This is a short note, which contains a simple dynamic factor model: Total (including dividends) real (inflation-adjusted) annual returns of Standard & Poor Composite Index is regressed upon earnings yield, which is defined as earnings (net income) per share of this index (summed over all companies in this index), divided by the current value of this index. This earnings yield is modeled as a simple autoregression. We use 7-year trailing earnings yield, with earnings averaged over the last 7 years. This version of earnings yield has maximal correlation with next year's total real returns. Regression residuals fail standard normality tests, but we still use this model, since we are interested in long-run modeling. To account for shortage of data (1935--2019 annual), we use Bayesian inference. We confirm the conventional wisdom that future long-run stock market returns are likely to be lower than the historical averages.
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