Compound Return Audit: Why Your Portfolio Differs From the Calculator

1) Begin with a reconciliation, not a return guess

The audit starts with an identity: ending wealth equals beginning wealth, plus net cash flows, plus investment gain or loss, minus costs that are not already included in the reported return. Write down the opening valuation date, closing valuation date, every deposit and withdrawal, and whether dividends were reinvested. A projection using FV = PV × (1 + r)^n assumes that the full present value was invested for all n periods. A real account rarely satisfies that assumption.

Do not start by forcing the account into a familiar 6%, 7%, or 8% scenario. First make the dollars reconcile. If the opening balance was $20,000, the investor added $5,000, and the closing balance was $26,400, the account did not simply “earn 32%.” Some of the ending wealth came from a contribution. The investment gain is $1,400 before considering the contribution date. Only after identifying that date can a return measure assign a sensible weight to the cash flow.

Table 1. Minimum compound-return audit ledger

Input	Required detail	Common error
Opening value	Date and market value	Using cost basis
Cash flows	Amount and exact date	Treating deposits as gains
Closing value	Same scope as opening value	Excluding cash
Income	Paid out or reinvested	Ignoring dividends

Footnote: This ledger is an accounting framework, not a forecast. Use the same currency and account scope for every line.

2) Rebuild the calculator's smooth path

Once the ledger is complete, reproduce the reference projection exactly. Record the starting principal, quoted rate, compounding frequency, horizon, and timing convention for contributions. An annual rate compounded monthly is not the same input as a monthly effective return. For a nominal annual rate r compounded m times per year for t years, the smooth-path value is PV × (1 + r/m)^(mt). For annual compounding, it reduces to PV × (1 + r)^n ^[7].

Contribution timing is a frequent source of false discrepancies. An annuity-due model places each contribution at the beginning of a period; an ordinary-annuity model places it at the end. Beginning-of-period money earns one extra period. A spreadsheet can therefore produce two different, internally correct answers from the same contribution amount and rate. State the convention beside the result instead of hiding it inside a function.

Table 2. Illustration: $10,000 at 6% for ten years

Convention	Formula	Approximate ending value
Annual	10,000 × 1.06^10	$17,908
Monthly, 6% nominal	10,000 × (1 + .06/12)^120	$18,194
Continuous	10,000 × e^(.06×10)	$18,221

Footnote: Rounded illustrative values; no contributions, fees, taxes, or inflation. The three rows use different compounding conventions and are not market forecasts.

This reference path is a control case. It is useful because each later adjustment can be measured against it. It is not evidence that an investment should earn the assumed rate.

3) Replace the constant rate with linked period returns

Market returns arrive as a sequence. If an asset gains 20% and then loses 20%, one dollar becomes $1.20 and then $0.96. The arithmetic average is zero, but the cumulative result is minus 4%. The constant annual rate that reproduces the final value is the geometric mean. This distinction is central to performance measurement and is covered in professional investment curricula ^[7].

To rebuild the account without external cash flows, multiply the growth factors: (1 + r1) × (1 + r2) × … × (1 + rn). The annualized geometric return is that product raised to 1/n, minus one. This method preserves the effect of losses: a 50% decline requires a 100% gain to recover because the gain applies to a smaller base. The result is arithmetic, not a behavioral slogan.

Table 3. Same arithmetic average, different compound result

Two-year path	Arithmetic average	Ending value of $100	Annualized geometric return
+10%, +10%	10.0%	$121	10.0%
+30%, −10%	10.0%	$117	about 8.2%
+50%, −30%	10.0%	$105	about 2.5%

Footnote: Illustrative two-period calculations. Values are rounded and exclude all cash flows and costs.

The more volatile paths compound at lower rates even though their arithmetic averages match. This is the first legitimate reason a smooth calculator can overstate a realized path.

4) Choose time-weighted or money-weighted return deliberately

When external cash flows occur, there is no single universally correct personal return. A time-weighted return breaks the history into subperiods at each cash flow and links the subperiod returns. It largely removes the effect of when the investor added or withdrew money, so it is useful for evaluating an investment process. A money-weighted return solves for the discount rate that equates dated cash flows with the ending value. It reflects the investor's actual experience, including cash-flow timing.

Suppose a portfolio rises sharply while the balance is small, receives a large deposit, and then falls. Its time-weighted result can remain respectable while its money-weighted result is poor because more dollars experienced the decline. Reverse the order and the personal result improves, even if the same two market returns occurred. This is why a fund factsheet and a household account can report different performance without either being arithmetically wrong.

Use time-weighted return when the question is “How did the strategy perform?” Use money-weighted return when the question is “How did my invested dollars perform?” Keep both when cash flows are material. For related measurement choices, see the benchmarking problem.

5) Separate fees from market performance

Costs lower the base that remains available to compound. Bogle's cost argument is especially powerful over long horizons: investors collectively receive the market return before costs, while their aggregate result must be lower after costs ^[1]. An audit should separate product expenses, advisory fees, trading costs, spreads, currency conversion, and account charges. Some are embedded in net asset value; others appear as explicit cash transactions. Subtracting both would double-count them. In practice, that double count is more dangerous than a small rounding difference because it creates a systematic false shortfall in every comparison.

For a clean illustration, $100,000 compounding for 30 years at 7% grows to about $761,225. At a constant 6% net rate, it grows to about $574,349. The difference is about $186,876, even though the annual rate differs by one percentage point. This example does not say that two funds will have identical gross returns. It isolates the mathematical effect of a constant annual drag.

