Standard Mean-variance Model Research Articles

Analytic solution to the portfolio optimization problem in a mean-variance-skewness model

ABSTRACTIn portfolio theory, it is well-known that the distributions of stock returns are often unimodal asymmetric distributions. Therefore, many researches have suggested considering the skew-normal distribution as an adequate model in quantitative finance. Such asymmetry explains why the celebrated mean-variance theory, which does not account to the skewness of distribution of returns, frequently fails to provide an optimal portfolio selection rule. In this paper, we provide a novel approach for solving the problem of optimal portfolio selection for asymmetric distributions of the stock returns, by putting it into a framework of a mean-variance-skewness measure. Moreover, our optimal solutions are explicit and are closed-form. In particular, we provide an analytical portfolio optimization solution to the exponential utility of the well-known skew-normal distribution. Our analytical solution can be investigated in comparison to other portfolio selection rules, such as the standard mean-variance model. The new methodology is illustrated numerically.

Portfolio Selection in Mean-Minimum Return Level-Expected Bounded First Passage Time Framework

This paper explores the selection of optimal portfolio by replacing the standard Mean-Variance model by Mean-Minimum Return Level (MRL) framework and adding one important dimension—expectation of bounded First Passage Time (FPT) towards the MRL. To measure how much a given portfolio is exposed to risk, the new model can capture both, the amount of the largest possible loss at a certain confidence level and time to such an event occurring. The novelty of this paper is the introduction of bounded first passage time towards MRL and taking its expectation into consideration as an additional factor in portfolio selection decision making. Assuming that the asset price dynamics follow multi-dimensional Geometric Brownian Motion with drift, we obtain a portfolio wealth process for multiple assets and we evaluate the lowest possible value to which it can drop by a high confidence level. Then we extend our examination of the optimal portfolio selection by ultimately obtaining the efficient surface of risky portfolios. As a result, the paper shows that the third dimension can make a significant difference while choosing the asset weights compared to classical models ignoring the portfolio return paths as long as they achieve a desired combination of risk and return.

Prize-linked savings mechanism in the portfolio selection framework

Prize-linked savings (PLS) instruments implement the lottery-like component into the structure of traditional financial products. Following existing research based on both real and experimental data, such programs appeared highly successful in raising the overall savings rates within the given environments. PLS accounts seem to be treated by decision-makers as substitutes to ordinary lotteries, but this does not hold when comparing PLS with traditional interest-bearing savings products. This paper explains such empirical observations in a framework of portfolio selection problem. For that purpose, two models have been presented and used for deriving optimal portfolios in a presence of PLS, lottery and savings products. As shown in the analysis, the standard mean-variance model does not allow for a PLS instrument to be of optimum choice, whereas in the case of behavioural portfolio model allocating all disposable income.

English

Behavioral finance is the study of the influence of psychology on the behavior of financial practitioners and the subsequent effect on markets. In this paper, concepts of behavioral finance are surveyed and then the portfolio selection model in framework of behavioral finance theories is presented and compared with the Mean-Variance rational pattern. Historical data of TEDPIX for 10 years has been used and separated to 2 parts of test and evaluation groups. The optimum weight for risky asset proposed by standard mean-variance and behavioral model based on returns for the first 7 years (test data) in the 3 months periods. After that, returns of 84 optimum portfolios in a three year evaluation period are calculated. Mean test (CL=95%) shows that in Tehran Stock Exchange, the research hypothesis return of behavioral model is greater than return of standard mean-variance model, was rejected.   Key words: Behavioral finance, investment portfolio, mental accounting, asymmetric risk preference, loss aversion.

Portfolio Optimization in Electricity Trading with Limited Liquidity

In principle, portfolio optimization in electricity markets can make use of the standard mean-variance model going back to Markowitz. Yet a key restriction in most electricity markets is the limited liquidity. Therefore the standard model has to be adapted to cope with limited liquidity. An application of this model shows that the optimal hedging strategy for generation portfolios is strongly dependent on the size of the portfolio considered as well as on the variance-covariancematrix used and the liquidity function assumed.

On the Non-Linear Negative Relationship between Growth and Volatility under International Capital Flows

This paper treats capital flows as risky growth opportunities for both investing and host countries in a standard mean-variance model. Differing optimal tradeoffs between growth and volatility on both sides of capital flows are examined on the basis of their different attitudes toward destabilizing risk, different considerations of capital market openness, and different levels of financial sector development. It is established that growth and volatility may have a positive or a negative relationship in theory, but in practice, they are correlated negatively with each other. This negative correlation is persistently non-linear after some normalization, and significantly holds not only for developing but also for developed countries. The paper explains why one side’s push for financial liberalization comes across the other side’s resistance to it. This conflict of interest can be resolved via negotiations for compromise equilibrium at which each side’s optimal tradeoff is made internationally compatible.

Testing a non-linear model of portflio behaviour with time-varying expectations and risks: the case of UK private sector persion funds

In this paper, we estimate a model of portfolio behaviour which extends the standard mean-variance model in three important ways. Firstly, we generalize the mean-variance utility function to allow ...