Portfolio selection models: A review and new directions

Modern Portfolio Theory (MPT) is based upon the classical Markowitz model which uses variance as a risk measure. A generalization of this approach leads to mean-risk models, in which a return distribution is characterized by the expected value of return (desired to be large) and a risk value (desired to be kept small). Portfolio choice is made by solving an optimization problem, in which the portfolio risk is minimized and a desired level of expected return is specified as a constraint. The need to penalize different undesirable aspects of the return distribution led to the proposal of alternative risk measures, notably those penalizing only the downside part (adverse) and not the upside (potential). The downside risk considerations constitute the basis of the Post Modern Portfolio Theory (PMPT). Examples of such risk measures are lower partial moments, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We revisit these risk measures and the resulting mean-risk models. We discuss alternative models for portfolio selection, their choice criteria and the evolution of MPT to PMPT which incorporates: utility maximization and stochastic dominance

A Stochastic Approach to Portfolio Optimization Using Competing Risk Metrics

This thesis presentation presents a stochastic approach to portfolio construction using various risk metrics as underlying models for portfolio optimization. The risk models utilized in this thesis include Mean-Variance, Minimum-Variance, Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR). To evaluate the efficiency and overall performance of these models, historical data for 30 specific stocks was selected. The stock selection process focused on the selecting stocks that are highly volatile and correlated with one another. Empirical results reveal that portfolio optimization strategies outperform the benchmark. Additionally, results showed that the Minimum-Variance model constructed the best portfolio for the predetermined backtesting time period

Mean univariate- GARCH VaR portfolio optimization: actual portfolio approach

In accordance with Basel Capital Accords, the Capital Requirements (CR) for market risk exposure of banks is a nonlinear function of Value-at-Risk (VaR). Importantly, the CR is calculated based on a bank’s actual portfolio, i.e. the portfolio represented by its current holdings. To tackle mean-VaR portfolio optimization within the actual portfolio framework (APF), we propose a novel mean-VaR optimization method where VaR is estimated using a univariate Generalized AutoRegressive Conditional Heteroscedasticity (GARCH) volatility model. The optimization was performed by employing a Nondominated Sorting Genetic Algorithm (NSGA-II). On a sample of 40 large US stocks, our procedure provided superior mean-VaR trade-offs compared to those obtained from applying more customary mean-multivariate GARCH and historical VaR models. The results hold true in both low and high volatility samples

A novel hybrid algorithm for mean-CVaR portfolio selection with real-world constraints

In this paper, we employ the Conditional Value at Risk (CVaR) to measure the portfolio risk, and propose a mean-CVaR portfolio selection model. In addition, some real-world constraints are considered. The constructed model is a non-linear discrete optimization problem and difficult to solve by the classic optimization techniques. A novel hybrid algorithm based particle swarm optimization (PSO) and artificial bee colony (ABC) is designed for this problem. The hybrid algorithm introduces the ABC operator into PSO. A numerical example is given to illustrate the modeling idea of the paper and the effectiveness of the proposed hybrid algorithm

Integrated assessment of crop management portfolios in adapting to climate change in the Marchfeld region

Portfolio optimization is an adequate tool to find optimal crop management options in adapting to climate change. The risk farmers have to face can be caused by different sources. In our study, we focus on the risk arising from unknown weather conditions. Therefore, we developed stochastic climate change scenarios for the Marchfeld region. Two portfolio models have been applied in the time periods 2008-2020, 2021-2030 and 2031-2040: a traditional non-linear mean-variance (E-V) model and a model using the Conditional Value at Risk (CVaR) as risk metric. Investigated crops are corn, winter wheat, sunflower and spring barley with different crop management alternatives. Minimum tillage appears in all portfolios. We found a decreasing share of winter wheat that gets partially substituted by sunflower over the time periods. When including environmental constraints (soil organic carbon content, nitrate leaching) the reverse effect on the resulting portfolio shares is observed with corn being included. The E-V model reveals more diversification with respect to the crops, whereas the CVaR model shows more diversification with respect to crop management options

Optimization Models for Applications in Portfolio Management and Advertising Industry

