Abstract:
The paper compares three portfolio optimization
models. Modern portfolio theory (MPT) is a short-horizon volatility model. The
relevant time horizon is the sampling interval. MPT is myopic and implies that
investors are not concerned with long-term variance or mean-reversion.
Intertemporal portfolio choice is a multiple period model that revises
portfolios continuously in response to relevant signals to reduce variance of
terminal wealth over the holding period. Digital portfolio theory (DPT) is a
non-myopic, discrete time, long-horizon variance model that does not include
volatility. DPT controls mean-reversion variances in single period solutions
based on holding period and hedging and speculative demand.

Abstract:
Portfolio Theory has during many decades been considered as the holy grail of investment despite the fact that very few empirical studies in the public domain have shown that portfolio theory outperforms a random equal weighted portfolio. We will in this paper empirically investigate how successful portfolio theory is when it comes to generating large positive returns with low return volatility. The dataset that is used consists of approximately 4000 US stocks. We find weak support that portfolio theory by itself would have generated any returns different than a random portfolio allocation. In general optimized historical cumulative returns are not the same as forward cumulative returns.

In this paper, we present the problem of portfolio optimization under investment. This area of investment is traced with works of Professor Markowitz way back in 1952. First, we determine the probability distribution of the Uganda Securities Exchange (USE) stocks returns. Secondly, we develop unrestricted portfolio optimization model based on the classical Modern Portfolio Optimization (MPT) model, and then we incorporate certain restrictions typical of the USE trading or investment environment and hence, develop the modified restricted model. Thirdly, we explore the possibility of diversification under a portfolio of averagely correlated assets. Determination of the model parameters and model development is all done using Excel spreadsheets. We explicitly go through the mathematics of the solution methods for both models. Validation of the models is done using the USE stocks daily trading data, in which case we use a random sample of 6 stocks out of the 13 stocks listed at the USE. To start with, we prove that USE stocks log returns are normally distributed. Data analysis results and the frontier curves show that our modified (restricted) model is valid as the solutions are all consistent with the theoretical foundations of the classical MPT-model butinferior to the unrestricted model. To make the model more useful, accurate and easy to apply and robust, we programmethe model using Visual Basic for Applications (VBA). We therefore recommend that before applying investment models such as the MPT, model modifications must be made so as to adapt them to particular investment environments. Moreover, to make

Abstract:
This study has three objectives. First, we investigate whether Modern Portfolio Theory can be applied on the financial decisions that made by investors or individual in order to increase their wealth through investment activities. Second, we examine the real behavior of each asset in terms of capital assets pricing models. Third, we determine whether our portfolio is the best model to produce a higher return in a given level of risk or a lowest risk in a particular level of return. It is found that three different stocks listed in the Indonesia Stock Exchange have a positive relationship with market returns. The reactions of the investor regarding these stocks are not influenced by each other. Lastly, the minimum variance portfolio (MVP) point which represents the single portfolio with the lowest possible level of standard deviation, occurs when the expected return of portfolio is approximately 2.2 percent at a standard deviation of 8.8 percent.

Abstract:
Mainstream asset pricing models are all inappropriate when they consistently insist on applying one single model to deal with a reality filled with different aspects of asset pricing. In addition, those models also treat the right environ-ment variable too lightly hence can not rightly do the job of asset pricing. In this study, based on the portfolio theory and the principle of supply and demand, a more reasonable asset pricing system including five different models will be suggested to provide a necessary function of automatic price stabilization and to better serve our financial market.

Abstract:
The author re-examines the demand-for-money theory in an intertemporal optimization model. The demand for real money balances is derived to be a function of real income and the rates of return of all financial assets traded in the economy. Unlike the traditional money-demand relation, however, where the elasticities are assumed to be constant, the coefficients of the explanatory variables are not constant and depend on the degree of an agent’s risk aversion, the volatilities of the price level and income, and the correlation of asset returns. The author shows that the response of households to increased volatilities in the financial markets, economic activity, and prices cannot be predicted, because a rise in general uncertainties has an ambiguous impact on the demand for money. This suggests that increased uncertainty is not very helpful for the planning decisions of households, because the optimal level of money holdings in the period of uncertainty cannot be ascertained.

