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We generalize the classic Shiller cyclically adjusted price-earnings ratio(CAPE) used for prediction of future total returns of the stock market. Wetreat earnings growth as exogenous. The difference between log wealth and logearnings is modeled as an autoregression of order 1 with linear trend 4.5\% andGaussian innovations. Detrending gives us a new valuation measure. Thisautoregression is significantly different from the random walk. Therefore, ourresults disprove the Efficient Market Hypothesis. Therefore, long-run totalreturns equal long-run earnings growth plus 4.5\%. We apply results toretirement planning. A withdrawal process governs how a retired capital ownerwithdraws a certain fraction of wealth annually. The fraction can vary fromyear to year. We study the long-term behavior of such processes.

A New Stock Market Valuation Measure with Applications to Retirement Planning