Revisiting modern portfolio theory

This paper revisits Modern Portfolio Theory and derives eleven properties of Efficient Allocations and Portfolios in the presence of leverage. With different degrees of leverage, an Efficient Portfolio is a linear combination of two portfolios that lie in different efficient frontiers - which allows for an attractive reinterpretation of the Separation Theorem. In particular a change in the investor risk-return preferences will leave the allocation between the Minimum Risk and Risk Portfolios completely unaltered - but will change the magnitudes of the tactical risk allocations within the Risk Portfolio. The paper also discusses the role of diversification in an Efficient Portfolio, emphasizing its more tactical, rather than strategic character

Modern Portfolio Theory Applied to Electricity Resource Planning

To meet electricity demand, electric utilities develop growth strategies for generation, transmission, and distributions systems. For a long time those strategies have been developed by applying least-cost methodology, in which the cheapest stand-alone resources are simply added, instead of analyzing complete portfolios. As a consequence, least-cost methodology is biased in favor of fossil fuel-based technologies, completely ignoring the benefits of adding non-fossil fuel technologies to generation portfolios, especially renewable energies. For this reason, this thesis introduces modern portfolio theory (MPT) to gain a more profound insight into a generation portfolio’s performance using generation cost and risk metrics. We discuss all necessary assumptions and modifications to this finance technique for its application within power systems planning, and we present a real case of analysis. Finally, the results of this thesis are summarized, pointing out the main benefits and the scope of this new tool in the context of electricity generation planning.

Has portfolio theory got any principles?

Recently, Portfolio Theory (PT) has been proposed for Information Retrieval. However, under non-trivial conditions PT violates the original Probability Ranking Principle (PRP). In this poster, we shall explore whether PT upholds a different ranking principle based on Quantum Theory, i.e. the Quantum Probability Ranking Principle (QPRP), and examine the relationship between this new model and the new ranking principle. We make a significant contribution to the theoretical development of PT and show that under certain circumstances PT upholds the QPRP, and thus guarantees an optimal ranking according to the QPRP. A practical implication of this finding is that the parameters of PT can be automatically estimated via the QPRP, instead of resorting to extensive parameter tuning.

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example

Bio-folio: applying portfolio theory to biodiversity

Genes, species and ecosystems are often considered to be assets. The need to ensure a sufficient diversity of this asset is being increasingly recognised today. Asset managers in banks and insurance companies face a similar challenge. They are asked to manage the assets of their investors by constructing efficient portfolios. They deliberately make use of a phenomenon observed in the formation of portfolios: returns are additive, while risks diversify. This phenomenon and its implications are at the heart of portfolio theory. Portfolio theory, like few other economic theories, has dramatically transformed the practical work of banks and insurance companies. Before portfolio theory was developed about 50 years ago, asset managers were confronted with a situation similar to the situation the research on biodiversity faces today. While the need for diversification was generally accepted, a concept that linked risk and return on a portfolio level and showed the value of diversification was missing. Portfolio theory has closed this gap. This article first explains the fundamentals of portfolio theory and transfers it to biodiversity. A large part of this article is then dedicated to some of the implications portfolio theory has for the valuation and management of biodiversity. The last section introduces three development openings for further research.

When does direct real estate improve portfolio performance?

For over twenty years researchers have been recommending that investors diversify their portfolios by adding direct real estate. Based on the tenets of modern portfolio theory (MPT) investors are told that the primary reason they should include direct real estate is that they will enjoy decreased volatility (risk) through increased diversification. However, the MPT methodology hides where this reduction in risk originates. To over come this deficiency we use a four-quadrant approach to break down the co-movement between direct real estate and equities and bonds into negative and positive periods. Then using data for the last 25-years we show that for about 70% of the time a holding in direct real estate would have hurt portfolio returns, i.e. when the other assets showed positive performance. In other words, for only about 30% of the time would a holding in direct real estate lead to improvements in portfolio returns. However, this increase in performance occurs when the alternative asset showed negative returns. In addition, adding direct real estate always leads to reductions in portfolio risk, especially on the downside. In other words, although adding direct real estate helps the investor to avoid large losses it also reduces the potential for large gains. Thus, if the goal of the investor is offsetting losses, then the results show that direct real estate would have been of some benefit. So in answer to the question when does direct real estate improve portfolio performance the answer is on the downside, i.e. when it is most needed.

