Portfolio selection with skewness: A multiple-objective approach

In the presence of skewness, the portfolio selection entails considering competing and conflicting objectives, such as maximizing both its expected returns and skewness, and minimizing its risk for decreasing absolute risk-aversion investors. Since it is unlikely that a portfolio can solve the multiple-objectives problem simultaneously, a portfolio selection must depend on the investor's preference among objectives. This article shows that investor preference can be incorporated into a polynomial goal programming problem from which a portfolio selection with skewness is determined. An inefficient mean-variance portfolio may be optimal in the mean-variance-skewness content. The features of applying polynomial goal programming in portfolio selection are 1) the existence of an optimal solution, 2) the flexibility of the incorporation of investor preference, and 3) the relative simplicity of computational requirements.     

Dynamic preferences for popular investment strategies in pension funds

In this paper, we characterize dynamic investment strategies that are consistent with the expected utility setting and more generally with the forward utility setting. Two popular dynamic strategies in the pension funds industry are used to illustrate our results: a constant proportion portfolio insurance (CPPI) strategy and a life-cycle strategy. For the CPPI strategy, we are able to infer preferences of the pension fund’s manager from her investment strategy, and to exhibit the specific expected utility maximization that makes this strategy optimal at any given time horizon. In the Black–Scholes market with deterministic parameters, we are able to show that traditional life-cycle funds are not optimal to any expected utility maximizers. We also prove that a CPPI strategy is optimal for a fund manager with HARA utility function, while an investor with a SAHARA utility function will choose a time-decreasing allocation to risky assets in the same spirit as the life-cycle funds strategy. Finally, we suggest how to modify these strategies if the financial market follows a more general diffusion process than in the Black–Scholes market.     

An Improvement of the Parameter Certainty Equivalence Method in Portfolio Selection

This paper discusses an improvement of the Parameter Certainty Equivalence method in portfolio selection. Specifically, we derive methods of portfolio selection that are superior to the Parameter Certainty Equivalence method from the viewpoint of maximizing expected utility. We additionally derive such a method from the Bayesian approach.     

The Ex Post Performance of Four Portfolio Selection Algorithms

This paper explores the ex post performance of four widely cited (and sometimes applied) normative portfolio selection models. Each is supposed to solve the same portfolio selection problem relative to the same mean-variance efficiency criteria. It has been shown elsewhere, and this paper confirms, that the models result in vastly different ex ante stock selection strategies. However, the acid test of normative theory is ex post performance relative to a set of efficiency criteria or some other standard. The empirical results reported here show that, with one exception, the ex post performance of the models is consistent with the same mean-variance efficiency criteria, and, over a predictable range of outcomes, consistently outperform the index portfolio based on Standard & Poor's 500 Stock Index.     

Asymmetric Risk Measures and Real Estate Returns

Rational investors distinguish between extremely high and extremely low returns. The measures of investment risk should reflect such asymmetric risk perception. This study presents six asymmetric risk metrics and empirically tests their abilities in explaining the cross-sectional variations of real estate returns. It finds strong evidence that systematic downside risk is associated with a risk premium, and skewness provides significant explanatory power to the variation of cross-sectional property returns. On the other hand, co-skewness does not explain real estate returns well and is not a good systematic risk measure.     

HARA utility maximization in a Markov-switching bond–stock market

We present a flexible multidimensional bond–stock model incorporating regime switching, a stochastic short rate and further stochastic factors, such as stochastic asset covariance. In this framework we consider an investor whose risk preferences are characterized by the hyperbolic absolute risk-aversion utility function and solve the problem of optimizing the expected utility from her terminal wealth. For the optimal portfolio we obtain a constant-proportion portfolio insurance-type strategy with a Markov-switching stochastic multiplier and prove that it assures a lower bound on the terminal wealth. Explicit and easy-to-use verification theorems are proven. Furthermore, we apply the results to a specific model. We estimate the model parameters and test the performance of the derived optimal strategy using real data. The influence of the investor’s risk preferences and the model parameters on the portfolio is studied in detail. A comparison to the results with the power utility function is also provided.     

Further evidence on performance evaluation: Portfolio holdings,recommendations, and turnover costs

This paper analyzes the performance of mutual funds in Spain between January 1980 and June 1990. The robustness of results to alternative measurements and benchmarks are analyzed. The results indicate that, with monthly returns alone, it is not possible to distinguish between selectivity and timing. We are only able to measure the magnitude of total performance. To be more precise about the reasons behind performance, portfolio holdings are necessary. This work employs a new data set based on monthly portfolio holdings of a representative sample of funds. A comparison of results using monthly returns and monthly portfolio holdings is made. In particular, thanks to the availability of portfolio holdings, we are able to separate selectivity and timing. Finally, the impact of turnover costs is considered.     

Portfolio Selection with Quadratic Utility Revisited

Considering a simple portfolio selection problem by agents with quadratic utility, an apparently counterintuitive outcome results. When such a choice is over two assets that can be ordered in terms of riskiness, an agent that is more risk averse may optimally invest a larger portion of wealth in the riskier asset. It is shown that such an outcome is not counterintuitive, since for the portfolios from which agents optimally choose, a larger proportion of investment in the riskier asset leads to a less risky portfolio.     

Portfolio optimization algorithms,simplified criteria,and security selection: A contrast and evaluation

The Markowitz full covariance model provides a general framework for analysis of the porfolio selection problem. Three alternative solution methodologies have been developed to facilitate normative applications, but this article shows that they lead to markedly different stock selection and portfolio weighting decisions. In sample-based applications, incompatibilities arise due to model misspecifications and different distributional assumptions, and from the interactive effects of estimation error, optimization model selection bias, and conflicting distributional assumptions.     

Martingales and Portfolio Decisions: A User’s Guide

This article gives an overview and introduction to the Martingale approach to multi-period (dynamic) portfolio decisions. While Martingale pricing techniques have long been used with considerable success in the pricing of derivatives and financial assets in general, their potential to improve the practice of dynamic portfolio decisions is not sufficiently recognized yet. This article shows that the approach is, in principle, not difficult to implement for readers equipped with standard option replication techniques if markets are sufficiently “complete” in order to provide investors with the relevant information about the pricing of financial risks. The article provides a practical guide to implement the basic features of the approach in a binomial framework.