Abstract:
The study of investment theory
plays an extremely important role in real-life investment activities and is the theoretical basis for determining how investors
invest. The traditional investment theory is mainly the portfolio theory
proposed by Markowitz. The core investment model is the expectation-variance model. However, the traditional expectation
variance model does not completely measure the risk. This paper focuses
on the concept of entropy in the original physics and information theory, and studies the rationality of the
method of measuring the risk in the financial investment field with entropy and
the advantages of other metrics such as the classical variance method. Based on
Markowitz’s portfolio theory, the expectation-variance model is optimized, the
entropy is used to measure the risk of income, and the entropy model is
established to select a more effective portfolio than the expectation-variance
model. This paper not only studies from the theoretical aspect, but also
collects the actual securities data, through the calculation of the actual
data, and uses MATLAB to simulate its
effective boundary, test the theory and the effect of the obtained optimization
model to verify the validity of the model, so that the entropy model can
apply to actual investment activities.

Abstract:
Our objective is to build different Precious Metals (gold, silver, palladium, platinum and rhodium) and Gold Numismatic Asset Portfolios. The purpose is being able to build the best portfolio for the different investors and to know The Market Portfolio. For that, by means of The Portfolio Theory methodology (Markowitz, 1952; 1959), we build the efficient frontier and we will trace the Capital Market Line, CML. The program we use is Matlab (financial Toolkit). Research sample is composed by gold numismatic assets and precious metals. Those assets have been issued by Spain, USA, Great Britain and France from 1900 to 2009, and the research period is to 2003-2009. The results obtained confirm those not financial assets selected to build the efficient portfolio and the Market Portfolio.

Abstract:
This paper introduces a novice solution methodology for multi-objective optimization problems having the coefficients in the form of uncertain variables. The embedding theorem, which establishes that the set of uncertain variables can be embedded into the Banach space C[0, 1] × C[0, 1] isometrically and isomorphically, is developed. Based on this embedding theorem, each objective with uncertain coefficients can be transformed into two objectives with crisp coefficients. The solution of the original m-objectives optimization problem with uncertain coefficients will be obtained by solving the corresponding 2 m-objectives crisp optimization problem. The R & D project portfolio decision deals with future events and opportunities, much of the information required to make portfolio decisions is uncertain. Here parameters like outcome, risk, and cost are considered as uncertain variables and an uncertain bi-objective optimization problem with some useful constraints is developed. The corresponding crisp tetra-objective optimization model is then developed by embedding theorem. The feasibility and effectiveness of the proposed method is verified by a real case study with the consideration that the uncertain variables are triangular in nature.

Abstract:
the analysis is similar in framework to the model developed by markowitz in 1952, known as modern portfolio theory (mpt). this model basically shows how to extract the maximum possible yield from a portfolio, given a certain level of risk, and also highlights the advantages of a properly diversified portfolio. the time frame of the analysis corresponds to the final decade of the 20th century, a period that in colombia was marked by large fluctuations in the country′s economic performance, as well as by important changes in the structure of its stock markets. despite this restructuring, however, the present state of colombia′s stock markets continues to be precarious. their total capitalization barely -13% of the country′s gross domestic product- is far below the level of other countries in latin america . the us economy, meanwhile, enjoyed a period of unprecedented growth during the same period, white technological change in the fields of communication and information technology enabled the country′s financial markets to achieve even further growth both at home and abroad. the application of markowitz′s model provides handy tools for risk analysis and decision-making in accordance with the individual investor′s risk tolerance. the article concludes with a performance comparison of domestic and international portfolios.