Advisory API Systems LLC

Methodology Disclosure

Effective Date: Upon First API Use
Version: 1.1
Last Updated: December 2025

1. INTRODUCTION

1.1 Purpose of This Disclosure

This Methodology Disclosure provides an overview of the theoretical foundations, analytical approaches, and key assumptions underlying the Advisory API Systems Portfolio Optimization API. This disclosure is intended to help API Users understand how the API generates portfolio recommendations and the factors considered in the optimization process.

1.2 Scope

This document describes the general methodology at a conceptual level. Specific algorithmic implementations, proprietary formulas, and technical parameters constitute confidential trade secrets and are not disclosed.

1.3 Advisory Context

Advisory API Systems provides investment advice to two categories of clients: (a) other registered investment advisers (“RIA Clients”) in a business-to-business capacity, and (b) individual members of the public (“Individual Clients”) in a business-to-consumer capacity. RIA Clients exercise independent professional judgment in determining whether and how to implement API outputs for their End Users. This disclosure is provided to inform Users’ evaluation of the methodology. See the Investment Advice Disclaimer for important risk disclosures.

2. THEORETICAL FOUNDATIONS

2.1 Modern Portfolio Theory

The API builds upon the foundational principles of Modern Portfolio Theory (MPT), developed by Harry Markowitz (Nobel Prize, 1990), which established that:

2.2 Continuous-Time Portfolio Optimization

The API extends classical MPT using continuous-time portfolio optimization techniques pioneered by Robert Merton (Nobel Prize, 1997). The Merton framework addresses:

2.3 Utility Theory and Risk Preferences

Portfolio optimization requires a measure of investor preferences. The API employs:

Constant Relative Risk Aversion (CRRA) Utility

CRRA utility is a widely-used framework where risk aversion is independent of wealth level. An investor with CRRA utility evaluates uncertain outcomes using a utility function of the form:

U(W) = W^(1-γ) / (1-γ)    for γ ≠ 1
U(W) = ln(W)               for γ = 1

Where:

Higher gamma values indicate greater risk aversion. Common academic estimates suggest gamma values between 2 and 5 for typical investors.

3. KEY METHODOLOGICAL FEATURES

3.1 Household-Level Optimization

Unlike traditional portfolio tools that focus on individual accounts, the API performs household-level optimization that:

3.2 Background Asset Integration

A distinguishing feature of the API is its comprehensive treatment of background assets—assets that affect optimal portfolio allocation but may not be readily tradable:

Social Security Benefits

Pensions and Annuities

Medicare and Health Benefits

Means-Tested Cash Benefits (SSI)

Real Estate

Human Capital

3.3 Risk Tolerance Measurement

The API determines risk tolerance through revealed preference methodology rather than subjective questionnaires:

Willingness-to-Pay Elicitation

The methodology converts elicited preferences into a CRRA gamma parameter that governs portfolio optimization.

3.4 Tax-Aware Optimization

The API incorporates comprehensive tax considerations:

Federal Income Tax

State Income Tax

Tax-Advantaged Accounts

Social Security Taxation

3.5 Asset Class Universe

Portfolio recommendations are expressed in terms of broad asset classes, which may be implemented through investment vehicles like ETFs:

Equity Asset Classes:

Fixed Income Asset Classes:

Alternative Asset Classes:

4. OPTIMIZATION PROCESS

4.1 Overview

The API optimization process can be summarized as:

  1. Data Collection: Receive household financial data via API request
  2. Background Asset Valuation: Calculate present values of non-tradable assets
  3. Risk Parameter Determination: Convert elicited preferences to CRRA gamma
  4. Optimization: Solve for optimal portfolio weights given constraints
  5. Output Generation: Return recommended allocations and supporting analytics

4.2 Optimization Objective

The optimization seeks to maximize expected utility of lifetime consumption, considering:

4.3 Constraints Considered

The optimization incorporates realistic constraints:

4.4 Rebalancing Assumptions

The model assumes periodic rebalancing to maintain target allocations. The optimal rebalancing frequency balances:

5. DATA INPUTS AND REQUIREMENTS

5.1 Required Inputs

The API requires the following categories of inputs:

Household Composition:

Income and Employment:

Assets and Accounts:

Liabilities:

Risk Preferences:

5.2 Data Quality

The quality of API outputs depends directly on input quality. Users should ensure:

6. OUTPUTS AND INTERPRETATION

6.1 Primary Outputs

The API returns:

Recommended Asset Allocation:

6.2 Interpretation Guidelines

API outputs constitute investment advice provided to User. Outputs should be interpreted as:

6.3 Limitations of Outputs

Outputs do not account for:

7. MODEL ASSUMPTIONS AND LIMITATIONS

7.1 Capital Market Assumptions

The model incorporates assumptions about expected returns, volatilities, and correlations. These assumptions:

7.2 Economic Assumptions

Key economic assumptions include:

7.3 Behavioral Assumptions

The model assumes rational, utility-maximizing behavior. It does not account for:

7.4 Known Limitations

Users should be aware of the following limitations:

  1. Point-in-Time Analysis: Recommendations are based on current data and assumptions
  2. Model Risk: Mathematical models may not capture all relevant factors
  3. Parameter Uncertainty: Input parameters are estimates, not certainties
  4. Policy Risk: Government policies (tax, Social Security) may change
  5. Black Swan Events: Extreme events outside historical experience cannot be predicted

8. VALIDATION AND TESTING

8.1 Model Validation

Advisory API Systems employs rigorous model validation procedures:

8.2 Ongoing Monitoring

Models are continuously monitored for:

8.3 Updates

Model methodologies are updated periodically to reflect:

9. ACADEMIC FOUNDATIONS

9.1 Key References

The API methodology draws upon extensive academic literature, including:

Portfolio Theory:

Human Capital and Background Risk:

Risk Preferences:

Tax-Efficient Investing:

9.2 Ongoing Research

Advisory API Systems monitors ongoing academic research and incorporates relevant findings into methodology updates.

10. PROPRIETARY ELEMENTS

10.1 Trade Secrets

While this disclosure describes the general methodology, the following elements are proprietary and confidential:

10.2 No Disclosure Obligation

Advisory API Systems is not obligated to disclose proprietary methodological details beyond this general overview.

11. CONTACT INFORMATION

Advisory API Systems LLC

Email: [email protected]
Phone: (310) 839-0358

This Methodology Disclosure is incorporated by reference into the User Agreement. By using the API, you acknowledge that you have read and understood this disclosure.