Transcript Portfolio Monitoring in Theory and Practice

Portfolio Monitoring*
Richard Michaud, David Esch, Robert Michaud
New Frontier Advisors
Boston, MA 02110
Presented to:
International Symposium on Forecasting
Boston Marriott Copley Place
June 25, 2012
* Forthcoming: Michaud, Esch, Michaud, 2012. “Portfolio Monitoring in Theory and Practice,”
Journal Of Investment Management.
© 2007 Richard Michaud and Robert Michaud
© 2012 New Frontier Management Company, LLC
About New Frontier
 Institutional research and investment advisory firm
 Pioneers in portfolio optimization in theory and practice
 Michaud and Michaud, 1998, Efficient Asset Management,
Harvard, 2008, 2nd ed. Oxford
 Inventors of Michaud Efficient Frontier
 Four U.S. patents, two pending; worldwide patents pending
 Managers of over $1B global ETF model portfolios
 Software providers to managers and consultants world wide
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Current Portfolio Monitoring Ad Hoc
 Calendar rebalancing
 Monthly, quarterly, yearly, three years, every five minutes
 Asset weight hurdle ranges
 Drifted portfolio relative to optimal weights
 Ranges may vary based on asset volatilities
 No theory to support practice
 Not portfolio based rules
 Often trading in noise or not trading when useful
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True Portfolio Monitoring
 A statistical similarity test:
 Is current drifted or a 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 is a separate issue
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Academic Portfolio Similarity Tests
 Shanken (1985), Jobson and Korkie (1985)
 Analytical significance tests
 Tests of CAPM
 Is “market” statistically mean-variance (MV) efficient?
 Limitations of the Shanken-Jobson-Korkie tests
 Hotellings T2
 Requires unconstrained MV optimization
 Invalid for investment practice
 Practice requires linear inequality constraints
 Constraints as part of defining test statistic
 See Markowitz (2005) on why constraints essential
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First Constrained Portfolio Similarity Test
 Michaud (1998, Ch. 7)
 Based on portfolio distance function relative to Michaud
efficient 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
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Michaud Resampling and the New Frontier
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Statistical Portfolio Monitoring Illustrated
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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
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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 may be a useful default value
 Balance between avoiding noise trading and being able to
detect true deviations from optimality
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Using Portfolio Monitoring Rule
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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?
• Low levels -- growth managers?
 Client Preferences, investment horizon
 Specialized investment classes
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Way to monitor universe of managed accounts
 Portfolio monitoring automation
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Limitations of the Michaud (1998) Rule
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Limitations of Michaud (1998) Test
 Low statistical power
 Infrequently rejects no-need-to-trade null hypothesis
 Poor power at high end of frontier
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Meta-Resampling Solution
 Patented meta-resampling (Michaud and Michaud 2002, 2008)
 Associates resampled with resampled frontiers
 Each simulated “parent” MV efficient frontier spawns a
“child” Michaud Efficient Frontier
 Child frontier portfolios used to compute probability
 Greatly enhanced statistical power across frontier
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Michaud Frontier Associated Meta-Resampled Portfolios
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estimated average return (%)
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standard deviation (%)
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Highly Compute Intensive Process
 Better computer technology
 Multi-core computers
 Network multi-core
 Cloud computing
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The Common Information Issue
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The Common Information Issue
 Information in current portfolio often based on similar information in
new optimal portfolio
 Common information means two portfolios similar all things equal
 Need-to-trade probability small
 No-trading-biased with 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
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Illustrating Conditional Monitoring Rule
 One year ago optimal portfolio P0
 X0= [x1,x2,…,x60] = original risk-return distribution
 T = number of periods = 60
 New optimal portfolio
 Xnew = [x13,x2,…,x72] = new risk-return distribution
 Common information: [x13,x2,…,x60]
 Compute k = number of random draws = 12 from Xnew distribution
 Add to common 48 months: [x13,x2,…,x60] = sim distribution
Compute simulated optimal and distance to current optimal
 Repeat above many times
 Compute P0 distance to optimal and percentile in distance
distribution (conditional need-to-trade probability C(k))
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Conditional Monitoring Rule
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Applications and Generalizations
 May be used as a measure of regime changes in markets
 In drifted period:
• Minimal market volatility – little need to trade
• High market volatility – likely need to trade
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Return distribution generalizations
 Simulations can be based on any distribution
 We generally use t-distribution
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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
 Michaud, Esch, Michaud conditional rebalancing rule
 Common information, increased statistical power
 Customizable to asset management processes
 Potential for automatable portfolio monitoring
 Highly compute intensive procedures
 Just finance catching up to real statistics
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© 2012 New Frontier Management Company, LLC
Richard O. Michaud
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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
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Thank You
New Frontier Advisors, LLC
Boston, MA 02110
www.newfrontieradvisors.com
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