Your account report shows a slightly positive time-weighted return for the year. Your transfers show that you put in $11,000 altogether, yet the ending balance is below $11,000. Is the report disguising a loss, or have you missed some money?
Neither calculation must be wrong. The report may ask how the investment process performed, while you want to know what happened to the amounts you invested at particular times. We will use the same account as G50 to separate those questions. First, however, the dollars must reconcile.
Keep one account while changing the measurement
Your tasks are to separate external flows from investment results, trades, and fees; divide the record at its contribution boundary and link the returns; then check the cash flows, timing, and solution convention for a money-weighted rate. Do not switch to a different performance history for each method.
Use C3-50-v1: dollars and twelve equally long teaching months, M1–M12, without actual calendar dates. Starting holdings are $6,000 in stocks, $3,000 in bonds, and $1,000 cash, totaling $10,000. This is a supplied holdings snapshot; do not invent an initial purchase fee. The sleeves are long-only, unlevered, continuously divisible, and cash earns zero.
One external contribution of $1,000 arrives after the M6 execution window, W6, and before M7 returns begin. Call this boundary t6, with t0 at the beginning and t12 at the end. The contribution is neither M6 profit nor an M7 month-end deposit. Use ending equity after W12 execution and fees, without forcing liquidation.
Targets are 60% stocks, 30% bonds, and 10% cash. The quarterly rule checks at M3, M6, M9, and M12. The threshold rule checks monthly and trades when any sleeve differs from target by at least five percentage points, including equality. On a trigger, stocks and bonds return to their target dollar amounts using the same pre-fee equity. Each trade costs five basis points of its value, with fees paid from cash, so post-fee weights differ slightly from targets.
Each Wm is a separate executable window after the complete month-end valuation. The exercise supplies no additional price movement between them; it does not claim a real fill at a close learned only afterward. Total-return inputs already include reinvested distributions; do not add dividend cash again. No other slippage, taxes, or management fees are modeled. The results are pretax and net of the specified model fees, not evidence of realistic all-in investment costs.
Find the contribution in all twelve rows
The table supplies every sleeve-return input, the external contribution, and threshold-rule equity. Cash returns are zero throughout. Sleeve returns are not account returns. Displayed balances have four decimals; calculations use the unrounded inputs and ledger.
| Month | Stock return | Bond return | Start-of-month external contribution | Threshold equity after contribution | Equity after execution and fees |
|---|---|---|---|---|---|
| M1 | 5% | 1% | 0 | 10000.0000 | 10330.0000 |
| M2 | −8% | −2% | 0 | 10330.0000 | 9765.4000 |
| M3 | 3% | 0.5% | 0 | 9765.4000 | 9954.1270 |
| M4 | 6% | 0% | 0 | 9954.1270 | 10312.3198 |
| M5 | −4% | −1% | 0 | 10312.3198 | 10029.3544 |
| M6 | 2% | 1% | 0 | 10029.3544 | 10180.3975 |
| M7 | 1% | 0.5% | 1000 | 11180.3975 | 11256.8446 |
| M8 | −12% | −4% | 0 | 11256.8446 | 10311.2329 |
| M9 | 4% | 1% | 0 | 10311.2329 | 10581.4077 |
| M10 | 3% | 0.5% | 0 | 10581.4077 | 10783.2282 |
| M11 | −2% | 0% | 0 | 10783.2282 | 10655.8873 |
| M12 | 5% | 0.5% | 0 | 10655.8873 | 10984.3270 |
Monthly investment profit equals ending equity after fees minus equity before that month's contribution, minus the external net contribution. M7 begins from $10,180.39746106, receives $1,000, and ends at $11,256.84455688. Its investment profit is approximately $76.4471, not $1,076.4471.
Sum these monthly investment profits and losses: the threshold rule loses $15.672997. Starting equity of $10,000, plus $1,000 contributed, minus that investment loss, produces ending equity of $10,984.327003. The balance rose $984.327003 from its earliest level, but that increase is not all profit.
Selling stocks for cash within the evaluated account changes its assets, not external withdrawals. Reinvested distributions belong in the supplied total returns. Commissions already reduce monthly results and ending equity; do not subtract them again from the $15.672997 loss. Draw the account boundary before labeling a cash flow.
