© 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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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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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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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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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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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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Resampling and the Michaud 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 often 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

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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Limitations of the Original 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 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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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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Highly Compute Intensive Process

Use better computer technology Multi-core computers Network multi-core Cloud computing

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Still A Persistent Problem in Practice

Need-to-trade probabilities often seemed too low in actual practice

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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

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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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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Actual Case: Conditional Monitoring Rule

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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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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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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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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