Time weighted portfolio optimisation

In estimating the inputs into the Modern Portfolio Theory (MPT) portfolio optimisation problem, it is usual to use equal weighted historic data. Equal weighting of the data, however, does not take account of the current state of the market. Consequently this approach is unlikely to perform well in any subsequent period as the data is still reflecting market conditions that are no longer valid. The need for some return-weighting scheme that gives greater weight to the most recent data would seem desirable. Therefore, this study uses returns data which are weighted to give greater weight to the most recent observations to see if such a weighting scheme can offer improved ex-ante performance over that based on un-weighted data.

Is there a place for property in the multi-asset portfolio?

The case for property has typically rested on the application of modern portfolio theory (MPT), in that property has been shown to offer increased diversification benefits within a multi asset portfolio without hurting portfolio returns especially for lower risk portfolios. However this view is based upon the use of historic, usually appraisal based, data for property. Recent research suggests strongly that such data significantly underestimates the risk characteristics of property, because appraisals explicitly or implicitly smooth out much of the real volatility in property returns. This paper examines the portfolio diversification effects of including property in a multi-asset portfolio, using UK appraisal based (smoothed) data and several derived de-smoothed series. Having considered the effects of de-smoothing, we then consider the inclusion of a further low risk asset (cash) in order to investigate further whether property's place in a low risk portfolio is maintained. The conclusions of this study are that the previous supposed benefits of including property have been overstated. Although property may still have a place in a 'balanced' institutional portfolio, the case for property needs to be reassessed and not be based simplistically on the application of MPT.

Fuzzy portfolio allocation models through a new risk measure and fuzzy sharpe ratio

A new portfolio risk measure that is the uncertainty of portfolio fuzzy return is introduced in this paper. Beyond the well-known Sharpe ratio (i.e., the reward-to-variability ratio) in modern portfolio theory, we initiate the so-called fuzzy Sharpe ratio in the fuzzy modeling context. In addition to the introduction of the new risk measure, we also put forward the reward-to-uncertainty ratio to assess the portfolio performance in fuzzy modeling. Corresponding to two approaches based on TM and TW fuzzy arithmetic, two portfolio optimization models are formulated in which the uncertainty of portfolio fuzzy returns is minimized, while the fuzzy Sharpe ratio is maximized. These models are solved by the fuzzy approach or by the genetic algorithm (GA). Solutions of the two proposed models are shown to be dominant in terms of portfolio return uncertainty compared with those of the conventional mean-variance optimization (MVO) model used prevalently in the financial literature. In terms of portfolio performance evaluated by the fuzzy Sharpe ratio and the reward-to-uncertainty ratio, the model using TW fuzzy arithmetic results in higher performance portfolios than those obtained by both the MVO and the fuzzy model, which employs TM fuzzy arithmetic. We also find that using the fuzzy approach for solving multiobjective problems appears to achieve more optimal solutions than using GA, although GA can offer a series of well-diversified portfolio solutions diagrammed in a Pareto frontier.

Calibrating a CGE model with NTBs that Incorporates Standard Models of Modern Trade Theory

We propose a way to incorporate NTBs for the four workhorse models of the modern trade literature in computable general equilibrium models (CGEs). CGE models feature intermediate linkages and thus allow us to study global value chains (GVCs). We show that the Ethier-Krugman monopolistic competition model, the Melitz firm heterogeneity model and the Eaton and Kortum model can be defined as an Armington model with generalized marginal costs, generalized trade costs and a demand externality. As already known in the literature in both the Ethier-Krugman model and the Melitz model generalized marginal costs are a function of the amount of factor input bundles. In the Melitz model generalized marginal costs are also a function of the price of the factor input bundles. Lower factor prices raise the number of firms that can enter the market profitably (extensive margin), reducing generalized marginal costs of a representative firm. For the same reason the Melitz model features a demand externality: in a larger market more firms can enter. We implement the different models in a CGE setting with multiple sectors, intermediate linkages, non-homothetic preferences and detailed data on trade costs. We find the largest welfare effects from trade cost reductions in the Melitz model. We also employ the Melitz model to mimic changes in Non tariff Barriers (NTBs) with a fixed cost-character by analysing the effect of changes in fixed trade costs. While we work here with a model calibrated to the GTAP database, the methods developed can also be applied to CGE models based on the WIOD database.

Modern elementary theory of numbers

Mode of access: Internet.

Modern quantum theory.

Includes bibliography.

Electricity : an expansion of Everett's Deschanel, part III, on the lines of modern electrical theory /

Mode of access: Internet.