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Imre Kondor

is faculty member of the Parmenides Foundation, Pullach b. Munich, external faculty of the London Mathematical Laboratory and the Complexity Science Hub, Vienna, and honorary professor of finance at Corvinus University of Budapest. In 1988-2011 he was professor of physics at the Department of the Physics of Complex Systems, Eötvös University, Budapest. In 1992 he founded Bolyai College, a school of excellence, from 1998 to 2002 he was the head of the Department of Market Risk Research at Raiffeisen Bank. In 2002-2008 he was the rector of Collegium Budapest – Institute for Advanced Study. He holds a PhD and DSc, three academic and two government prizes. He has published 85 papers, 2 books and one e-volume. He is coeditor of Fractals, JSTAT, and was review editor of Journal of Banking and Finance. His research experience includes the theory of condensed Bose systems, critical phenomena, random systems and spin glasses, and, presently, the application of statistical physics methods to problems in economics and finance (especially the theory of portfolios, risk management and regulation). Professor Kondor organized about 20 international conferences and served as chairman or member on various grant committees and science policy making bodies.

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Imre Kondor: Analytic approach to portfolio optimization under an l1 constraint

The optimization of the variance supplemented by a budget constraint and an asymmetric l1 regularizer is carried out analytically by the replica method borrowed from the theory of disordered systems. The asymmetric regularizer allows one to penalize short and long positions differently, so the present treatment includes the no-short-constrained portfolio optimization problem as a special case. Results are presented for the out-of-sample and the in-sample estimator of the variance, the relative estimation error, the density of the assets eliminated from the portfolio by the regularizer, and the distribution of the optimal portfolio weights. The dependence of these quantities on the ratio r of the portfolio's dimension N to the sample size T, and on the strength of the regularizer is presented. The analytic results are checked by numerical simulations, and general agreement is found. The regularization extends the interval where the optimization can be carried out, and suppresses the infinitely large sample fluctuations, but the performance of l1 regularization is disappointing: if the sample size is large relative to the dimension, i.e. r is small, the regularizer does not play any role, while for larger r's where the regularizer starts to be felt the estimation error is already so large as to make the whole optimization exercise pointless. Beyond the critical ratio r=2 the variance cannot be meaningfully optimized: a continuum of solutions with vanishing variance and weight vectors lying in the simplex emerge.

Last modified: 2017.10.18.