Lots of people think they've discovered the secret to getting rich in the stock market. Often, such claims are backward looking; they are based on historical data. But, past performance does not necessarily predict future results. In this study, Ivo Welch and Amit Goyal examine a long list of variables that others have claimed can predict stock returns.
Three Steps in an Econometric Study
Step 1: What Do You Want To Do?
It's all in the question at the top of this page: Is it possible to forecast stock returns? Answering this question requires developing a prediction model using one set of data and then evaluating it on different data.
Step 2: Formulate Your Research Design and Specify the Econometric Model
Welch and Goyal assemble 80 years of data on stock market returns and assemble 17 different prediction models. They use the early years in the sample to fit the econometric models, and then they see how well the models predict returns in the later years.
Step 3: Apply Statistical Theory
You'll learn how to do that in this class.
Welch and Goyal report results from two analyses, (1) in-sample (IS) predictions, which are backward looking because they fit the model and evaluate it on the same historical data, and (2) out-of-sample (OOS), which are forward looking because they fit the model on early data and evaluate it on later data. They calculate how much better the model is than a simple prediction based on the historical average return.
The graph shows results for one of the variables, the dividend-price ratio (dp). The OOS calculation shows that the model using dp is worse than using the historical average.
Overall, the models predict poorly and are unstable. They would not have helped an investor to profitably time the market.
Click here for more details on the study.