Generalised Mean Variance Analysis and Robust Portfolio Construction February 2006 Steve Wright Tel 44 20 7568

1874

2

Institutional fund management

— Low frequency noisy non stationary data

— Dominance of subjective analysis

— Regulatory and client pressure for accountability.

— Interactive tools add structure to the process

Mean Variance Analysis for portfolio diversification

— Widely accepted theory

— With practical problems

– Recommendations are sensitive to small changes in user inputs

– Out of sample performance of the risk models can be an issue

– Hence portfolio churn and lack of confidence in the process

A robust extension of Mean Variance analysis

Business Context

3

The investment process can be complex

Global Valuation

Research Analysts

Portfolio Construction

(Portfolio) Trading

Risk & Return modelling

Company Database

Company preferences

Ex ante statistics

Returns

Regional Preferences

Economics

Asset class Preferences

Sector Preferences

Strategy

Style Preferences

Ex post statistics

Debt Markets

Transaction cost control

FX Markets

Futures Markets

Third Party Data Providers

Mandates and Constraints

4

Mutually consistent across portfolios (more risk = more equity)

Simple and understandable by an intelligent non specialist.

Stable enough to avoid generating excessive volume of trades.

Reliable enough to have acceptable out of sample behaviour.

Capable of reflecting all likely practical operating constraints

Transparent enough to be monitored easily

A starting point for discussion of the key issues

An ideal investment process

5

A typical Asset Allocation Toolbox results screen

6

The effect of correlation matrix volatility

7

The perfect substitute problem

8

Is risk volatility or lack of diversification

German_Bond_3_5_year_maturity

US_Bond_3_5_year_maturity

Japanese_Bond_3_5_year_maturity

German_MSCI_Equity

Japanese_MSCI_Equity

American_MSCI_Equity

Minimum Risk Maximum Return

German_Bond_3_5_year_maturity

US_Bond_3_5_year_maturity

Japanese_Bond_3_5_year_maturity

German_MSCI_Equity

Japanese_MSCI_Equity

American_MSCI_Equity

Minimum Risk Maximum Return

Rank Optimisation

Standard MV

Optimisation

9

State Preference Theory -- 1

10

State Preference Theory -- 2

11

Conclusions

Forecast and portfolio construction is not an exact science. It is an art with no black and white answers. An interactive tools allow you to get a feel for these uncertainties.

Probability based methods can improve your forecast construction by bringing statistical rigour to qualitative analysis and making the results of quantitative analysis more intuitive and realistic.

We cannot eliminate risk, but we can improve the stability, reliability and relevance of the measures used

12

Disclaimer

UBS Limited, 1 Finsbury Avenue, London, EC2M 2PP, UK Phone: +44-20-7567 8000

UBS Customised Investment Research has been prepared solely for your use. This material has been prepared by UBS AG or an aff iliate thereof ("UBS"). It has no regard to the specif ic investment objectives, f inancial situation or particular needs of any specif ic recipient. It is published solely for informational purposes and is not to be construed as a solicitation or an offer to buy or sell any securities or related f inancial instruments. No representation or w arranty, either express or implied, is provided in relation to the accuracy, completeness or reliability of the information contained herein. Opinions expressed herein are subject to change w ithout notice and may differ or be contrary to opinions expressed by other business areas or groups of UBS as a result of using different assumptions and criteria. UBS is under no obligation to update or keep the information current. The securities described herein may not be eligible for sale in all jurisdictions or to certain categories of investors. UBS, its directors, off icers and employees or clients may have or have had interests or long or short positions in the securities or other f inancial instruments referred to herein, and may at any time make purchases and/or sales in them as principal or agent. UBS (excluding the US broker-dealer unless specif ically disclosed under Required Disclosures) may act or have acted as market-maker in the securities or other f inancial instruments discussed in this material. UBS may provide investment banking and other services to and/or serve as directors of the companies referred to in this report. Neither UBS nor any of its aff iliates, nor any of UBS' or any of its aff iliates, directors, employees or agents accepts any liability for any loss or damage arising out of the use of all or any part of this report. United Kingdom and rest of Europe: Except as otherw ise specif ied herein, this material is communicated by UBS Limited, a subsidiary of UBS AG, to persons w ho are market counterparties or intermediate customers (as detailed in the FSA Rules) and is only available to such persons. The information contained herein does not apply to, and should not be relied upon by, private customers. Sw itzerland: This report is being distributed in Sw itzerland by UBS AG to institutional investors only. United States: This report is being distributed to US persons by either UBS Securities LLC or UBS Financial Services Inc., subsidiaries of UBS AG, or by a group, subsidiary or aff iliate of UBS AG, that is not registered as a US broker- dealer (a "non-US aff iliate"), to major US institutional investors only. UBS Securities LLC or UBS Financial Services Inc. accepts responsibility for the content of a report prepared by another non-US aff iliate w hen distributed to US persons by UBS Securities LLC or UBS Financial Services Inc. All transactions by a US person in the securities mentioned in this report must be effected through UBS Securities LLC or UBS Financial Services Inc., and not through a non-US aff iliate. Canada: This report is being distributed by UBS Securities Canada Inc., a subsidiary of UBS AG and a member of the principal Canadian stock exchanges & CIPF. A statement of its f inancial condition and a list of its directors and senior off icers w ill be provided upon request. Hong Kong: This report is being distributed in Hong Kong by UBS Securities Asia Limited. Singapore: This report is being distributed in Singapore by UBS Securities Singapore Pte. Ltd. Australia: Distributed by UBS AG (Holder of Australian Financial Services Licence No. 231087) and UBS Securities Australia Ltd (Holder of Australian Financial Services Licence No. 231098). Additional information w ill be made available upon request.

© 2004 UBS. All rights reserved. This report may not be reproduced or distributed in any manner w ithout the permission of UBS.