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Suitability and Optimality in the Asset Allocation Process. Conflict and Resolution Paul Bolster, Northeastern University Sandy Warrick, S&S Software. Objectives. Develop a suitable asset allocation model using a robust methodology.

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Suitability and optimality in the asset allocation process l.jpg

Suitability and Optimality in the Asset Allocation Process

Conflict and Resolution

Paul Bolster, Northeastern University

Sandy Warrick, S&S Software

Objectives l.jpg

  • Develop a suitable asset allocation model using a robust methodology.

    • Suitability: The appropriateness of particular investments or portfolios of investments for specific investors.

  • Evaluate suitable asset allocation for mean-variance optimality.

  • Propose resolution if results conflict.

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Practical, Legal concept

Portfolio’s risk exposure is paramount

Correlations between asset classes considered in a subjective manner

A suitable portfolio need not be optimal


Econonmic, Statistical concept

Portfolio’s risk exposure is paramount

Correlations between asset classes considered explicitly.

An optimal portfolio need not be suitable

Distinguishing Suitability from Optimality

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Modeling Suitability

  • NYSE Rule 405

  • AMEX Rule 411

  • AIMR materials

    • Risk Tolerance

    • Time Horizon

    • Liquidity

    • Unique Factors (legal, tax, etc.)

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The Analytic Hierarchy Process

  • Developed by Saaty (1980)

  • Useful for evaluating relative value (conflicting ) qualitative criteria

  • Decomposes a complex decision into smaller components that are easier to associate with specific alternatives

  • Allows subjective judgements to be weighed consistently

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The Analytic Hierarchy Process

  • 1. Define the problem as a hierarchy.

  • 2. Assess the relative importance of factors at each level of the hierarchy using pairwise comparisons

  • 3. Evaluation of pairwise comparison matricies and determination of best alternative(s).

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AHP Step 2: Pairwise Comparisons (Saaty)

  • The 9-point comparison scale:

    • X to Y = 1 Equal importance

    • X to Y = 3 X mod. favored

    • X to Y = 5 X strongly favored

    • X to Y = 7 X clearly dominant

    • X to Y = 9 X super dominant

    • Note: X to Y = 3 implies Y to X = 1/3

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AHP Step 3: Evaluation of Pairwise Comparisons

  • Extract standardized eigenvector for each group of factors or subfactors.

  • The eigenvector can be interpreted as the weight, or importance of a specific factor relative to all other factors.

  • These weights reflect the full information contained in the pairwise comparison matrix

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Corporate site selection

Alternative uses for public land

Choice of environmental plan

Selection of R&D projects

Prediction of bond rating (Srinivasan & Bolster, 1990)

Mutual fund selection (Khasiri, et. al., 1989)

Asset allocation (Bolster, Janjigian, & Trahan, 1995)

AHP Applications

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The Suitability Hierarchy

1. Income

2. Source

3. Savings

4. Savings Rate

5. Cash Holdings

6. Fixed Income Holdings

7. Equity Holdings

1. Age

2. Dependents

3. Time Horizon

4. Investments Consumed

5. Loss Tolerance

6. Liquidity

7. Risk Attitude

1. Money Market

2. Fixed Income

3. Equity

18 Asset Classes

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Precious Metals

Money Mkt., Govt.

Money Mkt., Taxable

Money Mkt., Tax-Free

Mortgage Backed

Government Bonds

Bonds- HiGrade Corp.

Bonds- High Yield

Bonds- Global

Convertible Bonds

Utility Stocks

Income Stocks

International Equity

Growth and Income


Small Cap.

Aggressive Growth


The Suitability Hierarchy: Assets

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Data Requirements

  • Each matrix requires n(n-1)/2 comparisons

  • The “hardwired” portion of hierarchy requires evaluation of matricies of rank 7, 7, and 3. This represents 48 pairwise comparisons.

  • But each of the 17 subfactors spawns an 18x18 matrix => 18(18-1)/2 = 153 comparisons.

  • 5 levels per subfactor x 17 x 153 = 13,005!

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Data: Asset Class Proxies

  • Identify MF with

    • 10 years of history (120 months)

    • Choose 75th percentile fund using Sharpe ratio

    • Use CAPM return estimate for forecast

    • MF style should be consistent with fund classification

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Data: Investor Questionnaire

  • 17 questions (1 per subfactor)

  • 2-5 categorical responses

  • There are 76 distinct responses

    • 76 “suitability vectors” with 18 elements each

    • Total of 1368 pairwise comparisons

    • Remaining pairwise comparisons are inferred

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Data: Pairwise ComparisonsEvaluation of a moderately aggressive investor with above average savings (above $500,000)

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Mean-Variance Optimization

  • We estimate returns using a CAPM (single factor) model

  • The “market” is

    • 30% US Equities (70/15/15 large, mid, small)

    • 20% US Bonds

    • 30% Non-US Equities (EAFE)

    • 20% Non-US Bonds

  • Asset class betas derived from 10-yr. hist.

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Mean-Variance Optimization

  • MVO produces a smooth efficient frontier

  • Define Risk Acceptance Parameter

    • RAP = Var / E(Rp)

    • Higher RAP => Higher risk tolerance

    • Need to map questionnaire responses to RAP and identify the MVO portfolio with same RAP.

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Reconciling Suitability and Optimality

  • AHP underperforms marginally with an increase in shortfall as risk tolerance increases

  • How to reconcile?

    • alter pairwise comparisons?

    • alter RAPs?

    • alter CAPM parameters?

    • live with it?

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  • Minor alterations in AHP rule base (or minor change in inferred RAP) can close gap

  • AHP shortfall is always greatest for highest risk levels

  • Suitability and Optimality are not distant cousins