Time-weighted return: measure each side of the contribution
Time-weighted return, or TWR, divides the record at external-flow boundaries, calculates subperiod returns, and geometrically links their growth factors. This prevents a transfer itself from becoming a return. GIPS calculation methodology describes valuation at external cash flows and linking subperiods.[1] Using that calculation idea does not establish compliance with the entire GIPS standards.
Before the t6 contribution, threshold-rule equity is $10,180.39746106. With no earlier external flow, divide by $10,000 and subtract one: the first six months return about 1.803975%. The contribution immediately raises equity to $11,180.39746106, without an intervening market change. This larger amount is the second subperiod's starting denominator.
The endpoint is $10,984.32700283238. Divide by $11,180.39746106 and subtract one for a second-half return of about negative 1.753698%. Multiply growth factors 1.018039746106 and 0.982463015388, then subtract one. Full-year TWR is approximately 0.018640%. Do not simply add the percentages or place the contribution inside investment profit.
You can check it monthly: divide each after-fee endpoint by that month's starting equity after any contribution, then multiply all twelve factors. M7's denominator must include the $1,000 already received. Other months begin from the preceding net endpoint. This package supplies boundary valuations; a real account lacking them would need an identified approximation with its assumptions and limitations.
Removing the mechanical transfer does not mean the new cash cannot affect management. Here it first enters cash and may change weights, threshold triggers, and later holdings. TWR measures that actual management path. It does not rerun a hypothetical account that never received the contribution.
Money-weighted return: give each dollar its participation time
Money-weighted return, or MWR, reflects invested amounts and their timing, commonly expressed as an internal rate of return, or IRR.[1] Find a constant compound rate that would grow the amounts invested at their actual times into the ending value.
Use the investor's perspective consistently: negative $10,000 at t0, negative $1,000 at t6, and positive $10,984.32700283238 at t12. No actual liquidation occurs. The positive terminal amount represents the remaining assets' valuation for measurement, not another dividend or a fictional bank receipt.
The first amount participates for twelve months and the second for six. A monthly rate r must satisfy:
10000 × (1+r)^12 + 1000 × (1+r)^6 = 10984.32700283238
For a spreadsheet, create thirteen equally spaced rows indexed zero through twelve. Enter negative $10,000 in row zero, negative $1,000 in row six, and the positive terminal amount in row twelve. Put numerical zeros in the other ten rows. Apply IRR to all thirteen values to obtain a monthly rate. Using only the three nonzero amounts with ordinary IRR would compress each six-month gap into one interval. Microsoft's documentation requires regularly spaced periods and interprets flows in their listed order.[2]
The independently calculated monthly IRR is approximately negative 0.0124471832%. Under the teaching convention of twelve equal months per year, raise one plus that monthly rate to the twelfth power and subtract one. The effective twelve-month MWR is about negative 0.149264%, not simply twelve times the monthly number. It describes these supplied events, not a forecast of next year's return.
For irregular actual dates, XIRR may be appropriate, with every true date and amount retained. Microsoft specifies date-based discounting on a 365-day year.[3] This case has no real dates. Inventing three calendar dates would change the convention rather than make the original answer more sophisticated.
A positive TWR and a negative MWR can agree
The threshold account gained about 1.804% before the contribution and lost about 1.754% afterward. The later decline affects the new $1,000 as well as the original capital. Total dollars invested can therefore lose money even while the linked management-path return is slightly positive. The two results emphasize different features of the same history.
You can show ownership without rerunning the asset returns. Suppose investor A supplies the initial $10,000 and investor B adds $1,000 at the t6 account value. After t6, both bear the shared account's return and included fees in proportion to their units. This is an internal allocation assumption, not an actual partnership product.
A's original money is worth $10,180.39746106 at t6. Apply the second-half factor and its endpoint is about $10,001.863987. B's $1,000 becomes $982.463015. They sum to $10,984.327003: A gains slightly, B loses about $17.536985, and the combined investment loss is $15.672997.
B's different participation window does not establish inferior investing skill. Do not rank B's half-year result against A's full year without preserving the labels. This allocation divides one shared account, retains the policy that the contribution first enters cash, and does not imply that B could independently obtain identical trades and fees in a separate account.
The quarterly rule gives another comparison from the same original package. Fees are already included; the data do not change between calculation methods.
| Rule | Investment profit/loss, dollars | Twelve-month TWR | Monthly IRR | Effective twelve-month MWR |
|---|---|---|---|---|
| Quarterly | 53.925304 | 0.652387% | 0.042700% | 0.513606% |
| Five-percentage-point threshold | −15.672997 | 0.018640% | −0.012447% | −0.149264% |
Dollar profit asks how much investment value changed. Matching-period TWR describes the given management path. MWR reflects the investor's combination of amounts and times. None is always the more accurate answer to every question. A personal MWR cannot be compared mechanically with an index TWR that has different cash flows.
A solver's number is not necessarily unique
IRR solves an equation. Wrong signs, timing, or a duplicated terminal value can produce a precise-looking but meaningless answer. Check intermediate zeros, distributions, and fees, then substitute the result back into the equation and examine the residual. A software error is not automatically a zero return; it can mean incorrect inputs or failed convergence.
This package has two investments followed by one positive terminal value. For a positive monthly growth factor, the left side of its equation increases strictly, so exactly one solution exists. Do not extend that property to every cash-flow sequence.
Consider separate mathematical diagnostics, outside C3. Equally spaced flows of negative 100, positive 230, and negative 132 have zero net present value at both 10% and 20% per period. Multiple sign changes can permit multiple solutions but do not guarantee them. Flows of negative 100, positive 100, and negative 100 have no solution with a positive growth factor. Record a nonunique or unavailable result instead of selecting a preferred rate as certain performance.
Zero or negative subperiod starting values also invalidate a simple TWR division. Unusual accounts, borrowing, or missing flow-date valuations need a suitable method before the report can be completed. Multiple subaccounts likewise require aligned assets and flows; averaging their return percentages does not automatically produce the aggregate return.
Change the measurement window
First explain why subtracting net contributions helps find dollar profit but does not itself define a return rate. Identify the missing starting capital, denominator, and participation times. What happens if you subtract accumulated commissions from the endpoint again?
Now change only the evaluation window, leaving all C3-50 trades unchanged. Evaluate the quarterly rule in M7–M12. After W6, original equity is $10,180.413971237016. Add $1,000 before this half-year starts. After W12, equity is $11,053.925303545889. There are no flows inside this window. Someone subtracts $1,000 from the endpoint again to remove the contribution. Explain the error, calculate half-year TWR, and decide whether cumulative half-year MWR differs.
Reference answers · reveal
Answer guide: Starting equity is $11,180.413971237016. Endpoint divided by this start, minus one, gives approximately negative 1.131342%. The contribution already belongs in the starting denominator. Subtracting it from the endpoint removes it twice. With no intervening flows, matching-endpoint cumulative half-year MWR and TWR agree. Compound a monthly IRR over six months before comparing; label the result a half year, not a full year.
For the explanation, ending value minus net contributions must also subtract starting equity to give investment profit in dollars. A rate still needs a defined question, denominator, and timing. The package already includes fees in its endpoint, so deducting them again duplicates the loss. Knowing that a contribution is not profit is useful only if you can identify where it enters the calculation.
Save a T22 reconciliation sheet
For both C3-50 rules, record account boundary, currency, month-index convention, start, every external flow and its sign, valuations before and after flows, monthly investment profits, and endpoint. Retain TWR segments, the complete IRR input sequence, solved rate, compounding period, residual, and exceptional-result status.
Label the materials synthetic, pretax, and net of the specified fees. Preserve unrounded inputs. First reconcile starting value plus external net flows plus investment profit to the endpoint. Then check that every flow appears once at the correct boundary. Finally ask whether the rate answers your actual question. Missing dates, missing valuations, or multiple roots remain open issues; more decimals cannot resolve them.
Locate the flow boundary before comparing returns
When two reports give different rates, trace the same account, flows, and fees before choosing the higher result. One may measure the management path and the other the amounts invested at particular times. Once the dollars reconcile, their difference becomes interpretable. Explaining the sources of benchmark-relative performance is the next task.
References
- GIPS Standards Handbook for Firms, Calculation Methodology. Flow-boundary valuations, geometric linking, and MWR/IRR; using the methods does not claim full standards compliance.
- Microsoft Support: IRR Function. Equal intervals, signs, sequence, and iterative-solving limitations.
- Microsoft Support: XIRR Function. Actual dates, a 365-day basis, and solving requirements.
Sources inspected October 30, 2026. AI-assisted draft; independent AI full-text and bilingual review is complete. Human financial review and target-reader testing have not been performed. C3-50 is synthetic; the separate root diagnostics are mathematical examples, not real-market performance.