© 2007 Richard Michaud and Robert Michaud

1. Portfolio Monitoring* Richard Michaud, David Esch, Robert Michaud New Frontier Advisors Boston, MA 02110 Presented to: QWAFAFEW NYC September 27, 2012 * Forthcoming: Michaud, Esch, Michaud, 2012. “Portfolio Monitoring in Theory and Practice,” Journal Of Investment Management. © 2007 Richard Michaud and Robert Michaud © 2007 Richard Michaud and Robert Michaud © 2011 Richard Michaud and Robert Michaud

2. Institutional research and investment advisory firm Inventors and authors in investment technology Michaud and Michaud, Efficient Asset Management, 1998, Harvard, 2008., 2nd Edition, Oxford NFA is unique: Institutional investors who use our own software Global software providers who manage money Published authors in books and refereed journals Four U.S. patents, two pending About New Frontier

3. Current Portfolio Monitoring Ad Hoc • Calendar rebalancing • Monthly, quarterly, yearly, three years, every five minutes • Asset weight hurdle ranges • Drifted portfolio relative to neutral or optimal weights • Ranges typically vary based on asset volatilities • No theory to support practice • Not portfolio based rules • Often trading in noise or not trading when useful 17

4. True Portfolio Monitoring • A statistical similarity test: • Is the current drifted or given candidate portfolio statistically similar or different relative to optimal • If statistically similar, don’t trade • If statistically different, trade • Presentation scope: • Decision whether or not to trade • How to trade or how much to trade is a separate issue 17

5. Academic Portfolio Similarity Tests • Shanken (1985), Jobson and Korkie (1985), Levy and Roll (2010) • Tests of CAPM • Is “market” statistically mean-variance (MV) efficient • Limitations of academic tests • Analytical tests assume unconstrained MV optimization • Hotellings T2 and other analytic methods • Not useful for investment practice • Practice requires linear inequality constraints • Constraints part of defining test statistic • See Markowitz (2005) why constraints essential 17

6. First Constrained Portfolio Similarity Test • Michaud (1998, Ch. 7) • Portfolio distance function relative to Michaud frontier • Uses patented resampling technology • Computes need-to-trade probability • Relative to thousands of simulated investment scenarios • Technology used in NFA’s World Gold Council reports 17

7. Resampling and the Michaud Frontier 6

8. Statistical Portfolio Monitoring Illustrated

9. What the Monitoring Rule Computes • Associated simulated optimal portfolios provides a distance scale for monitoring portfolios • Portfolio distance function (one example) • Relative variance function = (P – P*) (P – P*) • A measure of distance in N-dimensional portfolio space • Sort distance low to high distribution • Defines probability scale from 0 to 99% • Compute distance from current to optimal • Defines probabilistically how far current from optimal 17

10. What the Rule Means • 10% need-to-trade probability means • Portfolio distance is 10% as far as others in distribution • 75% or more probability may indicate trading is recommendable • 50% probability often a useful default value • Balance between avoiding noise trading and being able to detect true deviations from optimality. 17

11. Using Portfolio Monitoring Rule • Decide on level of probability for trading • L = Probability level for trading • Recommend trading if probability > L • L depends on many investment and client issues • Investment Styles: • High levels -- value managers? • Lower levels -- growth managers? • Client Preferences, investment horizon • Specialized investment classes • Way to monitor universe of managed accounts • Portfolio monitoring automation 12

12. Limitations of the Original Michaud (1998) Rule

13. Limitations of Michaud (1998) Test • Low statistical power • Infrequently rejects no-need-to-trade null hypothesis • Poor power at high end of frontier 17

14. Meta-Resampling Solution • Patented meta-resampling (Michaud and Michaud 2002, 2008) • Associates resampled with Michaud efficient portfolios • Each simulated “parent” MV efficient frontier spawns a “child” resampled efficient frontier • Associated child resampled efficient frontier portfolios used to compute distance probability • Greatly enhanced statistical power • Nearly uniform power across frontier 17

15. Michaud Frontier Associated Meta-Resampled Portfolios

16. Highly Compute Intensive Process • Use better computer technology • Multi-core computers • Network multi-core • Cloud computing 17

17. Still A Persistent Problem in Practice • Need-to-trade probabilities often seemed too low in actual practice 17

18. The Common Information Issue

19. Information in current portfolio often based on similar information in new optimal Common information means two portfolios similar all things equal Need-to-trade probability necessarily small Test is no-trading-biased in presence of common information Michaud-Esch-Michaud conditional monitoring rule A new scale that includes common information Dramatically enhanced power for many practical applications Realistically sensitive to changes in current vs. optimal Three levels of resampling in general case The Common Information Issue

20. Illustrating Conditional Monitoring Algorithm • One year ago optimal portfolio P0 • X0= [x1,x2,…,x60] = defines original risk-return distribution • New optimal portfolio P* • Xnew = [x13,x2,…,x72] = defines new risk-return distribution • 48 months of common information: [x13,x2,…,x60] • Compute meta-resampled portfolios (simplest case) • Compute k = random draws = 12 from Xnew distribution • Add to common 48 months: [x13,x2,…,x60] = sim distribution • Compute meta-sim optimal and distance to P* • Repeat above many times • Sort and define distance distribution • Compute P0 distance to optimal and percentile in distance distribution (conditional need-to-trade probability C(k)) 4

21. Actual Case: Conditional Monitoring Rule

22. Applications • A measure of regime changes in markets • Assume a long-term strategic optimal portfolio • In drifted period • Minimal market volatility – little need to trade • High market volatility – likely need to trade • Return distribution generalizations • Simulations can be based on any distribution • We generally use t-distribution 4

23. Summary • Portfolio monitoring an essential asset management function • Prior methods ad hoc, academic methods invalid • Patented first practical monitoring rule Michaud (1998) • Limited statistical power • Patented Meta-resampling rule Michaud and Michaud (2002) • Enhanced statistical power across frontier • Customizable to asset management processes • Michaud-Esch-Michaud conditional monitoring algorithm • Common information, increased statistical power • Highly compute intensive procedures • Just finance catching up to real statistics 28

24. Extensions • Potential for large-scale automatable portfolio monitoring • A statistical context for general quadratic programming applications • Process monitoring and multivariate regression in the context of linear constraints and overlapping data 4

25. New Frontier Advisors, LLC Boston, MA 02110 www.newfrontieradvisors.com Thank You New Frontier Advisors, LLC Boston, MA 02110 www.newfrontieradvisors.com NFA SAA Portfolios 25 © 2011 New Frontier Management Company, LLC

26. Richard O. Michaud • President, Chief Investment Officer • Co-inventor (with Robert Michaud) of Michaud Resampled Efficient Frontier™, three other patents, two pending • Author: Efficient Asset Management, 1998. Oxford University Press, 2001, 2nd Edition 2008 (with Robert Michaud) • Many academic and practitioner refereed journal articles • CFA Institute monograph on global asset management. • Prior positions include: • Acadian Asset Management; Merrill Lynch • Graham and Dodd winner for work on optimization • Former Director and research director of the “Q” Group • Advisory Board member, Journal Of Investment Management • Former Editorial Board member Financial Analysts Journal, Journal Of Investment Management