CAPE : using its variants to predict the returns from investing in the S&P 500 index

Is the US stock market overvalued? I use Shiller's CAPE to predict the return of investing in the S&P500 index. Siegel argues that the recent fall in the share of earnings that are paid out as dividends has biased downwards predictions from the CAPE. I offer a solution to the problem of reduced dividends in the form of some alternative versions of CAPE, experiment with different time periods in calculating CAPE, and explore the role of previous peak earnings. While this study refers to the US stock market the issues are also important for valuing other markets