© 2007 Richard Michaud and Robert Michaud Portfolio Monitoring* Richard Michaud, David Esch, Robert...
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Transcript of © 2007 Richard Michaud and Robert Michaud Portfolio Monitoring* Richard Michaud, David Esch, Robert...
© 2007 Richard Michaud and Robert Michaud© 2007 Richard Michaud and Robert Michaud
Portfolio Monitoring*
Richard Michaud, David Esch, Robert MichaudNew Frontier AdvisorsBoston, MA 02110
Presented to: QWAFAFEW NYCSeptember 27, 2012
* Forthcoming: Michaud, Esch, Michaud, 2012. “Portfolio Monitoring in Theory and Practice,” Journal Of Investment Management.
© 2011 Richard Michaud and Robert Michaud
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© 2011 New Frontier Management Company, LLC
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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
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© 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
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© 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
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© 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
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© 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
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© 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
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© 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.
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© 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
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© 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
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© 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
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© 2011 New Frontier Management Company, LLC
Michaud Frontier Associated Meta-Resampled Portfolios
0 5 10 15 20 250
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standard deviation (%)
est
imate
d a
ve
rag
e r
etu
rn (
%)
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© 2011 New Frontier Management Company, LLC
Highly Compute Intensive Process
Use better computer technology Multi-core computers Network multi-core Cloud computing
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© 2011 New Frontier Management Company, LLC
Still A Persistent Problem in Practice
Need-to-trade probabilities often seemed too low in actual practice
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© 2011 New Frontier Management Company, LLC
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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
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© 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))
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© 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
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© 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
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© 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
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© 2011 New Frontier Management Company, LLC
New Frontier Advisors, LLC
Boston, MA 02110
www.newfrontieradvisors.comNFA SAA Portfolios
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© 2011 New Frontier Management Company, LLC
Thank You
New Frontier Advisors, LLC
Boston, MA 02110
www.newfrontieradvisors.com
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© 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