Abstract
Leshno and Levy (2002) proposed almost stochastic dominance (ASD) approach for decision makers with economically relevant preferences. Bali et al. (2009) applied ASD to their analysis and claimed that in the long run stocks will dominate bonds. However, Levy (2009) pointed out the drawbacks of ASD rules and argued that stocks should not be preferred over bonds over time. As a result, we follow Shorrocks (1983) and Shalit (2014) and employ Lorenz curve in the portfolio risk analysis. Furthermore, we establish a new framework called almost Lorenz dominance (ALD) and manage to find out the optimal weight of stocks in a portfolio with longer investment horizons