Relative Robust Portfolio Optimization

Considering mean-variance portfolio problems with uncertain model parameters, we contrast the classical absolute robust optimization approach with the relative robust approach based on a maximum regret function. Although the latter problems are NP-hard in general, we show that tractable inner and outer approximations exist in several cases that are of central interest in asset management

FARM FINANCIAL STRUCTURE DECISIONS UNDER DIFFERENT INTERTEMPORAL RISK BEHAVIORAL CONSTRUCTS

An alternative unconstrained expected-utility maximization model of farm debt is developed using the location-scale parameter condition that incorporates the empirically validated hypotheses of decreasing absolute and constant relative risk aversion. Simulation-optimization results based on the old and new model versions provide interesting implications for various levels of risk aversion and initial equity investments.Risk and Uncertainty,

THE USE OF MEAN-VARIANCE FOR COMMODITY FUTURES AND OPTIONS HEDGING DECISIONS

This study provides additional evidence of the usefulness of mean-variance procedures in the presence of options which can truncate and skew the returns distribution. Using a simulation analysis, price hedging decisions are examined for hog producers when options are available. Mean-variance results are contrasted with optimal decisions based on negative exponential and Cox-Rubinstein utility functions over 56 ending price scenarios and two levels of risk aversion. The findings from our simulation, which considers discrete contracts, basis risk, lognormality in prices, transactions costs, and alternative utility specifications, affirm the usefulness of mean-variance framework.Marketing,

STOCHASTIC TECHNOLOGY, RISK PREFERENCES AND ADOPTION OF SITE-SPECIFIC TECHNOLOGIES

This paper develops a model of farmer decision-making to examine the extent to which uncertainties about the performance of site-specific technologies (SSTs) and about the weather impact the value of these technologies. The model uses the jointly estimated risk and technology parameters to examine the impacts of SSTs on returns and nitrogen pollution. The availability of uncertain soil information and production uncertainty can lead risk-averse farmers to apply more fertilizers and generate more pollution. Ignoring the impact of uncertainty and risk preferences of farmers leads to a significant overestimation of the economic and environmental benefits of SSTs and underestimation of the required subsidy for inducing adoption of SSTs. The model that accounts for uncertainties about soil conditions and production as well as risk preferences of farmers provides an explanation for the low observed adoption rates of SSTs. Improvements in the accuracy of SSTs have the potential to increase the incentives for adoption.spatial variability, risk preferences, joint estimation, uncertainty, technology adoption, nitrogen runoff, Research and Development/Tech Change/Emerging Technologies,

A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability

We present a simulation-based method for solving discrete-time portfolio choice problems involving non-standard preferences, a large number of assets with arbitrary return distribution, and, most importantly, a large number of state variables with potentially path-dependent or non-stationary dynamics. The method is flexible enough to accommodate intermediate consumption, portfolio constraints, parameter and model uncertainty, and learning. We first establish the properties of the method for the portfolio choice between a stock index and cash when the stock returns are either iid or predictable by the dividend yield. We then explore the problem of an investor who takes into account the predictability of returns but is uncertain about the parameters of the data generating process. The investor chooses the portfolio anticipating that future data realizations will contain useful information to learn about the true parameter values.

Portfolio Choice for HARA Investors: When Does 1/γ (not) Work?

In the continuous time-Merton-model the instantaneous stock proportions are inversely proportional to the investorâs local relative risk aversion γ. This paper analyses the conditions under which a HARA-investor can use this 1/γ-rule to approximate her optimal portfolio in a finite time setting without material effects on the certainty equivalent of the portfolio payoff. The approximation is of high quality if approximate arbitrage opportunities do not exist and if the investorâs relative risk aversion is higher than that used for deriving the approximation portfolio. Otherwise, the approximation quality may be bad.HARA-utility, portfolio choice, certainty equivalent, approximated choice

Does Portfolio Optimization Pay?

All HARA-utility investors with the same exponent invest in a single risky fund and the risk-free asset. In a continuous time-model stock proportions are proportional to the inverse local relative risk aversion of the investor (1/γ-rule). This paper analyses the conditions under which the optimal buy and holdportfolio of a HARA-investor can be approximated by the optimal portfolio of an investor with some low level of constant relative risk aversion using the 1/γ-rule. It turns out that the approximation works very well in markets without approximate arbitrage opportunities. In markets with high equity premiums this approximation may be of low quality.HARA-utility, portfolio choice, certainty equivalent, approximated choice

Foraging under conditions of short-term exploitative competition: The case of stock traders

Theory purports that animal foraging choices evolve to maximize returns, such as net energy intake. Empirical research in both human and nonhuman animals reveals that individuals often attend to the foraging choices of their competitors while making their own foraging choices. Due to the complications of gathering field data or constructing experiments, however, broad facts relating theoretically optimal and empirically realized foraging choices are only now emerging. Here, we analyze foraging choices of a cohort of professional day traders who must choose between trading the same stock multiple times in a row---patch exploitation---or switching to a different stock---patch exploration---with potentially higher returns. We measure the difference between a trader's resource intake and the competitors' expected intake within a short period of time---a difference we call short-term comparative returns. We find that traders' choices can be explained by foraging heuristics that maximize their daily short-term comparative returns. However, we find no one-best relationship between different trading choices and net income intake. This suggests that traders' choices can be short-term win oriented and, paradoxically, maybe maladaptive for absolute market returns

A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems