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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. We treat earnings growth as exogenous. The difference between log wealth and log earnings is modeled as an autoregression of order 1 with linear trend 4.6  and Gaussian innovations. Detrending gives us a new valuation measure. Our results disprove the Efficient Market Hypothesis. Therefore, long-run total returns equal long-run earnings growth plus 4.6 Ẇe apply results to retirement planning. A withdrawal process governs how a retired capital owner withdraws a certain fraction of wealth annually. We study the long-term behavior of such processes.

The paper considers the problem of stress scenario selection, known as reverse stress testing, in the context of portfolios of financial assets. Stress scenarios are loosely defined as the most probable values of changes in risk factors for a given portfolio that lead to extreme portfolio losses. We extend the estimator of stress scenarios proposed in [P. Glasserman, C. Kang and W. Kang, Stress scenario selection by empirical likelihood, Quant. Finance 15 (2015), 1, 25–41] under elliptical symmetry to address the issue of data sparsity in the tail regions by incorporating extreme value techniques. The resulting estimator is shown to be consistent, asymptotically normally distributed and computationally efficient. The paper also proposes an alternative estimator that can be used when the joint distribution of risk factor changes is not elliptical but comes from the family of skew-elliptical distributions. We investigate the finite-sample performance of the two estimators in simulation studies and apply them on two financial portfolios.