To examine post-retirement asset allocation, an extension to the classic Markowitz risk-return framework is suggested. Assuming that retirees make constant (real dollar) annual withdrawals from their portfolios, reward and risk measures are defined to be the mean and standard deviation of wealth remaining at end of life. Asset returns and time of death are both treated as random variables. Assu...

In this paper, we compare the portfolio allocation model of multifractal detrended Fluctuation approach with the modern efficient frontier model and the asset allocation model from Chinese institution fund, the risk-return performance of the multifractal detrended Fluctuation turns out to be more optimal portfolio allocation than that from Chinese institution fund and the conclusions have impli...

This paper uses a grey forecasting model GM(1,1) on improving the investment performance of classical Markowitz efficiency frontier’s investment portfolio using the component markets’ indexes of MSCI World Index from 1999 to 2005 as the samples. Using grey Markowitz efficiency frontier’s investment portfolio models, we establish a more stable and correct connection between ex-ante model and ex-...

The traditional quadratic programming approach to portfolio optimisation is difficult to implement when there are cardinality constraints. Recent approaches to resolving this have used heuristic algorithms to search for points on the cardinality constrained frontier. However, these can be computationally expensive when the practitioner does not know a priori exactly how many assets they may des...

We consider the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. We examine the effects of applying buy-in thresholds, cardinality constraints and transaction roundlot restrictions to the portfolio selection problem. Such discrete constraints are of practical importance but make the efficient frontier discontinuous. The resulting quadratic mixed...

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...

Tests of the CAPM, the prototype model of equilibrium in financial markets, are usually based on returns computed from end-of-month closing prices. It is reasonable to doubt that these prices always reflect markets that are at equilibrium, thus raising the question whether and how inference is biased. Rather than exploring this issue using one of the many theoretical (but empirically unverified...

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal inves...

We study in this paper the portfolio selection problem with a stock index and European style options on the index. A refined mean-variance methodology is adopted in the study. Single-stage and two-stage investment models are studied and solved. In the later case a scenario tree and stochastic programming formulation are used. Explicit forms of the optimal portfolio and its corresponding efficie...

We show that the efficient frontier for a portfolio in which short positions precisely offset the long ones is composed of a pair of straight lines through the origin of the risk-return plane. This unique but important case has been overlooked because the original formulation of the mean-variance model by Markowitz as well as all its subsequent elaborations have implicitly excluded it by using ...