Asymmetry, Loss Aversion and Forecasting

Conditional volatility models, such as GARCH, have been used extensively in financial applications to capture predictable variation in the second moment of asset returns. However, with recent theoretical literature emphasising the loss averse nature of agents, this paper considers models which capture time variation in the second lower partial moment. Utility based evaluation is carried out on several approaches to modelling the conditional second order lower partial moment (or semi-variance), including distribution and regime based models. The findings show that when agents are loss averse, there are utility gains to be made from using models which explicitly capture this feature (rather than trying to approximate using symmetric volatility models). In general direct approaches to modelling the semi-variance are preferred to distribution based models. These results are relevant to risk management and help to link the theoretical discussion on loss aversion to emprical modellingAsymmetry, loss aversion, semi-variance, volatility models.

Climatology of daily rainfall semi-variance in The Netherlands

Rain gauges can offer high quality rainfall measurements at their locations. Networks of rain gauges can offer better insight into the space-time variability of rainfall, but they tend to be too widely spaced for accurate estimates between points. While remote sensing systems, such as radars and networks of microwave links, can offer good insight in the spatial variability of rainfall they tend to have more problems in identifying the correct rain amounts at the ground. A way to estimate the variability of rainfall between gauge points is to interpolate between them using fitted variograms. If a dense rain gauge network is lacking it is difficult to estimate variograms accurately. In this paper a 30-year dataset of daily rain accumulations gathered at 29 automatic weather stations operated by KNMI (Royal Netherlands Meteorological Institute) and a one-year dataset of 10 gauges in a network with a radius of 5 km around CESAR (Cabauw Experimental Site for Atmospheric Research) are employed to estimate variograms. Fitted variogram parameters are shown to vary according to season, following simple cosine functions. Semi-variances at short ranges during winter and spring tend to be underestimated, but semi-variances during summer and autumn are well predicted

Using variograms to detect and attribute hydrological change

There have been many published studies aiming to identify temporal changes in river flow time series, most of which use monotonic trend tests such as the Mann–Kendall test. Although robust to both the distribution of the data and incomplete records, these tests have important limitations and provide no information as to whether a change in variability mirrors a change in magnitude. This study develops a new method for detecting periods of change in a river flow time series, using temporally shifting variograms (TSVs) based on applying variograms to moving windows in a time series and comparing these to the long-term average variogram, which characterises the temporal dependence structure in the river flow time series. Variogram properties in each moving window can also be related to potential meteorological drivers. The method is applied to 91 UK catchments which were chosen to have minimal anthropogenic influences and good quality data between 1980 and 2012 inclusive. Each of the four variogram parameters (range, sill and two measures of semi-variance) characterise different aspects of the river flow regime, and have a different relationship with the precipitation characteristics. Three variogram parameters (the sill and the two measures of semi-variance) are related to variability (either day-to-day or over the time series) and have the largest correlations with indicators describing the magnitude and variability of precipitation. The fourth (the range) is dependent on the relationship between the river flow on successive days and is most correlated with the length of wet and dry periods. Two prominent periods of change were identified: 1995–2001 and 2004–2012. The first period of change is attributed to an increase in the magnitude of rainfall whilst the second period is attributed to an increase in variability of the rainfall. The study demonstrates that variograms have considerable potential for application in the detection and attribution of temporal variability and change in hydrological systems

A Heuristic Approach to Portfolio Optimization

Constraints on downside risk, measured by shortfall probability, expected shortfall, semi-variance etc., lead to optimal asset allocations which differ from the meanvariance optimum. The resulting optimization problem can become quite complex as it exhibits multiple local extrema and discontinuities, in particular if we also introduce constraints restricting the trading variables to integers, constraints on the holding size of assets or on the maximum number of different assets in the portfolio. In such situations classical optimization methods fail to work efficiently and heuristic optimization techniques can be the only way out. The paper shows how a particular optimization heuristic, called threshold accepting, can be successfully used to solve complex portfolio choice problems.Portfolio Optimization; Downside Risk Measures;Heuristic Optimization Threshold Accepting.

Re-evaluating Hedging Performance

Mixed results have been documented for the performance of hedging strategies using futures. This paper reinvestigates this issue using an extensive set of performance evaluation metrics across seven international markets. We compare the hedging performance of short and long hedgers using traditional variance based approaches together with modern risk management techniques including Value at Risk, Conditional Value at Risk and approaches based on Downside Risk. Our findings indicate that using these metrics to evaluate hedging performance, yields differences in terms of best hedging strategy as compared with the traditional variance measure. We also find significant differences in performance between short and long hedgers. These results are observed both in-sample and out-of-sample.Hedging Performance; Lower Partial Moments; Downside Risk; Variance; Semi- Variance; Value at Risk, Conditional Value at Risk

Local Search Techniques for Constrained Portfolio Selection Problems

We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the cardinality of the portfolio and on the quantity of individual shares. Such constraints better capture the real-world trading system, but make the problem more difficult to be solved with exact methods. We explore the use of local search techniques, mainly tabu search, for the portfolio selection problem. We compare and combine previous work on portfolio selection that makes use of the local search approach and we propose new algorithms that combine different neighborhood relations. In addition, we show how the use of randomization and of a simple form of adaptiveness simplifies the setting of a large number of critical parameters. Finally, we show how our techniques perform on public benchmarks.Comment: 22 pages, 3 figure

Portfolio selection models: A review and new directions

Modern Portfolio Theory (MPT) is based upon the classical Markowitz model which uses variance as a risk measure. A generalization of this approach leads to mean-risk models, in which a return distribution is characterized by the expected value of return (desired to be large) and a risk value (desired to be kept small). Portfolio choice is made by solving an optimization problem, in which the portfolio risk is minimized and a desired level of expected return is specified as a constraint. The need to penalize different undesirable aspects of the return distribution led to the proposal of alternative risk measures, notably those penalizing only the downside part (adverse) and not the upside (potential). The downside risk considerations constitute the basis of the Post Modern Portfolio Theory (PMPT). Examples of such risk measures are lower partial moments, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We revisit these risk measures and the resulting mean-risk models. We discuss alternative models for portfolio selection, their choice criteria and the evolution of MPT to PMPT which incorporates: utility maximization and stochastic dominance

Moments and Semi-Moments for fuzzy portfolios selection

The aim of this paper is to consider the moments and the semi-moments (i.e semi-kurtosis) for portfolio selection with fuzzy risk factors (i.e. trapezoidal risk factors). In order to measure the leptokurtocity of fuzzy portfolio return, notions of moments (i.e. Kurtosis) kurtosis and semi-moments(i.e. Semi-kurtosis) for fuzzy port- folios are originally introduced in this paper, and their mathematical properties are studied. As an extension of the mean-semivariance-skewness model for fuzzy portfolio, the mean-semivariance-skewness- semikurtosis is presented and its four corresponding variants are also considered. We briefly designed the genetic algorithm integrating fuzzy simulation for our optimization models.Fuzzy moments, Credibility theory, Portfolios, Asset allocation, multi-objective optimization