Optimal Portfolio Construction Research Articles

Development, Implementation and Evaluation of Multistage Investment Strategies

Construction of optimal investment portfolio is very complicated task due to many diverse factors which might affect risk and return of the portfolio in the future. Values and impact level of unique factors on the portfolio are changing over time; therefore every investor should take into account the fact that there always will be a certain level of risk associated with any portfolio involving stocks. There is a number of ways to form a collection of most appropriate stocks and bonds for investment portfolio as well as to allocate weights of assets based on various criteria. All of these methods, dedicated for selection and allocation of assets, have their specific features and some disadvantages. In order to be able to conclude which of the asset selection methods have least disadvantages, four popular techniques were analysed and compared. These techniques were based on different variables: correlation coefficients between asset returns, maximisation of the utility function (diverse values of risk aversion coefficients were analysed), selection of assets with highest historical returns, and employment of modified price-to-earnings ratio. The article deals with multistage extension to the mean-variance and expected utility maximisation portfolio choice. Multistage investing consists of several essential stages, where each stage forms a basis for the next stage by providing useful input data, derived by stage-specific analysis. For construction of optimal portfolio the following stages are used: asset allocation, security selection, investment strategy development, construction of the model and its evaluation. After asset allocation was made and stocks for the portfolios had been selected, different theoretical asset allocation models (equal weight asset allocation, Markowitz model, Capital Asset Pricing Model (CAPM), model where risk free asset is incorporated when constructing a portfolio) have been modified and adapted in order to become suitable for real market situation. Such prerequisites as normal distribution of stock returns were not satisfied by most Lithuanian companies’ stocks when different interims were investigated, therefore authors set a presupposition that distribution properties of the stocks can be disregarded when Markowitz and CAPM models were applied to real market. Some other changes for the prerequisites of models were made; otherwise these theoretical models could not have been applied to Lithuanian market. After all models had been applied in Lithuanian equity market, back testing was carried out and certain characteristics of outcomes of different investment strategies were compared. Results were judged against characteristics of popular stock exchange indices of Baltic States in order to obtain conclusions. Most models were developed for broad financials markets (global markets). In the paper we analyse financial market of Lithuania. Since this market does not fit assumed conditions of general models, the models were slightly modified to apply for Lithuania market. The results of portfolio were compared with Baltic States index. It was concluded that the highest return rate is achieved by constructing the investment portfolio with employing modified Capital Asset Pricing Model. The best technique for selecting stocks proved to be the maximisation of utility function when risk aversion coefficient A=3. In addition to this, after comparison of different asset selection methods, it was noted that the highest value of the Sharpe ratio was achieved by utilising the same technique. After investigation it was noted that investors should add a risk free asset into portfolio of stocks because it usually improves the results of most portfolios, irrespective of their contents. Constructing portfolios based on asset allocation according to indices analysed in the paper is not recommended because characteristics of indices were worse than the ones of constructed portfolios. Stocks of every company quoted in NASDAQ OMX Baltic (2011) Stock Exchange in Vilnius Official list for more than 10 years (2001 beginning – 2010 end) were investigated. Stocks of 14 companies satisfied preset 10 year interim criterion.DOI: http://dx.doi.org/10.5755/j01.ee.23.2.1542

Principles for drafting an investment policy with illustrations

During the past few decades, significant theoretical advances in portfolio theory and asset pricing have substantially increased our understanding of how to construct optimal portfolios. These theoretical developments have challenged professional portfolio management to develop appropriate tools to incorporate these novel ideas. In this paper, we contribute by focusing on the critical role of the investment policy as a tool that connects portfolio theory to portfolio management. We select, list, discuss and illustrate with examples several principles that are essential items of an investment policy.

