Optimal Portfolio Analysis Using Power and Natural Logarithm Utility Functions with E-Commerce Data

In recent years portfolio optimization models that consider more criteria than the expected return and variance objectives of the Markowitz model have become popular. These models are harder to solve than the quadratic mean-variance problem. Two approaches to find a suitable portfolio for an investor are possible. In the multiattribute utility theory (MAUT) approach a utility function is constructed based on the investor's preferences and an optimization problem is solved to find a portfolio that maximizes the utility function. In the multiobjective programming (MOP) approach a set of efficient portfolios is computed by optimizing a scalarized objective function. The investor then chooses a portfolio from the efficient set according to his/her preferences. We outline these two approaches using the UTADIS method to construct a utility function and present numerical results for an example.

Portfolio Optimization Under Generalized Hyperbolic Skew Student's <i>t</i>-Distribution and Exponential Utility

We study the optimal dynamic trading strategy between a riskless asset and a risky asset with momentum (momentum asset). The most salient characteristic of momentum is that positive price shocks predict positive future returns. This characteristic leads to big swings in returns over multiple periods. Investors with relative risk aversion greater than one dislike such big swings. We show that it is optimal for such investors to reverse momentum by holding less or even shorting the momentum asset. We find that the optimal portfolio weight also depends on the historical price path, in addition to momentum. Different historical price paths, even if they have the same momentum, lead to different optimal portfolio weights. In particular, with rebound path (a historical price path that decreases at the beginning and then rebounds later to have a positive momentum), it is optimal for investors to hold less or may short the momentum asset and hence suffer less or even benefit from momentum crashes.

We study a finite-horizon optimal consumption and investment problem in a complete continuous-time market where consumption is restricted within fixed upper and lower bounds. Assuming constant relative risk aversion (CRRA) preferences, we employ the dual-martingale approach to reformulate the problem and derive closed-form integral representations for the dual value function and its derivatives. These results yield explicit feedback formulas for the optimal consumption, portfolio allocation, and wealth processes. We establish the duality theorem linking the primal and dual value functions and verify the regularity and convexity properties of the dual solution. Our results show that the upper and lower consumption bounds transform the linear Merton rule into a piecewise policy: consumption equals L when wealth is low, follows the unconstrained Merton ratio in the interior region, and is capped at H when wealth is high.

Non-convex optimal portfolio sets and constant relative risk aversion

This thesis consists of three essays in financial economics, more precisely in the field of asset pricing and optimal portfolio choice. The first essay studies the asset pricing implications of heterogeneity in preferences coupled with long run risk in a dynamic general equilibrium pure exchange economy. It is concerned with the understanding of how risk sharing among different types of agents affects the assets returns moments in equilibrium and moreover, how these agents reacts dynamically to the long run risk that they perceive. The second and third essay approach the question of optimal portfolio with stochastic opportunity sets. The second essay proposes an approximation methodology for deriving approximate closed form solutions of dynamic optimal portfolio allocation problems. The third essay examines the optimal consumption, portfolio rule and life insurance purchase problem of a wage earner having uncertain lifetime when the market price of risk follows a mean-reverting stochastic process.

This paper presents a reliable emergency facility location optimization model that considers complex polygon barriers and the risk of facility disruption. From a sustainable perspective, with capacity, cost, and demand constraints, the model maximizes time satisfaction and minimizes cost as the objective function to determine the optimal facility location and allocation. The paper proposes the barrier path optimization algorithm and the Kepler optimization algorithm (KOA) to solve the model and validates the model and algorithm through simulation experiments of various scales. Finally, the paper conducts a sensitivity analysis of the disruption probability using the control variable method to explore the impact of parameter changes on the decision results and compare the advantages of considering a sustainable perspective versus not considering it. The results show that the model and algorithm designed in this paper can effectively optimize the barrier path and obtain the optimal location-allocation scheme. The research findings will provide mathematical models and methodological strategies for emergency facility location decision-making.

