*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.
The full report (pdf)
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