Growth-oriented portfolio selection based on stochastic holding periods

Based on the concept of time optimal portfolio selection, a specific model is developed which is designed for investors who wish to attain a certain predefined level of wealth and whose preferences can be defined on the distribution of the time at which this goal level is reached for the first time. This time marks the end of a then stochastic holding period for any risky investment strategy. In contrast to the meanwhile classic approach to portfolio selection originated by Markowitz, the portfolio choice is not based on the distribution of the portfolio value at a given future point in time, but on the distribution of the holding period after which the portfolio value reaches the desired level the first time. The model is based on assumptions which are compatible to those of the classic one period mode. A portfolio is considered the more desirable, the shorter the mean and the lower the variance of the holding period is. This implements a mean-variance-type model based on stochastic holding periods. The asset price dynamics is modeled by an arithmetic Brownian process. The resulting portfolio frontier is isomorphic to the portfolio frontier of the standard model for positive mean returns. The efficient set instead shows highly different qualitative properties, which are investigated in detail and exemplified using realistic data. The set of efficient portfolios of the time optimal model is a subset of those of the standard model.