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. l 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.

Distinguishing Suitability from Optimality §Suitability l Practical, Legal concept l Portfolio’s risk exposure is paramount l Correlations between asset classes considered in a subjective manner l A suitable portfolio need not be optimal §Optimality l Econonmic, Statistical concept l Portfolio’s risk exposure is paramount l Correlations between asset classes considered explicitly. l An optimal portfolio need not be suitable

Modeling Suitability §NYSE Rule 405 §AMEX Rule 411 §AIMR materials l Risk Tolerance l Time Horizon l Liquidity l Unique Factors (legal, tax, etc.)

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

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).

AHP Step 1: Forming the Hierarchy Alt 1Alt 2Alt 3

AHP Step 2: Pairwise Comparisons (Saaty) §The 9-point comparison scale: l X to Y = 1Equal importance l X to Y = 3X mod. favored l X to Y = 5X strongly favored l X to Y = 7X clearly dominant l X to Y = 9X super dominant l Note: X to Y = 3 implies Y to X = 1/3

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

AHP Applications §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)

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

The Suitability Hierarchy: Assets §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 §Growth §Small Cap. §Aggressive Growth §Specialty

Pairwise Comparisons

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!

Data: Asset Class Proxies §Identify MF with l 10 years of history (120 months) l Choose 75th percentile fund using Sharpe ratio l Use CAPM return estimate for forecast l MF style should be consistent with fund classification

Data: Asset Class Proxies

Data: Investor Questionnaire §17 questions (1 per subfactor) §2-5 categorical responses §There are 76 distinct responses l 76 “suitability vectors” with 18 elements each l Total of 1368 pairwise comparisons l Remaining pairwise comparisons are inferred

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

Results from Suitability Model

Mean-Variance Optimization §We estimate returns using a CAPM (single factor) model §The “market” is l 30% US Equities (70/15/15 large, mid, small) l 20% US Bonds l 30% Non-US Equities (EAFE) l 20% Non-US Bonds §Asset class betas derived from 10-yr. hist.

Mean-Variance Optimization §MVO produces a smooth efficient frontier §Define Risk Acceptance Parameter l RAP =  Var /  E(R p ) l Higher RAP => Higher risk tolerance l Need to map questionnaire responses to RAP and identify the MVO portfolio with same RAP.

Mean-Variance Optimization

Reconciling Suitability and Optimality

§AHP underperforms marginally with an increase in shortfall as risk tolerance increases §How to reconcile? l alter pairwise comparisons? l alter RAPs? l alter CAPM parameters? l live with it?

Reconciling Suitability and Optimality: Implied Returns

Conclusions §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