Classical mean variance utility of Markowitz [1952] and Tobin [1958] have relied on objective expected utility hypothesis. This paper presents a choice-based axiomatization of mean variance utility, in a Savage-type setting of ambiguity, which neither assumes nor implies that individual’s preferences over portfolios conform to the expected utility hypothesis.

● The classic Markowitz model that optimizes for the Sharpe ratio has proven to be suboptimal. ○ Summary is used directly as prediction. ○ Variance is not a good risk measurement since it penalizes positive shocks and says little about tail risks ● Other risk measurements such as Value-at-Risk and Expected Shortfall introduce non-linear, non-convex risk constraints and render the mean-variance ...

The Markowitz model of portfolio optimization quantifies the problem in a lucid form of only two criteria: the mean, representing the expected outcome, and the risk, a scalar measure of the variability of outcomes. The classical Markowitz model uses the variance as the risk measure, thus resulting in a quadratic optimization problem. Following Sharpe’s work on linear approximation to the mean–v...

The Markowitz model of portfolio optimization quantifies the problem in a lucid form of only two criteria: the mean, representing the expected outcome, and the risk, a scalar measure of the variability of outcomes. The classical Markowitz model uses the variance as the risk measure, thus resulting in a quadratic optimization problem. Following Sharpe’s work on linear approximation to the mean–v...

Following the seminal work by Markowitz, the portfolio selection problem is usually modeled as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model, the risk is measured with variance. Several other risk measures have been later considered thus creating the entire family of mean-risk (Markowitz type) ...

Stock portfolio selection is a classic problem in finance, and it involves deciding how to allocate an institution’s or an individual’s wealth to a number of stocks, with certain investment objectives (return and risk). In this paper, we adopt the classical Markowitz mean-variance model and consider an additional common realistic constraint, namely, the cardinality constraint. Thus, stock portf...

This paper gives an asymptotic analysis of the mean-variance (Markowitz-type) portfolio selection under mild assumptions on the market behavior. Theoretical results show the rate of underperformance of the risk aware Markowitz-type portfolio strategy in growth rate compared to the log-optimal portfolio strategy, which does not have explicit risk control. Statements are given with and without fu...

The mean-variance formulation by Markowitz in 1956 and its efficient solution by Wolfe in 1959 paved a foundation for modern portfolio selection. In this work we start reviewing basic concepts about portfolio selection, showing one starting solution and then the mean-variance analysis proposed by Markowitz. We show an algorithm for efficient frontier derivation, proposed by Wolfe, and analyze t...

The mathematical model of portfolio optimization is usually represented as a bicriteria optimization problem where a reasonable trade–off between expected rate of return and risk is sought. In a classical Markowitz model the risk is measured by a variance, thus resulting in a quadratic programming model. As an alternative, the MAD model was proposed where risk is measured by (mean) absolute dev...