VaR Limits for Pension Funds: An Evaluation

This paper evaluates the effects of imposing Value-at-Risk (VaR) limits and quantitative restrictions on portfolio choices in the context of a risk-based supervision framework for defined contribution pension funds. It shows the conditions under which VaR constraints are equivalent to constraints on volatility. The paper also presents some further considerations that regulators should take into account when adopting a risk-based supervision framework when contributions are mandatory and a significant part of the pension depends on the performance of past investments.Portfolio Choice; VaR

Optimal Dynamic rading Strategies with Risk Limits

Value at Risk (VaR) has emerged in recent years as a standard tool to measure and control the risk of trading portfolios.Yet,existing theoretical analyses of the optimal behavior of a trader subject to VaR limits have produced a negative view of VaR as a risk-control tool. In particular,VaR limits have been found to induce increased risk exposure in some states and an increased probability of extreme losses. However, these conclusions are based on models that are either static or dynamically inconsistent. In this paper we formulate a dynamically consistent model of optimal portfolio choice subject to VaR limits and show that the conclusions of earlier papers are incorrect if, consistently with common practice,the portfolio VaR is reevaluated dynamically making use of available conditioning information. In particular, we ?nd that the risk exposure of a trader subject to a VaR limit is always lower than that of an unconstrained trader and that the probability of extreme losses is also lower.We also consider risk limits formulated in terms of Tail Conditional Expectation (TCE),a coherent risk measure often advocated as an alternative to VaR,and show that in our dynamic setting it is always possible to transform a TCE limit into an equivalent VaR limit,and conversely.

Forecasting Based On Open Var Model

Considering as a starting point certain advantages and limits of the VAR model, we propose an opening to include some approaches suggested particularly by economic theory, such as economic policy role and that concerning corrections applied to restore an equilibrium state or a forecast error. In order to improve the forecasting quality we introduced in the VAR model certain variables that express previous approaches. The open VAR model was applied to short-time prognoses regarding the main prices in economy (consumer price index, exchange rate, monthly wage, interest rate).interdependence, autoregressive, simultaneous equations model, structural form, reduce form, lagged variables, error correction, test, ex-post forecast, system, intercept parameter, qualitative variable

Industry Market Value at Risk in Australia

Value at Risk (VaR) is an important issue for banks since its adoption as a primary risk metric in the Basel Accords and the requirement that it is calculated on a daily basis. Relative industry risk measurement is also very important to Banks in their management of risk, such as for setting risk concentration limits and developing investment and credit policy. This paper examines market Value at Risk (VaR) and Conditional VaR (CVaR) in Australia from an industry perspective using a set of Australian industries. VaR and CVaR are compared between these industries over time, and a variety of metrics are used including diversified and undiversified VaR, as well as parametric and nonparametric CVaR methods. There has been no prior investigation of industry based VaR metrics in Australia to the authorsÌ knowledge. The relative riskiness of different industry sectors is examined and using diversified VaR, the study .nds the highest risk is in the Technology Sectors, whilst the lowest risk is found in the Finance and Utilities Sectors. Composite riskiness is also explored and the existence of correlation between industry risk rankings over time is found to depend on the number of years of data used. There is evidence of rank correlation over time using a 7 year window approach, but not when using 1 year data tranches. This highlights the importance of using both short and long time frames in order to cover different economic cycles as well as consider current conditions. It is important to note that there is found to be no significant difference between diversified and undiversified industry VaR rankings, or between parametric and nonparametric CVaR approaches. This means that bankers can be reasonably confident of the robustness of any one of these metrics when calculating and applying them, not only for the purposes of Basel compliance, but also for the determination of relative industry risk.Conditional value at risk (CVaR), Industry risk, Basel compliance

A VAR Model for the Analysis of the Effects of Monetary Policy in the Euro Area

This paper, by the estimation of a structural VAR model on aggregate data from 1980 to 2002, examines the macroeconomic effects of an unexpected change in monetary policy on the euro area. The results are in line with the economic theory and they are close to the one estimated by other authors. These results, considering the formation of the European Monetary Union, give rise to some doubts and require some considerations. Thus, this paper discusses the limits of both the econometric technique used, and the data compilation methodology usually applied in these works.

