing, most of us live in Lake Wobegon; we believe we can select winning stocks and top quartile managers. Most of us think we are above average.1 Indeed, the irony is that it is the select few who aspire to achieve middling results—the 20% of investors who index—who achieve consistent net-of-fees outperformance against Lake Wobegon investors.
When conducting manager searches, we hope to find skilled managers who know which stocks are misvalued and can translate this information into meaningful outperformance. Inevitably, however, when choosing money managers about half of us will be below average. Those who accept that it is hard to find managers who consistently outperform opt for index investing. A passive index does not have the informational advantage that an active manager might possess, but at least the investors will earn a market return without the high cost of active management.
In this issue, we are uninterested in rehashing the old topic of the benefit of index investing. Instead we question one of the key tenets of index investing.
Is it, in fact, true that traditional index investors have earned returns that can be reasonably earned by uninformed investors? Is it true that by investing in the cap-weighted index we receive the average return associated with an uninformed selection of stocks? Surprisingly, we find that traditional indexing—and active managers who hug the benchmark (closet indexers)—deliver below-average returns.2 They systematically deliver returns that are inferior to the expected returns of uninformed investors.
Uninformed investors cannot distinguish between good stocks and bad ones, and their portfolio returns will deviate from the return of an average stock in a random manner. In comparison, informed investors invest more in stocks that are likely to perform well, and avoid those that are likely to perform worse. There is an intuitive mathematical identity which captures this idea and decomposes any portfolio’s expected return into the sum of two components:
Covariance measures how much two variables move together: If the strategy assigns more weight to better-performing stocks, covariance is positive; if the strategy assigns more weight to worse-performing stocks, it is negative; and if the stock assignment is random, this term is zero. The covariance of stock weights and returns reflects how informed the investor is. In other words, it captures the investor’s skill.
The relationship above is widely used in the financial literature to estimate the skill of managers.4 The expected return of a portfolio is the sum of the return for an average stock and the return due to the investor’s skill. The first component is quite intuitive. The return of an average stock is the expected return of the uninformed investor who selects stocks haphazardly. An informed investor would invest more in stocks expected to have higher returns and less in stocks expected to have lower returns. The better the investor is able to predict stocks’ relative returns, and the more conviction with which these views are expressed in the portfolio, the higher the portfolio return.
The “Skill” of an Index Portfolio
Recognizing that they are unlikely to select skilled money managers, many market participants choose index-based alternatives which presumably deliver the return that would be similar to a portfolio of stocks chosen by an uninformed investor; that is, the return of the average stock. Choosing an index spares investors from paying high fees to unskilled managers.
The return decomposition that we introduced in the previous section can help us determine whether index investing offers expected returns equivalent to the returns that uninformed investors can, in principle, achieve. We can simulate index weights and check the level of skill represented by the covariance between the index constituents’ weights and subsequent returns. If the index does indeed deliver a return matching that of an uninformed manager, then the covariance term showing skill will be zero. We will examine the following five options, four smart beta indices and one traditional cap-weighted index:
- An equal-weighted strategy;
- The average of 100 portfolios of 30 randomly selected stocks;
- A minimum variance strategy;
- A fundamentally weighted strategy, where the weights are proportional to company size as represented by financial accounting measures; and
- A cap-weighted index.
Some of these options have been around for many years and have large amounts of assets under management; others are younger and only now gaining widespread acceptance. The first four indices fall into the category of smart betas, strategy indices which do not base weights on price-related measures such as capitalization.5 Ironically the category of smart beta also includes the portfolios of randomly selected stocks. Table 1 shows the return decomposition for the five strategies.