On the Equity and Interest Rate Predictability for Balanced Portfolios and Coverage Ratios for Pension Plans

The purpose of this study is twofold. On one hand we derive an optimal allocation framework between stocks and bonds, with and without a momentum factor, taking into account a regime-switching model based on monthly equity and interest rate data since 1870. On the other, we investigate the optimal portfolio construction for the manager of a pension plan, where the pension’s liabilities are valued in present value terms. Assuming such a pension plan is exposed to two risk factors only, an equity factor and an interest rate factor, the manager needs to decide on the exposure to equities (the beta to equities measured at the level of the total portfolio), and the level of exposure to interest rates, relative to the benchmark defined by the liabilities. Using over 140 years of monthly data pertaining to US equities and 10-year yields, I show that combining a momentum factor with a Markov regime switching approach provides a very robust framework with optimal allocations to stocks and bonds in each regime for the traditional manager, and a well defined equities (beta) exposure and interest rate hedge policy for the manager of the pension plan.

Portfolio Optimization with Asian Hedge Funds: A Comparison between the Mean - Variance and the Polynomial Goal Progamming Methods

This study attempts to construct optimal portfolios of Asian hedge funds (AHFs) by employing both the traditional mean - variance (MV) method and the polynomial goal programming (PGP) method. In addition, further issues such as the existence of optimal number of funds and the contribution of a specific fund characteristic to the performance of a portfolio of AHFs are also investigated. From the Eurekahedge database, a sample consisting of 95 AHFs was selected for this study, covering the period of 1st January 2000 - 31st May 2009. Results confirmed that (1) diversification benefits exist in AHFs, (2) optimal number of funds exist for a portfolio of AHFs, (3) many portfolios of AHFs with specific fund characteristics achieved high probabilities of being either the first or the second best-performing portfolios at various levels of standard deviations, and (4) the PGP method was shown to be more effective than the MV method as it enables different efficient frontiers to be constructed according to individual investors’ risk preferences.

Uniform quasi-concavity in probabilistic constrained stochastic programming

A probabilistic constrained stochastic linear programming problem is considered, where the rows of the random technology matrix are independent and normally distributed. The quasi-concavity of the constraining function needed for the convexity of the problem is ensured if the factors of the function are uniformly quasi-concave. A necessary and sufficient condition is given for that property to hold. It is also shown, through numerical examples, that such a special problem still has practical application in optimal portfolio construction.

Statistical and Algorithm Aspects of Optimal Portfolios

Presentation slides for proposed high frequency optimal portfolio construction, optimization and execution framework.

Estimating Security Betas Using Prior Information Based on Firm Fundamentals

We propose a hybrid approach for estimating beta that shrinks rolling window estimates toward firm-specific priors motivated by economic theory. Our method yields superior forecasts of beta that have important practical implications. First, unlike standard rolling window betas, hybrid betas carry a significant price of risk in the cross-section even after controlling for characteristics. Second, the hybrid approach offers statistically and economically significant out-of-sample benefits for investors who use factor models to construct optimal portfolios. We show that the hybrid estimator outperforms existing estimators because shrinkage toward a fundamentals-based prior is effective in reducing measurement noise in extreme beta estimates.

An Asset Allocation Model Based on a Semi Variance Adjusted Sharpe Ratio

In asset allocation processes the estimation of standard deviations is often measured with error. As a result, the risk adjusted return ratios will be subject to estimation error. Since risk estimation is crucial in investment decisions, several risk measures have been suggested to take into consideration that risk changes through time. The choice of different risk measures can considerably change asset allocation decisions in the way in which assets are ranked on the basis of their risk-return profile. This paper is concerned with how to construct optimal portfolios that adapt quickly to changes in risk using a time varying asset allocation model based on a modified Sharpe Ratio measure.

Return forecasts and optimal portfolio construction: a quantile regression approach

In finance there is growing interest in quantile regression with the particular focus on value at risk and copula models. In this paper, we first present a general interpretation of quantile regression in the context of financial markets. We then explore the full distributional impact of factors on returns of securities and find that factor effects vary substantially across quantiles of returns. Utilizing distributional information from quantile regression models, we propose two general methods for return forecasting and portfolio construction. We show that under mild conditions these new methods provide more accurate forecasts and potentially higher value-added portfolios than the classical conditional mean method.

