Using geometric illustrations, we investigate what implications of portfolio optimization in equilibrium can be generated by the simple mean-variance framework, under margin borrowing restrictions. First, we investigate the case of uniform marginability on all risky assets. It is shown that...

The efficient frontier is a parabola in the mean-variance space which is uniquely determined by three characteristics. Assuming that the portfolio asset returns are independent and multivariate normally distributed, we derive tests and confidence sets for all possible arrangements of these...

In a traditional mean-variance approach a portfolio is represented by the allocation vector optimized in terms of expected returns and variances. Basic assumption is that the allocation vector may only be the driver of a portfolio risk-reward trade-off, while all constituent assets are fully...

We solve a mean-variance optimisation problem of a defined contribution pension scheme in the accumulation phase. The financial market consists of: (i) the risk-free asset, (ii) a risky asset following a GBM, and (iii) a bond driven by a stochastic interest rate following the Vasicek [1977]...

We provide a Matlab quadratic optimization tool based on Markowitz's critical line algorithm that significantly outperforms standard software packages and a recently developed operations research algorithm. As an illustration: For a 2000 asset universe our method needs less than a second to...

The purpose of this study is to apply polynomial goal programming to establish a new portfolio selection model that considers the tradeoffs between expected return and Value-at-Risk (VaR) of portfolios and the flexibility of incorporating investor's preferences. The historical data of 10...

We consider the portfolio selection problem in the accumulation phase of a defined contribution pension scheme in continuous time, and compare the mean-variance and the expected utility maximization approaches. Using the embedding technique pioneered by Zhou and Li (2000) we first find the...

This paper considers an optimal portfolio selection problem under Markowitz's mean-variance portfolio selection problem in a multi-period regime-switching model. We assume that there are n + 1 securities in the market. Given an economic state which is modelled by a finite state Markov chain, the...

The principal portfolios of the standard Capital Asset Pricing Model (CAPM) are analyzed and found to have remarkable hedging and leveraging properties. Principal portfolios implement a recasting of any correlated asset set of N risky securities into an equivalent but uncorrelated set when short...

We consider the portfolio selection problem in the accumulation phase of a defined contribution pension scheme in continuous time, and compare the mean-variance and the expected utility maximization approaches. Using the embedding technique pioneered by Zhou and Li (2000) we first find the...