Inspectable Arithmetic for the Advisor Fee Calculator

Version 1.0
Last updated: February 2026

Transparent arithmetic is the operating system of this calculator.

This document publishes the formulae, computational structure, and assumptions used to generate the outputs displayed on the calculator page.

No opinions. No hidden assumptions. Just arithmetic.

Purpose

This calculator models the long-run effect of advisor fees and optional fund MERs charged as a percentage of assets under management (AUM), comparing portfolio outcomes with and without those costs under constant return and contribution assumptions.

Definitions

Let:

• B₀ = initial portfolio balance (equal to starting balance P)
• B_t = portfolio balance at the end of month t
• P = starting balance
• C = monthly contribution
• r = annual nominal return (gross, before fees)
• f_a = annual advisor fee rate
• f_m = annual MER rate (if enabled)
• T = investment horizon in years
• N = 12T = total number of months

Monthly rates:

Formulae

The portfolio is simulated month-by-month.

1. Growth Without Advisor Fee or MER

Rationale: Models deterministic monthly compounding with fixed contributions.

Limitation: Assumes constant return and fixed contribution schedule; does not model volatility or sequence-of-returns risk.

2. Growth With Advisor Fee and MER

Gross monthly growth:

Total monthly cost rate:

Fee deducted:

Net balance:

Algebraically equivalent expression when fees are applied after growth:

Rationale: Advisor fees and MERs are modeled as proportional deductions from assets under management.

Limitation: Actual billing schedules may vary (e.g., quarterly billing, in arrears, average daily balance). This model applies a proportional monthly drag consistent with monthly compounding.

3. Default Tiered Advisor Fee Schedule

If “Use default advisor fee schedule” is enabled:

The annual advisor fee rate f_a is determined each month based on the portfolio’s current AUM tier. The applicable annual rate for that tier is applied to the entire portfolio balance (non-blended schedule).

Rationale: Many advisory platforms use declining percentage schedules based on AUM.

Limitation: Some real-world fee schedules are blended marginal tiers; this model applies the single rate associated with the current tier.

4. Total Fees Paid

Rationale: Tracks cumulative dollar amount explicitly deducted from the portfolio due to advisor fees and any included MER.

Limitation: Excludes trading costs, taxes, commissions, and other indirect costs.

5. Ending Values

6. Lost Compounding

Rationale: Separates direct fee dollars from the additional growth lost because those dollars were removed from the compounding base.

7. Total Calculated Cost

This equals:

8. Break-Even Advisor Performance

Break-even performance is the additional annual return Δr required such that:

This is solved numerically by adjusting return until:

Rationale: Determines the constant annual outperformance required to offset the modeled fee drag.

Limitation: Assumes consistent additional return each year; does not model risk-adjusted or volatility-adjusted performance.

Assumptions

1. Returns are modeled as constant and deterministic.
2. Contributions occur monthly and remain constant.
3. Advisor fee and MER are applied proportionally each month.
4. The default tiered schedule applies a single rate to the entire portfolio based on current AUM.
5. No taxes, commissions, asset allocation changes, or behavioral responses are modeled.
6. Rounding occurs at the display layer; internal calculations use full numerical precision.

Implementation Notes

• The model iterates month-by-month over the full horizon.
• Fee dollars are tracked explicitly each month.
• Break-even return is solved using an iterative numerical method.
• All calculations use floating-point arithmetic; rounding occurs only for display.

If any discrepancy is identified between this documentation and the calculator output, the arithmetic here governs.