Maria A. Osorio, Nalan Gulpinar, Bert Rustem and Reuben Settergren
     Department of Computing
     Imperial College of Science, Technology, and Medicine
     180 Queen's Gate, London SW7 2BZ, UK
     [maosorio, ng, br, reuben]@doc.ic.ac.uk

Taxes have a great impact on returns and expected income from different investments. Investment decisions about portfolios must be personalized and adjusted to real life expectations for every investor. The present research
introduces a way to get post tax portfolio optimisation that takes in account real life events and special British taxation rules for three different wrappers utilized by a bank in the UK.
Traditional financial investment models are usually extremely simplified and cannot always be applied in real life. To make investment recommendations we need to consider (i) the expected income and capital returns from the asset classes as well
as risk; (ii) the tax treatment of various types of income and gains; and (iii) the tax implications of the various investment æwrappers'. The purpose is to optimise (i.e. balance risk/return) the after tax performance, using differing asset
allocations to reflect different attitudes to risk/return.
We take a stochastic approach to the multistage version of this problem. Consequently, asset performance information is specified in a scenario tree. We integrate the tax rules with the stochastic programming formulation to yield an overall tax and return-efficient multistage portfolio.
In order to carry out the appropriate analysis, a model should have the ability to compare a variety of investments and wrappers in conjunction with differing investor situations. As stated, there are numerous permutations, depending not only
on the actual wrapper, but also on the underlying investment holdings. It is also necessary to consider for how long investments will be held. Besides, profits realised on the disposal of certain types of assets are subject to capital gains
tax. These include direct holdings of shares and property, as well as unit trusts. However, there is some mitigation of this tax in the form of taper relief. Taper relief is a gradual reduction of the amount of tax payable, dependent on the length
of time an asset has been held.
We allow the initial investment to be split into the three wrappers and a portfolio of n assets and consider its optimal distribution over a given period of time, dealing with specific taxation for each asset inside each wrapper, developing a MIP model that represents in detail investor's real life situationsÆ impact in the model. We show the model's performance in several case studies.