A Bayesian Panel Data Approach to Explaining Market Beta Dynamics

We characterize the process that drives the market betas of individual stocks by setting up a hierarchical Bayesian panel data model that allows a flexible specification for beta. We show that combining the parametric relationship between betas and conditioning variables specified by economic theory with the robustness of an autoregressive specification delivers superior estimates of firm-specific betas. Our model also improves the accuracy of beta forecasts, which we use to construct optimal portfolios subject to target beta constraints. We further provide empirical support for the prediction of conditional asset pricing theory that individual stocks exhibit different risk dynamics. Finally, we document strong cross-sectional heterogeneity in firm-specific betas within the 25 size-B/M portfolios that are commonly used to test asset pricing models.

Pompian, M. (2006): Behavioral Finance and Wealth Management – How to Build Optimal Portfolios That Account for Investor Biases

In “Behavioral Finance and Wealth Management—How to Build Optimal Portfolios That Account for Investor Biases,” Michael Pompian summarizes results from the area of behavioral finance and shows how to construct optimal portfolios in the presence of biases. I recommend the book to anyone working in the field of portfolio management because it delivers a good overview of investors’ behavioral biases. The book is divided into 27 chapters which are organized in four parts. The first part is an introduction to the field of behavioral finance. Part 2 overviews the relevant literature of different behavioral biases and presents hands-on advice for practice. Case studies are presented in the third part. In the last part, original research of the author is presented. The first chapter includes the challenges to the two standard finance assumptions, rational markets and the homo oeconomicus. The most prominent researchers/figures in the area as well as their main contributions are introduced. Subsequently, the history of the field is presented, from its emergence to the most recent developments. The focus is on findings in microeconomics, since the aim of the book is to show the implications for private investors. Practical applications start in the third and final chapter of this part. This chapter introduces the framework for portfolio management. Instead of presenting an analytical framework, the author gives particular advice on how to diagnose behavioral biases within investors. The second part of the book presents the contribution of the book. Each of the 20 chapters presents one particular bias and its behavioral explanation. Additionally a concrete practical application shows the use of the bias in practical situations and outlines implications for investors for each bias. A thorough discussion of the relevant literature is held in each chapter. Also, practical advice is given, such as how

The Errors-in-Variable Model in the Optimal Portfolio Construction

In the paper we consider a modification of Sharpe’s method used in classical portfolio analysis for optimal portfolio building. The conventional theory assumes there is a linear relationship between asset’s return and market portfolio return, while the influence of all the other factors is not included. We propose not to neglect them any more, but include them into a model. Since the factors in question are often hard to measure or even characterize, we treat them as a disturbances on random variables used by classical Sharpe’s method.The key idea of the paper is the modification of the classical approach by application of the errors-in-variable model. We assume that both independent (market portfolio return) as well as dependent (given asset’s return) variables are randomly distributed values related with each other by linear relationship and we build the model used for parameters’ estimation.To verify the model, we performed an analysis based on archival data from Warsaw Stock Exchange. The results are also included.

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract: Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay‐offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall‐based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean‐shortfall portfolios can be much greater than for mean‐variance portfolios. Using empirical hedge fund return data we show that the optimal mean‐shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short‐put payoffs are optimal for a mean‐shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.

What Investors Want! Behavioural Finance Implications in Optimal Portfolio Construction

The paper outlines some thoughts on portfolio construction that take into account investors' asymmetric risk tolerance as commonly argued by adherents to behavioural finance. The paper develops previous empirical findings of investor risk tolerances determined using Choice Modelling of alternate portfolios and argues that portfolio optimisation may need to consider insurance if it is to maximize investor utility. Further, the paper makes the point that while the cost of insurance acts as a drag on returns, the value of insurance allows investors to take greater risks. And while on an aggregate basis pricing of insurance must act to compensate for aggregate downside risk take, on an individual level, the value function works to provide better utility to the individual investor.

Portfolio optimization when risk factors are conditionally varying and heavy tailed

Assumptions about the dynamic and distributional behavior of risk factors are crucial for the construction of optimal portfolios and for risk assessment. Although asset returns are generally characterized by conditionally varying volatilities and fat tails, the normal distribution with constant variance continues to be the standard framework in portfolio management. Here we propose a practical approach to portfolio selection. It takes both the conditionally varying volatility and the fat-tailedness of risk factors explicitly into account, while retaining analytical tractability and ease of implementation. An application to a portfolio of nine German DAX stocks illustrates that the model is strongly favored by the data and that it is practically implementable.

