CLUSTER ANALYSIS FOR FINANCIAL ASSET PORTFOLIO DESIGN Presenter LIN GIRALT

 Review of key objectives & critical success factors.  Assets evaluated  Portfolio One  Portfolio Two  Period of Analysis  Portfolio One  Determining number of clusters  Cluster Composition  Forward test in 5 year increments  Portfolio Two  Determining number of clusters  Cluster Composition  Forward test in 2 year increment  Conclusions  Next Steps Agenda

 Hypothesis under study is to evaluate the usefulness of K-Means Cluster analysis as a tool in portfolio design  Simplifying design process  Facilitating management of Sharpe Ratios  Improving performance and portfolio management over time  Critical Success Factors  Whether portfolio designed around clusters performs better over time than simple stock picking and cluster analysis complements traditional measures and procedures  Whether this can be backtested over different periods and lengths of periods  Understanding limitations and advantages of Cluster Analysis in Portfolio Design Review of Key Objectives & Critical Success Factors

Assets Evaluated Portfolio One 27 Assets (from Jan Feb.02.09) Portfolio Two 18 Assets (from April to Nov Widely diversified groups of assets similar to what any Portfolio Manager would consider Funds and ETF’s have been picked over the individual assets they represent to give more robustness and breadth of asset coverage to our discussion

Our period of analysis is as tumultuous and representative as any in recent history  S&P 500 went from 1229 to1257 between Nov 1999 and Jan 2011  Crisis following 9/11 and financial crisis of  Strong breakdowns and periods of sustained recovery

 Determining number of clusters  Cluster Composition  Forward test in 5 year increment Portfolio One

Determining number of clusters  Using ‘Elbow Analysis’ on first 60 data points to determine Sum of Errors per Variable vs. Number of Clusters  Visual analysis indicates four as the optimum number of clusters for this dataset

Cluster Composition Four clusters show strong differentiation in terms of composition and performance over the initial 60 month range Performance measured monthly

Forward test in Five Year Increment MEAN OF MONTHLY RETURNS ST DEV OF RETURNS  Clusters maintain differentiated performance in second 60 month range Little variation

 Determining number of clusters  Cluster Composition  Forward test in 2 year increment Portfolio Two

Determining number of clusters  Using ‘Elbow Analysis’ on first 21 data points to determine Sum of Errors per Variable vs. Number of Clusters  Visual analysis indicates six as the optimum number of clusters for this dataset, but four would have been acceptable as well Four or six clusters would have been acceptable

Cluster Composition Six clusters also show clear differentiation in terms of composition and performance over the initial 22 month range Four clusters would have collapsed the three stock based clusters into one, much like Portfolio One Performance measured monthly

Forward test in Two Year Increment  Clusters maintain differentiated performance in second 22 month range  Returns improved and Volatility reduced or remained the same

Conclusions- Cluster analysis may offer insights into portfolio design and performance and facilitate decisions Asset View Cluster View

Clusters also have less correlation between each other than individual assets making for more efficient portfolio construction  In this example from Portfolio Two, only 5 out of 15 cross-correlations are above 80% while 6 are below 40%  This allows more efficient portfolio construction

Sharpe ratios can be developed for portfolio building

Conclusions Cluster analysis may produce portfolios with groups of stocks that produce comparable returns with improvements in volatility

 Developing the use of cluster analysis in portfolio design requires validation of these limited results using a more robust and long term source of data for asset performance and clustering across different markets and asset classes  Creation of building blocks of clusters instead of from different individual assets or funds seems to facilitate intelligent diversification, where clusters are added cognizant of their correlation to other assets and their contribution to overall diversification  Cluster analysis links assets with similar performance into clusters, avoiding the unknowing overlap of assets with similar risk/returns and high correlations into a portfolio  This impact needs to be further studied and reviewed Next Steps