Table 4. Cost-reconciliation questions

Cost	Where it may appear	Audit treatment
Expense ratio	Inside fund NAV	Do not subtract again from net return
Advisory fee	Cash debit or security sale	Record date and amount
Spread/slippage	Execution price	Compare with a defined benchmark price
Currency fee	Conversion transaction	Separate FX movement from fee

Footnote: Cost presentation varies by provider and jurisdiction. Confirm statement definitions before classifying a charge.

Morningstar's research also treats fees as an important predictor of the share of returns an investor keeps ^[5]. See turnover, taxes, and active-management costs for a broader friction audit.

6) Model taxes as dated cash flows, not a universal haircut

Taxes do not behave like a single expense ratio. Their timing depends on account type, jurisdiction, distributions, realized gains and losses, holding periods, and the investor's facts. A taxable distribution removes money when the liability is paid unless cash from outside the account covers it. A deferred liability leaves more capital invested now but may create a later withdrawal. An exempt account follows a different cash-flow pattern. Therefore, applying one permanent “tax rate” to every annual return is usually only a rough scenario, not a reconciliation.

Keep the investment return calculation pre-tax first. Then add actual tax-related cash flows by date. For planning, build multiple clearly labeled cases rather than one false precision estimate. Never infer a personal tax outcome from a generic article; current rules and individual circumstances require appropriate local guidance.

Tax-aware comparison also requires matching turnover and distribution assumptions. Two strategies with the same pre-tax geometric return can leave different spendable wealth if one realizes gains earlier. Yet the higher-turnover strategy might also earn a different gross return, so the audit must not attribute the entire outcome to tax alone. The goal is an explainable bridge from gross investment performance to the investor's net cash result, not a claim that one account type is always superior.

7) Convert nominal wealth into purchasing power

A statement reports nominal currency. A long-term goal is usually expressed in future purchasing power. The exact real return for a period is (1 + nominal return) / (1 + inflation) − 1, not simply nominal return minus inflation. Subtraction is a close approximation only when both rates are modest. FRED and long-run datasets such as Shiller's provide inflation series that can support a historical conversion ^[4][8], but the chosen index must fit the question.

A broad consumer-price index measures an average basket, not a household's exact future cost. Education, housing, medical care, and international spending may follow different paths. State which inflation series, geography, dates, and frequency were used. If the investment is denominated in another currency, separate asset return, currency return, fees, and domestic inflation rather than burying them in one number.

Table 5. Illustration of nominal and real compounding

Nominal return	Inflation	Exact real return	Real value of $10,000 after 20 years
6%	2%	about 3.92%	about $21,560
6%	3%	about 2.91%	about $17,740
6%	4%	about 1.92%	about $14,620

Footnote: Rounded constant-rate scenarios in today's purchasing power; no tax, fees, or contributions. Inflation is assumed constant solely to isolate the formula.

8) Diagnose sequence risk around large cash flows

Without external cash flows, reversing a set of period returns does not change the final product. With contributions or withdrawals, order matters because different amounts are exposed in each period. A decline immediately after a large contribution hurts more dollars. A decline early in retirement can force sales from a reduced base, leaving fewer assets for a later recovery. This is sequence risk.

Audit it by keeping the same returns and changing only their order. Then repeat with the actual contribution or withdrawal schedule. The difference between paths reveals sensitivity to sequence rather than expected return. Do not select one especially favorable or unfavorable order and label it a forecast. Use a set of historical blocks, deterministic stress paths, or clearly documented simulations, and disclose all assumptions.

This analysis changes decisions only when it connects to a control: a cash reserve, withdrawal flexibility, a different allocation, or a limit on near-term commitments. It does not prove that the next downturn is predictable. Long-run equity evidence can explain why investors accept volatility ^[2], but it cannot make a fixed withdrawal schedule immune to bad timing. Review why drawdowns matter alongside the compound-return audit.

9) Close the audit with an explainable bridge

The final deliverable is a bridge, not a single percentage. Start with the smooth reference projection. Replace its constant rate with linked realized returns. Add the effect of dated contributions and withdrawals. Reconcile embedded and explicit fees. Add taxes only with a stated convention, then convert nominal wealth to purchasing power with a named inflation series. The reconstructed ending value should match the statement within rounding and known valuation differences. The key point: an unexplained percentage is not a performance diagnosis, even when the spreadsheet formula itself is correct.

If it does not match, investigate scope before inventing an explanation. Typical causes include unsettled cash, excluded dividends, an account transfer recorded on only one side, different market-close times, foreign-exchange translation, or comparing a total-return benchmark with a price-only account series. Document each residual difference and its size. An unexplained residual is a finding, not permission to adjust the return until it looks right.

The practical conclusion is modest: the compound formula is usually not the source of the disagreement. Inputs, timing, and definitions are. A disciplined audit makes those choices visible and produces a result another reader can reproduce.

Sources & Further Reading

1. Bogle, J. C. (2007). The Little Book of Common Sense Investing: The Only Way to Guarantee Your Fair Share of Stock Market Returns. Wiley. Source
2. Siegel, J. J. (2014). Stocks for the Long Run: The Definitive Guide to Financial Market Returns and Long-Term Investment Strategies (5th ed.). McGraw-Hill Education. Source
3. Shiller, R. J. (2025). Online Data for 'Irrational Exuberance' (S&P 500, dividends, earnings, CPI). Yale University. Source
4. S&P Dow Jones Indices. (2025). S&P 500 Index Methodology. Source
5. Morningstar, Inc. (2024). The Impact of Fees on Fund Returns. Morningstar Research. Source
6. Malkiel, B. G. (2019). A Random Walk Down Wall Street (12th ed.). W. W. Norton & Company. Source
7. CFA Institute. (2023). Time Value of Money and Compounding. CFA Program Curriculum overview. Source
8. Federal Reserve Bank of St. Louis. (2025). FRED Economic Data. Useful for inflation and rate series referenced in real-return analysis. Source