KTH Matematik  

Matematisk Statistik

Tid: 1 juni 2016 kl 14.30-15.00.

Seminarierummet 3424, Institutionen för matematik, KTH, Lindstedtsvägen 25, plan 4. Karta!

Föredragshållare: Daniel Isaksson (Master Thesis)

Titel: Robust portfolio optimization with expected shortfall

Abstract This thesis project studies robust portfolio optimization with Expected Shortfall applied to a reference portfolio consisting of Swedish linear assets with stocks and a bond index. Specifically, the classical robust optimization definition, focusing on uncertainties in parameters, is extended to also include uncertainties in log-return distribution. My contribution to the robust optimization community is to study portfolio optimization with Expected Shortfall with log-returns modeled by either elliptical distributions or by a normal copula with asymmetric marginal distributions. The robust optimization problem is solved with worst-case parameters from box and ellipsoidal uncertainty sets constructed from historical data and may be used when an investor has a more conservative view on the market than history suggests. With elliptically distributed log-returns, the optimization problem is equivalent to Markowitz mean-variance optimization, connected through the risk aversion coefficient. The results show that the optimal holding vector is almost independent of elliptical distribution used to model log-returns, while Expected Shortfall is strongly dependent on elliptical distribution with higher Expected Shortfall as a result of fatter distribution tails. To model the tails of the log-returns asymmetrically, generalized Pareto distributions are used together with a normal copula to capture multivariate dependence. In this case, the optimization problem is not equivalent to Markowitz mean-variance optimization and the advantages of using Expected Shortfall as risk measure are utilized. With the asymmetric log-return model there is a noticeable difference in optimal holding vector compared to the elliptical distributed model. Furthermore the Expected Shortfall increases, which follows from better modeled distribution tails. The general conclusions in this thesis project is that portfolio optimization with Expected Shortfall is an important problem being advantageous over Markowitz mean-variance optimization problem when log-returns are modeled with asymmetric distributions. The major drawback of portfolio optimization with Expected Shortfall is that it is a simulation based optimization problem introducing statistical uncertainty, and if the log-returns are drawn from a copula the simulation process involves more steps which potentially can make the program slower than drawing from an elliptical distribution. Thus, portfolio optimization with Expected Shortfall is appropriate to employ when trades are made on daily basis.

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Sidansvarig: Filip Lindskog
Uppdaterad: 25/02-2009