Return Forecasts and Optimal Portfolio Construction: A Quantile Regression Approach

In finance, there is growing interest in quantile regression with the particular focus on value at risk and copula models. In this paper, we first present a general interpretation of quantile regression in the financial market. We then explore the full distributional impact of factors on returns of securities, and find that factor effects vary substantially across quantiles of returns. Utilizing distributional information from quantile regression models, we propose two general methods for the return forecasting and portfolio construction. We show that under mild conditions these new methods provide more accurate forecasts and potentially more valueadded portfolios than the classical conditional mean method.

Optimal Portfolio Balancing Under Conventional Preferences and Transaction Costs Explains the Equity Premium Puzzle

Following Constantinides' (1986) seminal approach and introducing transaction costs in the Pagano (1989) model, conventional CARA investors with heterogeneous endowments trade to construct optimal portfolios. We calibrate to the 1896-1994 equity and bond markets to show that gains from trade are high and, thus, investors require a high illiquidity premium even for a modest transactional charge. Excluding risk premia, exchange of equity and bonds by N strategic investors, as , under a mere 1% round-trip transaction cost induces a 6% illiquidity (equity) premium. Unlike existing literature, our findings are consistent with most stylized empirical facts. We recover the elasticity of trading demand from the excess equity return to confirm a major implication of the model. Among many other, so called, anomalies, we appear to explain the apparent irrational exuberance of equity markets, the 600% price premium for otherwise identical A stock over B stock in China, the low risk-free rate, the 20% letter stock premium and the lower return on the run bonds. Because illiquidity premia do not necessarily imply consumption volatility, variance bounds tests become irrelevant.

Risk Measurement and Listed Property Trust Investment Strategies : Focusing on the Downside

Measuring investment risk precisely is critical to investment strategies. In common practice, the most popular measure of risk is standard deviation. However, standard deviation makes no distinction between positive and negative deviations from the mean. Such risk measurement could lead to biased decision making, given that asset returns are generally not symmetrically distributed.In this paper, risk is confined to adverse outcomes that are measured by the negative semi-deviation. By examining Australian Listed Property Trusts (LPTs) for the period of 1985- 2004, this paper illustrates how the differentiation between risk (semi-deviation) and uncertainty (standard deviation) make significant differences in performance measurement and optimal portfolio construction. This paper demonstrates that the concept and application of downside risk is a valuable construct to LPT investment strategies.

Optimal Portfolios of Foreign Currencies

Empirical evidence suggests that forward exchange rates are biased predictors of future spot exchange rates. Currencies with higher nominal interest rates tend to appreciate rather than depreciate as predicted by the forward rates. Simultaneously, exchange rates also turn out to be notoriously difficult to predict using plausible macroeconomic variables. The authors demonstrate how these two hypotheses can be combined with standard mean–variance analysis to construct optimal currency portfolios. They simulate the optimal portfolio strategies on historically observed data for the period 1989–1999 for DEM, JPY, GBP, and CHF (with the USD as the base currency). These portfolios generate positive excess returns. Moreover, the returns on optimal currency portfolios do not appear to be correlated with the returns on major fixed–income and equity indexes. These findings suggest that the methodology can provide a useful benchmark against which to evaluate more elaborate active currency strategies.

Optimal Risk-Adjusted Portfolios with Multiple Managers

Previous research demonstrated how current measures of risk–adjusted performance are insufficient for ranking investment managers or structuring portfolios, and provided an alternative measure called correlation–adjusted performance (CAP). The new measure accounts for differences in standard deviations, the correlation between portfolios and the benchmark, and the fact that investors have a target relative risk. In this article, the author extends the analysis for institutional investors with multiple manager portfolios. This technique facilitates optimal portfolio construction by combining the risk–free asset, the benchmark, and many investment managers. Since managers are less than perfectly correlated with each other, unattractive managers on a stand–alone basis may be chosen for their diversification properties and overall risk–adjusted performance can be increased over that of the highest yielding manager. The author also shows that the case for passive management is greatly diminished under this paradigm.