Optimization problems in two different application fields are investigated: the first one is the popular portfolio optimization problem and the second one is the newly developed online display advertising problem. The portfolio optimization problem has two main concerns: an appropriate statistical input data, which is improved with the use of factor model and, the inclusion of the transaction cost function into the original objective function. Two methods are applied to solve the optimization problem, namely,the conditional value at risk (CVaR) method and the reliability based (RB) method. Asset allocation problem in finance continues to be of practical interest because decisions as to where to invest must be made to maximize the total return and minimizing the risk of not attaining the target return. However, the commonly used Markowitz method, also known as the mean-variance approach, uses historic stock prices data and has been facing problems of parameter estimation and short sample errors. An alternative method that attempts to overcome this problem is the use of factor models. This thesis will explain this model in addition to explaining the basic portfolio optimization problem. Conditional value at risk and the reliability based optimization method are applied to solve the portfolio optimization problem with the consideration of transaction costs in the objective function.They are applied and evaluated by simulation in terms of their convergence, efficiency and results. The online display advertising problem extends a normal deterministic revenue optimization model to a stochastic allocation model. The incorporation of randomness makes it more realistic for the estimation of demand, supply and market price. Revenues are considered as a combination of gains from guaranteed contracts and unguaranteed spot market. The objective is not only to maximize the revenue but also to consider the quality of ads, so that the whole market obtains long-term benefits and stability. The thesis accomplishes in solving the online display advertising allocation problem in a stochastic case with the measure of conditional value at risk algorithm

Portfolio-optimization models for small investors

Since 2010, the client base of online-trading service providers has grown significantly. Such companies enable small investors to access the stock market at advantageous rates. Because small investors buy and sell stocks in moderate amounts, they should consider fixed transaction costs, integral transaction units, and dividends when selecting their portfolio. In this paper, we consider the small investor's problem of investing capital in stocks in a way that maximizes the expected portfolio return and guarantees that the portfolio risk does not exceed a prescribed risk level. Portfolio-optimization models known from the literature are in general designed for institutional investors and do not consider the specific constraints of small investors. We therefore extend four well-known portfolio-optimization models to make them applicable for small investors. We consider one nonlinear model that uses variance as a risk measure and three linear models that use the mean absolute deviation from the portfolio return, the maximum loss, and the conditional value-at-risk as risk measures. We extend all models to consider piecewise-constant transaction costs, integral transaction units, and dividends. In an out-of-sample experiment based on Swiss stock-market data and the cost structure of the online-trading service provider Swissquote, we apply both the basic models and the extended models; the former represent the perspective of an institutional investor, and the latter the perspective of a small investor. The basic models compute portfolios that yield on average a slightly higher return than the portfolios computed with the extended models. However, all generated portfolios yield on average a higher return than the Swiss performance index. There are considerable differences between the four risk measures with respect to the mean realized portfolio return and the standard deviation of the realized portfolio retur

Optimal Portfolio Selection Under the Estimation Risk in Mean Return

This thesis investigates robust techniques for mean-variance (MV) portfolio optimization problems under the estimation risk in mean return. We evaluate the performance of the optimal portfolios generated by the min-max robust MV portfolio optimization model. With an ellipsoidal uncertainty set based on the statistics of the sample mean estimates, minmax robust portfolios equal to the ones from the standard MV model based on the nominal mean estimates but with larger risk aversion parameters. With an interval uncertainty set for mean return, min-max robust portfolios can vary significantly with the initial data used to generate the uncertainty set. In addition, by focusing on the worst-case scenario in the mean return uncertainty set, min-max robust portfolios can be too conservative and unable to achieve a high return. Adjusting the conservatism level of min-max robust portfolios can only be achieved by excluding poor mean return scenarios from the uncertainty set, which runs counter to the principle of min-max robustness. We propose a CVaR robust MV portfolio optimization model in which the estimation risk is measured by the Conditional Value-at-Risk (CVaR). We show that, using CVaR to quantify the estimation risk in mean return, the conservatism level of CVaR robust portfolios can be more naturally adjusted by gradually including better mean return scenarios. Moreover, we compare min-max robust portfolios (with an interval uncertainty set for mean return) and CVaR robust portfolios in terms of actual frontier variation, portfolio efficiency, and portfolio diversification. Finally, a computational method based on a smoothing technique is implemented to solve the optimization problem in the CVaR robust model. We numerically show that, compared with the quadratic programming (QP) approach, the smoothing approach is more computationally efficient for computing CVaR robust portfolios