When several investors with different risk aversions trade competitively in a capital market, the allocation of wealth fluctuates randomly among them and acts as a state variable against which each market participant will want to hedge. This hedging motive complicates the investors' portfolio choice and the equilibrium in the capital market. This article features two investors, with the same degree of impatience, one of them being logarithmic and the other having an isoelastic utility function. They face one risky constant- return-to-scale stationary production opportunity and they can borrow and lend to and from each other. The behaviors of the allocation of wealth and of the aggregate capital stock are characterized, along with the behavior of the rate of interest, the security market line, and the portfolio holdings. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Real estate ratios have increased in recent years. This article thus examines the diversification potential of real estate investments that German investors can achieve at a global scale. To this end, it analyzes how the illiquidity of some real estate investments or the illiquidity preference of an investor can bring about optimal investment ratios. Optimum allocation quotas for German investors with a wide range of mixed-asset allocations are examined. In addition to traditional optimizations, this article applies the three-fund theorem to include liquid and illiquid forms of real estate investment and to determine optimum allocation ratios. While real estate may be an essential component in a mixed-asset portfolio, it is not included in all optimal portfolios. An optimal portfolio also depends on the investment form, insofar as real estate vehicles are not always suitable for diversifying the portfolio risk or for improving the performance of a mixed-asset portfolio. Moreover, illiquid investment vehicles can often provide strong diversification benefits. The optimum allocations to real estate thus depend on the investor’s illiquidity acceptance, even if allocation dominance has increased in recent years. While many studies have demonstrated the advantage that investors gain from adding certain real estate assets, such as those obtained by direct investments, this study goes further by examining the comparative advantage of different real estate investment forms within a variety of asset classes. New insights can thus be gained by considering investors’ liquidity preferences within a given portfolio. One of these insights is that there is a trade-off between illiquidity and diversification potential. Another is that optimum portfolio allocations depend on illiquidity acceptance. These findings therefore also provide practical guidance not only to German investors with a global portfolio diversification but also to practitioners who add illiquid asset classes to their portfolio, to say nothing of the valuable field knowledge it offers to researchers in this field.

Using a stochastic representation of the optimal wealth process in the classical Merton problem, we calculate its cumulative distribution and density functions and provide bounds and monotonicity results for these quantities under general risk preferences. We also show that the optimal wealth and portfolio processes for different utility functions are related through a deterministic transformation and appropriately modified initial conditions. We analyze the value at risk (VaR) and expected shortfall (ES) of the optimal wealth process and show how each can be used to infer a constant relative risk aversion (CRRA) investor's risk aversion coefficient. Drawing analogies to the option greeks, we study the sensitivities of the optimal wealth process with respect to the cumulative excess stock return, time, and market parameters. We conclude with a study of how sensitivities of the excess return on the optimal wealth process relate to the portfolio's beta.

Singapore being an island economy and a financial hub with residents from diverse backgrounds, huge ethnic diversity, coming from different part of the world. This study aims to gain insights and information into the factors that affect investment planners, financial advisers and individuals need to consider improving their choice of the portfolio and its performance. People’s investment decisions and hence their portfolio, which hitherto has not been tested. Furthermore, it intends to identify the factors that drive investors to choose one investment over another and determine how they make their investment portfolios. The survey was modelled using the smart-pls statistical package (PLS-SEM), which is partial least squares structural equation modelling.

We implement a dynamically regularized, bootstrapped two-stage out-of-sample parametric portfolio policy to evaluate characteristics’ efficacy in the conditional stock return-generating process in the metric of expected power utility. Traditional characteristics, such as momentum and size afforded large utility gains before 1999. These opportunities have since vanished. Overfitting—imprecision in weight estimation—is correlated with the optimal portfolio’s variance. Therefore, it is not a problem for power utility investors with coefficients of relative aversion greater than four. For more risk-tolerant investors, we successfully reduce estimation error by increasing the curvature of the loss function relative to the investor’s utility function. (JEL L200; C110; C350)

