Original hypothetical USD calculations with explicit timing and valuation assumptions. Primary references establish narrow concepts only; scenarios are neither empirical forecasts nor promised financial results.
Separate account growth from investment-generated value
The SEC's account-statement guide distinguishes deposits, withdrawals, interest receipts and valuation changes. A portfolio can grow because money was added even while the investments lose value. Measuring performance therefore requires a dated external-flow ledger and a consistent valuation basis. This is particularly relevant for bond accounts where coupons move into cash, accrued interest changes and new purchases may occur between reporting dates.
We use a fictional portfolio with two equal half-year intervals and one contribution at their boundary. Beginning and ending portfolio values include securities, retained coupon cash and accrued interest. The numbers are supplied after any internal transfers so those transfers cannot be mistaken for contributions. There are no fees or withdrawals. These definitions allow a transparent comparison of exact linked subperiod return with an approximate full-period measure.
Supporting references: 1. SEC Investor.gov: Better Understanding Your Brokerage Account Statement
Reconcile the dollar result before computing a rate
The portfolio starts at USD 10,000 and reaches USD 10,200 just before the midpoint contribution. The investor then deposits USD 10,000, raising value to USD 20,200. By year-end the whole portfolio is worth USD 19,998. The first interval earns USD 200; the second loses USD 202. Full-year investment profit is therefore minus USD 2, equal to ending value less starting value less the contribution.
A statement showing balance growth of USD 9,998 would be correct as a balance change but misleading if called investment profit. Dividing that balance change by the initial USD 10,000 produces 99.98 percent, almost entirely due to new money. The first control is always the dollar reconciliation. If deposits and withdrawals cannot be distinguished from generated cash, a sophisticated return formula will not repair the missing records.
Hypothetical worked example
Measure Portfolio Return When New Money Arrives Between Bond Valuations: hypothetical case
Model setup
Read these assumptions before comparing the scenarios.
- Hypothetical USD portfolio: start 10,000; midpoint before deposit 10,200; deposit 10,000; end 19,998.
- Two equal half-year intervals; actual deposit immediately after midpoint valuation.
- All values include retained coupons and accrued interest; no withdrawals, taxes or fees.
- Timing sensitivity holds dollar gain constant only to isolate the denominator, not simulate a market path.
Modified Dietz approximation (percent)
- 1. Present for full year
- -0.01
- 2. Present for half year, actual case
- -0.01
- 3. Arrives at endpoint
- -0.02
Shared zero-based value scale. Range: -0.02 to 0.00, in the units above. Case numbers match the labels; no probability or time trend is implied.
Hypothetical model, not observed market data or a forecast. Assumptions above; original values and calculations below.
| Contribution-weight sensitivity | Contribution time weight (fraction) | Weighted capital (USD) | Modified Dietz approximation (percent) |
|---|---|---|---|
| Present for full year | 1 | 20000 | -0.01 |
| Present for half year, actual case | 0.5 | 15000 | -0.013333333333333 |
| Arrives at endpoint | 0 | 10000 | -0.02 |
Calculation details
- Investment dollar gain
- -2.00 USD
((19998 - 10000) - 10000) - First interval return
- 2.00 percent
(((10200 / 10000) - 1) * 100) - Linked full-year return
- 0.98 percent
(((1.02 * 0.98999999999999999) - 1) * 100) - Actual Dietz approximation
- -0.01 percent
((-2 / (10000 + (10000 * 0.5))) * 100)
Link periods around the contribution
The first half-year return is USD 200 divided by USD 10,000, or 2 percent. The second is minus USD 202 divided by USD 20,200, or minus 1 percent. A time-weighted result links the two growth factors: 1.02 multiplied by 0.99 minus one equals 0.98 percent for the full year. It describes the compounded experience of a unit exposed to both intervals, neutralizing the size of the external contribution.
A positive linked result can coexist with a USD 2 investment loss because more investor money was present during the losing interval. There is no contradiction. The linked number answers how the investment path compounded across periods; the dollar ledger answers how much money was earned on the actual amounts deployed. Neither should be relabeled as the other just because the sign difference feels uncomfortable.
Estimate when an interim valuation is missing
If only starting value, ending value and the contribution date are available, a Modified Dietz approximation divides the USD 2 loss by starting capital plus the time-weighted contribution. With the contribution present for half the year, the denominator is USD 10,000 plus one-half of USD 10,000, or USD 15,000. The approximate full-year rate is minus 0.01333 percent. That is not the exact time-weighted result and not an exact internal rate of return.
The weight records the fraction of the measurement interval during which external capital is present. It does not represent confidence in the deposit or its contribution to market risk. The approximation can be useful for a cash-flow-adjusted account view when records are limited, but it cannot reconstruct the two subperiod returns without the midpoint valuation. Labeling it precisely matters more than displaying extra decimal places.
Stress flow timing and valuation consistency
As an algebraic sensitivity only, hold the full-year dollar loss at minus USD 2 and change the contribution's time weight. A start-of-year weight of one produces a USD 20,000 denominator and minus 0.01 percent. An end-of-year weight of zero produces a USD 10,000 denominator and minus 0.02 percent. The table compares these timing assumptions; it does not claim that moving a deposit would leave actual market earnings unchanged.
A bond-specific error arises if beginning value excludes accrued interest but ending value includes it. The apparent gain then contains a valuation-convention change. Similarly, a coupon retained inside the portfolio is an internal flow, whereas a coupon transferred out to household spending is an external withdrawal for whole-account measurement. Reconcile security value and cash together, and keep cash-flow classifications consistent at every date.
Match the reported metric to the decision
FINRA distinguishes bond yields from realized return. The same care applies at portfolio level: a contractual yield is not a substitute for a return computed from account values and flows. If the question concerns the investment path independent of investor timing, value the portfolio around material external flows and link subperiod returns. If it concerns actual dollars earned, begin with the investment-profit reconciliation and acknowledge when the chosen rate is approximate.
The decision boundary is whether a precise interim valuation exists and which question the report needs to answer. Request the method used by a provider before comparing two percentages with different definitions. Large flows during volatile periods can make approximations especially sensitive to missing timing information. This exercise verifies arithmetic under supplied values; it does not certify a reporting standard, evaluate a manager or infer future performance from the positive linked result.
Supporting references: 2. FINRA: Understanding Bond Yield and Return
Limits of this analysis
- Modified Dietz is an approximation and is not presented as an exact money-weighted IRR.
- Timing sensitivity holds profit fixed artificially to isolate denominator effects.
- Unreliable valuations or inconsistent accrued-interest treatment corrupt all methods.
Sources and scope
- SEC Investor.gov: Better Understanding Your Brokerage Account Statement
Statement activity distinguishes deposits and withdrawals from interest, reinvestment and valuation changes.
Scope: Primary conceptual or convention evidence only; numerical inputs and analysis are original hypothetical models, not source findings.. Reference accessed 2026-10-29.
- FINRA: Understanding Bond Yield and Return
Bond yields and realized total returns have different definitions.
Scope: Primary conceptual or convention evidence only; numerical inputs and analysis are original hypothetical models, not source findings.. Reference accessed 2026-10-29.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards
