Inspectable Arithmetic for the Advisor Fee Calculator

Version 1.1
Last verified: May 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 equal gross return and constant contribution assumptions.

For plain-language context on fee drag and compounding, see The True Cost of Financial Advisor Fees.

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 (used only for the flat user override; not a single rate on the whole balance when the default tier schedule is enabled)
• F_adv(B) = annual advisor fee in dollars under the default marginal tier schedule, for balance B
• f_m = annual MER rate (if enabled)
• T = investment horizon in years
• N = 12T = total number of months

Monthly growth factor and MER rate on balance:

Formulae

The portfolio is simulated month-by-month.

1. Growth Without Advisor Fee or MER

Let g = (1 + r)^1/12 (monthly compounding consistent with the simulation).

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 balance after contribution and growth:

MER fee (always a flat percentage of current AUM):

Advisor fee (default schedule — marginal / blended tiers):

Advisor fee (user override — single flat annual rate on total AUM):

Total fee and net balance:

Rationale: MER is modeled as a proportional monthly drag on AUM. Default advisor fees use dollar-based marginal tiers each month (see below), so the advisor leg is not generally expressible as a single effective rate times the whole balance.

Limitation: Real-world billing may use daily accrual, tax treatment of fees, or embedded commissions; this model uses one monthly step.

3. Default Tiered Advisor Fee Schedule (Blended)

When the default schedule is enabled, fee tiers are applied progressively, similar to tax brackets: each tier’s annual rate applies only to the dollars inside that tier’s band. The monthly advisor fee is one-twelfth of the resulting annual dollar fee for the current balance.

For tiers j = 1…J with lower bound L_j, upper bound U_j (exclusive, except the top open tier), and annual rate r_j:

The published bands are: $0–$250,000 at 2.00%; $250,000–$500,000 at 1.75%; $500,000–$1,000,000 at 1.50%; $1,000,000–$2,000,000 at 1.25%; over $2,000,000 at 1.00% (half-open intervals, consistent with the table on the calculator page).

4. Total Fees Paid

5. Ending Values

6. Lost Compounding

7. Total Calculated Cost

8. Break-Even Advisor Performance

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

This is solved numerically until:

This section exists because the base model does not assume persistent advisor outperformance; it calculates the constant additional return required to offset fee drag.

Assumptions

1. Returns are modeled as constant and deterministic.
2. Contributions occur monthly and remain constant.
3. The compared scenarios assume the same gross pre-fee market return.
4. The advisor-managed portfolio is assumed to match the market before fees, not to generate persistent outperformance. This is consistent with the empirical record: SPIVA Canada data show that the majority of actively managed funds underperform their benchmarks over long time horizons, net of costs.
5. MERs are applied each month as a fixed percentage of current AUM. When the default advisor schedule is enabled, advisor fees use marginal tiering on current AUM (not a single bracket rate on the entire balance).
6. Fee tiers are applied progressively, similar to tax brackets.
7. The model isolates fee drag by holding other structural variables constant between scenarios.
8. The self-directed investor is assumed to contribute consistently, remain invested, and follow a simple long-term plan with similar discipline.
9. No taxes, commissions, asset allocation changes, withdrawals, or advisor value-add beyond portfolio management are modeled.
10. 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 numerically.
• 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.

What This Calculator Does Not Include

• Tax treatment of advisory fees (e.g., deductibility in non-registered accounts).
• HST/GST on advice, trailer fees, or other embedded product compensation.
• Withdrawals, changing contribution rates, glide paths, or asset-allocation drift.
• Market volatility, sequence-of-returns risk, or cash balances outside the invested portfolio.
• Behavioral gaps (timing of contributions, panic selling) and implementation shortfall.

Sources and References

• SPIVA Canada — long-horizon active vs passive performance context.
• Government of Canada — general regulatory and consumer context.
• OSFI — banking and supervisory context for large Canadian institutions.