Cross-Sectional Models for Forecasting Expected Stock Returns

# What is the current state of the art method to predict the equity risk premium one month ahead?


# What is the current state of the art method to predict the equity risk premium one month ahead?












I am aware of Goyal, Welch and Zafirov's paper A Comprehensive 2022 Look at the Empirical Performance of Equity Premium Prediction that seems to imply there is nothing one can do to predict the return of the stock market next month. Just wondering whether anyone has a different view of this or a different reference.

## Answer by Julien Maas (score 1)

https://quant.stackexchange.com/a/78492

I believe it depends on if you are speaking of an individual stock return or a cross section of stock returns. While for the former a stochastic model may seem best, for a cross sectional approach, where we form portfolios based on expected returns, we can use firm based characteristic models using rolling FM slopes such as in;

Lewellen, J. (2015). The cross-section of expected stock returns. Critical Finance Review, 4(1), 1–44. https://doi.org/10.1561/104.00000024

Open access link; Lewellen 2015.

and

Drobetz, W., Haller, R., Jasperneite, C., & Otto, T. (2019). Predictability and the cross section of expected returns: Evidence from the European Stock Market. Journal of Asset Management, 20(7), 508–533. https://doi.org/10.1057/s41260-019-00138-0

Many alternative approaches also exist that focus more on using risk factors or macro economic variables.

Yet of course the point that nbbo2 and Goyal, Welch and Zafirov make is still valid. I can give 2 explanations for this on the spot;

- Based on rational pricing theory, Once information of mispricing is published, investors will trade on it, making the mispricing dissapear, thereby diminishing the predictive power of certain anomalies.

Hence it's likely best to have your own model and keep it private if you want to trade on it.

- Economic conditions and markets change over time. Remember that we hold a lot of variables fixed and that as regulation, technology and economic conditions change, the impact of certain variables on returns may change. Including risk factors and macroeconomic variables.

Yet despite these two caveats, I'd say it's possible to have an reliable "estimate" of the average return for a cross section of expected stock returns.

Yet that's it's best to use up to date information and your own private model.

EDIT: To strengthen this case; consider that in the abstract of Lewellen 2015, He states that

> Empirically, the forecasts vary substantially across stocks and have strong predictive power for actual returns. For example, using ten-year rolling estimates of Fama-MacBeth slopes and a cross-sectional model with 15 firm characteristics (all based on low-frequency data), the expected-return estimates have a cross-sectional standard deviation of 0.87% monthly and a predictive slope for future monthly returns of 0.74, with a standard error of 0.07.

Likewise Drobetz (2019) states in his conclusion on page 529:

> We provide evidence for the predictability in the cross section of European stock returns, using characteristics-based models that are estimated using the classical Fama and MacBeth (1973) approach. Our analysis is strictly out of sample, mimicking an investor who exploits both historical and realtime information on multiple firm characteristics to predict excess returns. Our predictions are not predominantly driven by any single predictor variable, but are rather based on the full interaction of all characteristics included. The composite forecast models capture a considerable amount of the cross-sectional variation in true expected excess returns, as indicated by predictive slopes close to one.