The convergence of optimization based estimators : theory and application to a GARCH-model

The convergence of estimators, e.g. maximum likelihood estimators, for increasing sample size is well understood in many cases. However, even when the rate of convergence of the estimator is known, practical application is hampered by the fact, that the estimator cannot always be obtained at tenable computational cost. This paper combines the analysis of convergence of the estimator itself with the analysis of the convergence of stochastic optimization algorithms, e.g. threshold accepting, to the theoretical estimator. We discuss the joint convergence of estimator and algorithm in a formal framework. An application to a GARCH-model demonstrates the approach in practice by estimating actual rates of convergence through a large scale simulation study. Despite of the additional stochastic component introduced by the use of an optimization heuristic, the overall quality of the estimates turns out to be superior compared to conventional approaches. --GARCH,Threshold Accepting,Optimization Heuristics,Convergence

Autonomously Interacting Banks

The great financial turmoil that started 2007 has brought bank regulation back into the political debate. There is talk about imposing new regulations on banks and other financial intermediaries. Yet, we are not convinced that it is completely understood how the existing regulation affects systemic stability, let alone what the effect of new proposed rules would be. In order to better understand these issues, we study the interaction of hetero- geneous financial agents in a market that features several properties we believe to be realistic. Our agents develop heterogeneous views about the correct valuation of a risky asset. Some agents (banks) operate with substantial leverage and thus bankruptcy is a possibility. Agents may engage in fire sales, either because they face real financial trouble, or because they are forced to by regulation. Moreover, through their trading activities, agents exert externalities on each other’s balance sheets due to mark-to-market. Through this mechanism, fire sales can lead to contagion, and one failing bank can cause several more to follow suit.bank regulation, BIS capital adequacy requirements, Basel II, Basel III, leverage ratio, default rate, systemic stability, fire sales, contagion, autonomous agents, simulation

Index Mutual Fund Replication

This paper discusses the application of an index tracking technique to mutual fund replication problems. By using a tracking error (TE) minimization method and two tactical rebalancing strategies (i.e. the calendar based strategy and the tolerance triggered strategy), a multi-period fund tracking model is developed that replicates S&P 500 mutual fund returns. The impact of excess returns and loss aversion on overall tracking performance is also discussed in two extended cases of the original TE optimization respectively. An evolutionary method, namely Differential Evolution, is used for optimizing the asset weights. According to the experiment results, it is found that the proposed model replicates the first two moments of the fund returns by using only five equities. The TE optimization strategy under loss aversion with tolerance triggered rebalancing dominates other combinations studied with regard to tracking ability and cost efficiency.Passive Portfolio Management, Fund Tracking, MultiPeriod Optimization, Differential Evolution

Asset Allocation under Hierarchical Clustering

This paper proposes a clustering asset allocation scheme which provides better risk-adjusted portfolio performance than those obtained from traditional asset allocation approaches such as the equal weight strategy and the Markowitz minimum variance allocation. The clustering criterion used, which involves maximization of the in-sample Sharpe ratio (SR), is different from traditional clustering criteria reported in the literature. Two evolutionary methods, namely Differential Evolution and Genetic Algorithm, are employed to search for such an optimal clustering structure given a cluster number. To explore the clustering impact on the SR, the in-sample and the out-of-sample SR distributions of the portfolios are studied using bootstrapped data as well as simulated paths from the single index market model. It was found that the SR distributions of the portfolios under the clustering asset allocation structure have higher mean values and skewness but approximately the same standard deviation and kurtosis than those in the non-clustered case. Genetic Algorithm is suggested as a more efficient approach than Differential Evolution for the purpose of solving the clustering problem.Asset Allocation, Clustering Technique, Sharpe Ratio, Evolutionary Approach, Heuristic Optimization

Optimal Lag Structure Selection in VEC-Models

For modelling economic and financial time series, multivariate linear and nonlinear systems of equations have become a standard tool. These models can also be applied to non-stationary processes. However, the resulting finite-sample estimates may depend strongly on the specification of the model dynamics. We propose a method for automatic identification of the dynamic part of VEC-models. Model selection is based on a modified information criterion. The lag structure of the model is selected according to this objective function allowing for "holes". The resulting complex discrete optimization problem is tackled using a hybrid heuristic combining ideas from threshold accepting and memetic algorithms. We present the algorithm and the results of a simulation study showing the method's performance both with regard to the dynamic structure and the rank selection in the VEC-model. The results indicate that the selection of the cointregation rank might depend strongly on the specification of the dynamic part of the VEC-modelModel selection; cointegration rank; reduced rank regression

Channels of Sovereign Risk Spillovers and Investment in the Manufacturing Sector

This paper identifies endogenous and exogenous indicators of firms’ investment activity, and examine, in particular, the effect that these variables have in co-determining firms’ investment decisions. Two channels of spillovers from sovereign risk to firms’ capital expenditures are defined. The first channel, the “direct channel”, describes responses in capital expenditures from an innovation in sovereign risk. The second channel, the “indirect channel”, is a transmission mechanism in which spillovers from changes in sovereign risk indirectly affect a firm’s capital expenditures via its capital market risk and profitability. While we observe that the direct risk channel is of major importance in Emerging and Developing Economies, it is comparatively small in Advanced Economies. In the case of the latter, contagion from changes in sovereign risk on firms’ capital market risk plays a much more important role

Regime-switching recurrent reinforcement learning for investment decision making

This paper presents the regime-switching recurrent reinforcement learning (RSRRL) model and describes its application to investment problems. The RSRRL is a regime-switching extension of the recurrent reinforcement learning (RRL) algorithm. The basic RRL model was proposed by Moody and Wu (Proceedings of the IEEE/IAFE 1997 on Computational Intelligence for Financial Engineering (CIFEr). IEEE, New York, pp 300-307 1997) and presented as a methodology to solve stochastic control problems in finance. We argue that the RRL is unable to capture all the intricacies of financial time series, and propose the RSRRL as a more suitable algorithm for such type of data. This paper gives a description of two variants of the RSRRL, namely a threshold version and a smooth transition version, and compares their performance to the basic RRL model in automated trading and portfolio management applications. We use volatility as an indicator/transition variable for switching between regimes. The out-of-sample results are generally in favour of the RSRRL models, thereby supporting the regime-switching approach, but some doubts exist regarding the robustness of the proposed models, especially in the presence of transaction cost

Autonomously Interacting Banks

The great financial turmoil that started 2007 has brought bank regulation back into the political debate. There is talk about imposing new regulations on banks and other financial intermediaries. Yet, we are not convinced that it is completely understood how the existing regulation affects systemic stability, let alone what the effect of new proposed rules would be.In order to better understand these issues, we study the interaction of heterogeneous financial agents in a market that features several properties we believe to be realistic. Our agents develop heterogeneous views about the correct valuation of a risky asset. Some agents (banks) operate with substantial leverage and thus bankruptcy is a possibility. Agents may engage in fire sales, either because they face real financial trouble, or because they are forced to by regulation. Moreover, through their trading activities, agents exert externalities on each other’s balance sheets due to mark-to-market. Through this mechanism, fire sales can lead to contagion, and one failing bank can cause several more to follow suit