Capital market anomalies are empirical relationships between firm characteristics and
returns that are not explained by standard asset pricing models. The existence of these
anomalies has been inferred predominantly from the examination of average realized
returns. The authors examine whether the existence of these anomalies can be inferred from
expected *ex ante* returns as well.

## Whatâ€™s Inside?

Relying on average realized returns to estimate expected returns has its limitations. For example, previous researchers have found that expected return estimates based on realized returns can be imprecise because of large standard errors in estimated factor loadings and factor risk premiums.

The authors estimate expected returns on dollar-neutral long–short (high-minus-low) strategies based on a comprehensive list of 12 anomaly variables. They use an accounting-based approach, determining the implied rate of return that equates the present value of expected future residual incomes to the stock price under the residual income cost of capital model.

## How Is This Research Useful to Practitioners?

The authors’ key finding is that their expected return estimates differ dramatically from average realized returns for the vast majority of anomalies. These differences include inconsistencies in magnitude, sign, and statistical significance.

In addition, long–short expected returns estimated using analysts’ earnings forecasts—which are likely to be biased—are largely similar to long–short expected returns estimated using cross-sectional forecasting regressions. The authors conclude that the bias in analysts’ forecasts does not vary systematically with firm characteristics. For example, analysts’ forecasts for firms with low asset growth are no more upwardly biased than those for firms with high asset growth.

The authors interpret their key finding in two ways: mispricing and measurement errors in expected returns.

Under behavioral mispricing, average realized returns that differ from expected returns are a manifestation of predictable pricing errors caused by such behavioral biases as overconfidence, self-attribution, and representative heuristics. To the extent that the accounting-based estimates provide reasonable proxies for expected returns, the authors’ key finding is inconsistent with rational models.

As a measure of expected return, the implied rate of return calculated using the residual income model is not perfect. It is a proxy for expected returns, but specifically for the long term. So, the horizon difference between the longer-term expected returns estimated by the model and shorter-term (a holding period of less than one year) average realized returns can also explain the authors’ key finding. In addition, the implied rates of return from the residual income model can differ from expected returns when expected returns are stochastic.

## How Did the Authors Conduct This Research?

The authors obtain monthly data on stock returns, stock prices, and number of shares outstanding from the Center for Research in Security Prices (CRSP). They use nonfinancial firms listed in the CRSP monthly stock return and Compustat annual industrial files from 1965 through 2011. They include only firms with ordinary common equity, thus excluding American Depositary Receipts and real estate investment trusts.

In defining the 12 anomaly variables, the authors closely follow the existing literature. For each anomaly variable, they calculate firm-level average realized returns; they also estimate “baseline” expected returns (implied costs of equity from a baseline residual model, which uses analysts’ earnings forecasts from I/B/E/S) and “modified” expected returns (implied costs of equity from modified residual income models, which use full and simplified Fama–French return- forecasting regressions).

The authors construct one-way quintile portfolios based on each anomaly variable, using
NYSE breakpoints to sort all NYSE, Amex, and NASDAQ stocks listed on CRSP into five groups.
They calculate value-weighted average realized, baseline expected, and modified expected
returns for high-minus-low quintile portfolios and assess the returns’ significance
using heteroscedasticity- and autocorrelation-consistent *t*-statistics,
apparently in conjunction with the “*t*-statistic greater than 2”
rule of thumb.

By constructing two-way sorted portfolios to control for long-term-growth forecasts, the authors confirm the robustness of their key finding. They also check robustness through the implementation of methods that estimate expected return and expected growth simultaneously at the portfolio level.

## Abstractorâ€™s Viewpoint

Overall, the authors’ key finding runs counter to the notion that anomalies exist
*ex ante*. Their interpretation of their finding — primarily in terms
of behavioral mispricing — may be of particular interest to investment
professionals.

The value and firm size anomalies are well documented within the finance literature. Nevertheless, I would have appreciated more discussion about why estimated expected returns turn out to be similar to average realized returns for book to market and market capitalization of equity.