Report

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 © 2011 Richard Michaud and Robert Michaud About New Frontier • 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 22 © 2011 New Frontier Management Company, LLC 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 3 17 © 2011 New Frontier Management Company, LLC 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 4 17 © 2011 New Frontier Management Company, LLC 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 5 17 © 2011 New Frontier Management Company, LLC 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 6 17 © 2011 New Frontier Management Company, LLC Resampling and the Michaud Frontier 67 © 2011 New Frontier Management Company, LLC Statistical Portfolio Monitoring Illustrated 88 © 2011 New Frontier Management Company, LLC 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 9 17 © 2011 New Frontier Management Company, LLC 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. 10 17 © 2011 New Frontier Management Company, LLC 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 11 12 © 2011 New Frontier Management Company, LLC Limitations of the Original Michaud (1998) Rule 12 © 2011 New Frontier Management Company, LLC Limitations of Michaud (1998) Test Low statistical power Infrequently rejects no-need-to-trade null hypothesis Poor power at high end of frontier 13 17 © 2011 New Frontier Management Company, LLC 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 14 17 © 2011 New Frontier Management Company, LLC Michaud Frontier Associated Meta-Resampled Portfolios 12 estimated average return (%) 10 8 6 4 2 0 0 5 15 © 2011 New Frontier Management Company, LLC 10 15 standard deviation (%) 20 25 Highly Compute Intensive Process Use better computer technology Multi-core computers Network multi-core Cloud computing 16 17 © 2011 New Frontier Management Company, LLC Still A Persistent Problem in Practice Need-to-trade probabilities often seemed too low in actual practice 17 17 © 2011 New Frontier Management Company, LLC The Common Information Issue 18 © 2011 New Frontier Management Company, LLC The Common Information Issue 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 19 19 © 2011 New Frontier Management Company, LLC 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)) 20 4 © 2011 New Frontier Management Company, LLC Actual Case: Conditional Monitoring Rule 21 © 2011 New Frontier Management Company, LLC 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 22 4 © 2011 New Frontier Management Company, LLC 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 23 28 © 2011 New Frontier Management Company, LLC 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 24 4 © 2011 New Frontier Management Company, LLC Thank You New NewFrontier FrontierAdvisors, Advisors,LLC LLC Boston,MA MA 02110 02110 NFABoston, SAA Portfolios www.newfrontieradvisors.com www.newfrontieradvisors.com 25 25 © 2011 New Frontier Management Company, LLC 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 26 © 2011 New Frontier Management Company, LLC