In investing, you get what you don’t pay for.
Abstract
We consider an investor with $10,000 who contributes $500 monthly for 40 years, earning a 6.4% nominal gross return with inflation at 2.5%. Raising the annual fee from 0.03% to 0.66% reduces terminal wealth from $434,479 to $363,095 in today’s dollars — the difference, $71,384, amounts to 20.7% of the lifetime investment gains the market provided. The fee difference compounds geometrically. In this model every simulated scenario applies the same recurring fee drag to the same market path; unlike future returns, that cost is known in advance and remains under the saver’s direct control.
Saver profile
Market assumptions — the world
Portfolio: 80% equities · 20% bonds
Fee scenarios — the subject
| Scenario | Terminal (real) | Cost of fee | Share of gains | Catch-up | Wealth ratio |
|---|---|---|---|---|---|
| Gross (frictionless) | $438,242 | — | — | — | 1.00 |
| 0.03%· Total-market index | $434,479 | −$3,763 | 1.1% | 2 mo | 0.991 |
| 0.07%· Peer index | $429,516 | −$8,727 | 2.5% | 4 mo | 0.980 |
| 0.66%· Typical active fund | $363,095 | −$75,147 | 21.8% | 3 yr 1 mo | 0.829 |
The miracle of compounding returns is overwhelmed by the tyranny of compounding costs.
Four basis points sounds like nothing. Held for 40 years, the difference between 0.03% and 0.07% on this saver’s path is $13,326 in nominal terms — $4,963 in today’s dollars. Whether that is “nothing” is a question about your hourly wage, not about arithmetic.
| 0.03% | $1,166,604 | $434,479 |
| 0.07% | $1,153,277 | $429,516 |
| Difference | $13,326 | $4,963 |
| Fee | Nominal | Real |
|---|
Inflation is not an investment fee; it is a loss of purchasing power. At a constant 2.5% annual rate, money loses half its purchasing power in about 28.1 yr. This paper therefore reports real dollars by default.
Equities have historically paid a premium over bonds for bearing greater risk. An investor cannot choose that premium; the controllable decision is how much exposure to accept. The ladder below shows the modeled wealth effect of that allocation under the stated return assumptions.
| Equity weight | Deterministic (real) | MC median | MC 5th pct. | P(beat inflation) |
|---|---|---|---|---|
| 0% equity | $232,261 | — | — | — |
| 20% equity | $270,433 | — | — | — |
| 40% equity | $315,853 | — | — | — |
| 60% equity | $369,958 | — | — | — |
| 80% equitycurrent | $434,479 | — | — | — |
| 100% equity | $511,489 | — | — | — |
Money management has become a loser’s game.
A fee can buy a service. The arithmetic here prices the cost, not whether help changes your decisions. The Price of Advice compares recurring fees with finite avoided mistakes and disciplined DIY.
Cash has a different job. The SWAN Number examines the compounding tradeoff of building a reserve before investing, using the same starting wealth and saving budget.
Deterministic engine. Monthly recursion with the contribution at month end, net growth factor ((1+g_p)(1−f))^(1/12), contributions growing annually by g_c. The portfolio return is the blend g_p = w·g_e + (1−w)·g_b (6.40% here); the deterministic engine ignores rebalancing and volatility interactions — the Monte Carlo handles those properly. Real figures deflate by (1+π)^(m/12).
Monte Carlo. A two-asset monthly model with a geometric (median-growth) parameterization: the median compound growth equals g, while the arithmetic mean is higher by the volatility drag σ_p²/2 = 0.84%. Monthly log-returns use a Box–Muller pair per month from a mulberry32 stream.
Common random numbers. One set of monthly draws is shared by every fee scenario — fees do not move markets — so scenario differences are pure fee effects. This is the paper’s methodological signature. Every base path is paired with its sign-flipped antithetic twin for variance reduction.
Seed & paths. Seed 42 — same seed and inputs reproduce bit-identical results. Currently 10,000 effective paths.
Analytic cross-check. For a pure lump sum, the terminal-wealth ratio between two fees is exactly ((1−f₂)/(1−f₁))^T = 0.776566. On this saver’s contributing path the realized ratio is 0.835703 (contributions enter at different times, so the two differ slightly).
Delay cost. The smallest number of extra months the fee-paying saver must keep contributing (at the year-T rate, growth still net of fee) for the balance to reach the frictionless terminal, capped at 1,200 months.
Limitations. No taxes, no stochastic inflation, no withdrawal phase, no glide paths, and a single annual fee drag per scenario. Total contributions here are $250,000; the two extreme loaded fees are 0.03% and 0.66%. Educational model output, not advice.
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