Model Uncertainty and Bayesian Model Averaging in Vector Autoregressive Processes

Economic forecasts and policy decisions are often informed by empirical analysis based on econometric models. However, inference based upon a single model, when several viable models exist, limits its usefulness. Taking account of model uncertainty, a Bayesian model averaging procedure is presented which allows for unconditional inference within the class of vector autoregressive (VAR) processes. Several features of VAR process are investigated. Measures on manifolds are employed in order to elicit uniform priors on subspaces defined by particular structural features of VARs. The features considered are the number and form of the equilibrium economic relations and deterministic processes. Posterior probabilities of these features are used in a model averaging approach for forecasting and impulse response analysis. The methods are applied to investigate stability of the "Great Ratios" in U.S. consumption, investment and income, and the presence and effects of permanent shocks in these series. The results obtained indicate the feasibility of the proposed method.Posterior probability; Grassman manifold; Orthogonal group; Cointegration; Model averaging; Stochastic trend; Impulse response; Vector autoregressive model.

On four species of Copepoda new to Chesapeake Bay, with a description of a new variety of Paracalanus crassirostris Dahl

At this time, four additional species, unreported by Wilson [1932], can be added to the list of those species to be found within the limits of the bay. These are Acartia tonsa Dana, Cyclops vernalis Fischer, Diaptomus spatulocrenatus Pearse, and Paracalanus crassirostris Dahl var. nudus nov. The specimens from which identifications were made were collected by means of Clarke-Bumpus nets, in use on the motor ship "Mahatru.

Model uncertainty and Bayesian model averaging in vector autoregressive processes

Economic forecasts and policy decisions are often informed by empirical analysis based on econometric models. However, inference based upon a single model, when several viable models exist, limits its usefulness. Taking account of model uncertainty, a Bayesian model averaging procedure is presented which allows for unconditional inference within the class of vector autoregressive (VAR) processes. Several features of VAR process are investigated. Measures on manifolds are employed in order to elicit uniform priors on subspaces defined by particular structural features of VARs. The features considered are the number and form of the equilibrium economic relations and deterministic processes. Posterior probabilities of these features are used in a model averaging approach for forecasting and impulse response analysis. The methods are applied to investigate stability of the “Great Ratios†in U.S. consumption, investment and income, and the presence and effects of permanent shocks in these series. The results obtained indicate the feasibility of the proposed method.cointegration;Grassman manifold;impulse response;model averaging;posterior probability;stochastic trend;orthogonal group;vector autoregressive model

Existence of solutions to a general geometric elliptic variational problem

We consider the problem of minimising an inhomogeneous anisotropic elliptic functional in a class of closed $m$ dimensional subsets of $\mathbf{R}^n$ which is stable under taking smooth deformations homotopic to the identity and under local Hausdorff limits. We prove that the minimiser exists inside the class and is an $(\mathscr{H}^m,m)$~rectifiable set in the sense of Federer. The class of competitors encodes a notion of spanning a boundary. We admit unrectifiable and non-compact competitors and boundaries, and we make no restrictions on the dimension $m$ and the co-dimension $n-m$ other than $1 \le m < n$. An important tool for the proof is a novel smooth deformation theorem. The skeleton of the proof and the main ideas follow Almgren's 1968 paper. In the end we show that classes of sets spanning some closed set $B$ in homological and cohomological sense satisfy our axioms.Comment: This is a pre-print of an article accepted for publication in Calc. Var. PD

A decision rule to minimize daily capital charges in forecasting value-at-risk

Under the Basel II Accord, banks and other Authorized Deposit-taking Institutions (ADIs) have to communicate their daily risk estimates to the monetary authorities at the beginning of the trading day, using a variety of Value-at-Risk (VaR) models to measure risk. Sometimes the risk estimates communicated using these models are too high, thereby leading to large capital requirements and high capital costs. At other times, the risk estimates are too low, leading to excessive violations, so that realised losses are above the estimated risk. In this paper we propose a learning strategy that complements existing methods for calculating VaR and lowers daily capital requirements, while restricting the number of endogenous violations within the Basel II Accord penalty limits. We suggest a decision rule that responds to violations in a discrete and instantaneous manner, while adapting more slowly in periods of no violations. We apply the proposed strategy to Standard & Poor’s 500 Index and show there can be substantial savings in daily capital charges, while restricting the number of violations to within the Basel II penalty limits.value-at-risk;daily capital charges;optimizing strategy;risk forecasts;endogenous violations;frequency of violations