Contents: Acknowledgements General Introduction PART I HARRY M. MARKOWITZ Introduction to Part I Howard R. Vane and Chris Mulhearn 1. Harry Markowitz (1952a), 'Portfolio Selection' 2. Harry Markowitz (1952b), 'The Utility of Wealth' 3. H. Levy and H.M. Markowitz (1979), 'Approximating Expected Utility by a Function of Mean and Variance' 4. Harry M. Markowitz and Eric L. van Dijk (2003), 'Single-Period Mean-Variance Analysis in a Changing World' PART II MERTON H. MILLER Introduction to Part II Howard R. Vane and Chris Mulhearn 5. Franco Modigliani and Merton H. Miller (1958), 'The Cost of Capital, Corporation Finance and the Theory of Investment' 6. Franco Modigliani and Merton H. Miller (1959), 'The Cost of Capital, Corporation Finance and the Theory of Investment: Reply' 7. Merton H. Miller and Franco Modigliani (1961), 'Dividend Policy, Growth, and the Valuation of Shares' 8. Franco Modigliani and Merton H. Miller (1963), 'Corporate Income Taxes and the Cost of Capital: A Correction' 9. Merton H. Miller and Franco Modigliani (1966), 'Some Estimates of the Cost of Capital to the Electric Utility Industry, 1954-57' 10. Merton H. Miller (1977), 'Debt and Taxes' PART III WILLIAM F. SHARPE Introduction to Part III Howard R. Vane and Chris Mulhearn 11. William F. Sharpe (1963), 'A Simplified Model For Portfolio Analysis' 12. William F. Sharpe (1964), 'Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk' 13. William F. Sharpe (1966), 'Mutual Fund Performance' 14. William F. Sharpe (1978), 'Bank Capital Adequacy, Deposit Insurance, and Security Values' PART IV ROBERT C. MERTON Introduction to Part IV Howard R. Vane and Chris Mulhearn 15. Robert C. Merton (1969), 'Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case' 16. Robert C. Merton (1971), 'Optimum Consumption and Portfolio Rules in a Continuous-Time Model' 17. Robert C. Merton (1973a), 'Theory of Rational Option Pricing' 18. Robert C. Merton (1973b), 'An Intertemporal Capital Asset Pricing Model' 19. Robert C. Merton (1974), 'On the Pricing of Corporate Debt: The Risk Structure of Interest Rates' 20. Robert C. Merton (1977), 'On the Pricing of Contingent Claims and the Modigliani-Miller Theorem' PART V MYRON S. SCHOLES Introduction to Part V Howard R. Vane and Chris Mulhearn 21. Fischer Black and Myron Scholes (1972), 'The Valuation of Option Contracts and a Test of Market Efficiency' 22. Fischer Black and Myron Scholes (1973), 'The Pricing of Options and Corporate Liabilities' 23. Fischer Black and Myron Scholes (1974), 'The Effects of Dividend Yield and Dividend Policy on Common Stock Prices and Returns' 24. Myron Scholes and Joseph Williams (1977), 'Estimating Betas from Nonsynchronous Data' 25. Merton H. Miller and Myron S. Scholes (1978), 'Dividends and Taxes' Name Index

In this article, we are interested in an investment problem with stochastic volatilities and Portfolio constraints on proportions. We model the risky assets by jump diffusion processes and we consider a power utility function. The objective is to maximize the expected utility from terminal wealth. The value function is known to be a viscosity solution of an integro-differential Hamilton-Jacobi-Bellman (HJB) equation. Thanks to an exponential transformation, we reduce the nonlinearity of the HJB equation to a semi-linear equation. We prove existence of a smooth solution to the latter equation and we state a verification theorem which relates this solution to the value function. We derive the backward stochastic differential equation (BSDE) associated with the semi-linear equation. We propose a numerical scheme for the resolution of the BSDE based on iterative regressions on function bases and Monte-Carlo method. We illustrate an example which shows the importance of this reduction for the optimal portfolio numerical study. Therefore, we compute the optimal investment strategy by solving the associated BSDE.

Portfolio Analysis is one of the alternative alternative tools in making investment decisions in stocks. In investing, if it only depends on one type of stock, it is likely that many investors will bear the risk. This stage involves identifying which securities will be chosen to form a portfolio and what proportion of funds will be invested in each of these securities. The selection of these securities (in other words, investors diversify) is intended to minimize the risk borne. The selection of these securities will be influenced by risk preferences, cash needs patterns, and tax status. Investment decisions are decisions taken by investors to allocate the funds they have in the form of certain assets (financial assets) in the hope that they will get economic benefits in the future. If the decision taken is to buy a certain number of shares, then that is expected to get dividends and capital gains if the shares are resold. The main consideration for fund owners (investors) in optimizing investment decisions is to maximize the level of return on investment (risk) for certain investments (Saragih et al., 2006). The making of an investment decision framework largely determines the success of an investor in optimizing the level of investment returns and reducing as little as possible the risks faced (Markowitz, 1952). In connection with the above, the main problem in this study is how to design an optimal portfolio simulation which is a combination of LQ 45 liquid stocks listed on the Indonesia Stock Exchange (IDX). The research data was conducted on LQ 45 shares during the period March - June 2012. The variables of this study were stock prices, returns, standard deviations of returns. The statistical method used is the F-test for homogeneity of variants. The results showed that only 16 stocks had optimal portfolios. Optimal portfolio, characterized by high return and low risk.