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

1  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

2 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

3  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

4 A typical Asset Allocation Toolbox results screen

5 The effect of correlation matrix volatility

6 The perfect substitute problem

7 Is risk volatility or lack of diversification Minimum Risk Maximum Return Rank Optimisation Standard MV Optimisation

8 State Preference Theory -- 1

9 State Preference Theory -- 2

10 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

11 Disclaimer