Portfolio deposits and returns: separate account growth from investment performance

Start with three different questions

An account balance can rise because investments earned money, because you deposited savings, or because both happened. A performance worksheet should answer three separate questions: how much wealth is in the account, how many dollars the investments gained or lost, and what rate of return describes the experience. A percentage displayed beside a balance is not interpretable until you know which question it answers.

This tutorial builds one hypothetical account from a dated cash ledger. All amounts, dates relative to the measurement period, and returns below are invented for education. They are not a live portfolio, a forecast, or a recommended investment. The first calculations exclude fees, taxes and withdrawals. Keeping that deliberately simple baseline makes it easier to identify what changes when money arrives midway through a period.

Reconcile dollars before calculating a percentage

Imagine an account starts with $10,000. At the end of its first year, immediately before any new deposit, its value is $11,000. You then contribute another $10,000, taking the account to $21,000. During the second year it falls to $18,900. There are no further external flows.

The ending balance exceeds the starting balance by $8,900. Dividing that increase by the initial $10,000 produces 89%, but that is account growth including your contribution. It is not investment return. The investment dollar result is ending value minus starting value minus deposits plus withdrawals. Here that is $18,900 minus $10,000 minus $10,000, or a $1,100 loss.

Reconcile that loss another way: the first year earned $1,000, and the second year lost $2,100. Their sum is negative $1,100. These two independent calculations should agree. If they do not, search the transaction history for an omitted transfer, income payment, expense or valuation discrepancy before debating which return formula to use.

Dividing the $1,100 loss by the $20,000 contributed gives negative 5.5%. Label it a loss relative to total contributions, not an annualized performance rate. The two deposits were invested for different lengths of time. A denominator that simply adds them does not capture that difference.

Calculate the return of the investment path

CFA Institute's discussion of performance reporting distinguishes a time-weighted return, which removes the effect of external contribution and withdrawal timing, from a money-weighted return, which incorporates that timing. Neither makes the account statement unnecessary. They summarize different aspects of the same history.

For our example, divide the measurement interval at the contribution. The first subperiod return is $11,000 divided by $10,000 minus one: positive 10%. The second is $18,900 divided by $21,000 minus one: negative 10%. Link their growth factors: 1.10 multiplied by 0.90 equals 0.99. Subtract one to obtain a cumulative two-year time-weighted return of negative 1%.

A gain of 10% followed by a loss of 10% therefore does not cancel out. A hypothetical dollar following that investment path finishes at 99 cents. The arithmetic average of the two yearly percentages is zero, but the compound result is negative 1%. The order of those two factors does not change their product.

The annualized equivalent is the square root of 0.99 minus one, approximately negative 0.5013%. Clearly distinguish that annualized number from the cumulative two-year result. CFA Institute's GIPS standards describe geometrically linking subperiod returns when calculating time-weighted performance; this simplified worksheet illustrates the mathematics and does not claim that a personal spreadsheet complies with every GIPS requirement.

Calculate the return experienced by the dollars

A money-weighted calculation asks which constant rate reconciles the actual cash commitments with the ending value. With our equally spaced annual dates, let r be the yearly rate. The initial $10,000 compounds for two years and the next $10,000 for one. The equation is: $10,000 × (1 + r)² + $10,000 × (1 + r) = $18,900.

Set x equal to 1 + r. After dividing by $10,000, x² + x = 1.89. The economically relevant positive solution is x = (√8.56 − 1) / 2, approximately 0.962874. Thus the annual money-weighted return is approximately negative 3.7126%. Substituting that factor back into the equation reproduces the $18,900 ending value, subject to rounding.

Why is this more negative than the annualized time-weighted result? The account had $21,000 exposed during the losing year, versus $10,000 at the start of the winning year. More dollars experienced the decline. The difference does not prove that either report is wrong, nor does it isolate investment selection skill from the investor's funding decisions.

In a spreadsheet using equally spaced annual periods, the investor-perspective cash-flow sequence is negative $10,000, negative $10,000, then positive $18,900. Contributions are outflows from the investor; the terminal value is treated as a hypothetical liquidation inflow. For irregular dates, use a dated cash-flow method and inspect its annualization convention rather than pretending every interval is one year. Preserve the actual dates alongside the amounts.

Reverse the path to test your explanation

Run a second hypothetical case with the same starting $10,000 and another $10,000 contributed after the first year. This time the portfolio loses 10% first, reaching $9,000. The contribution increases it to $19,000, and a subsequent 10% gain brings it to $20,900.

The time-weighted result remains negative 1%, because 0.90 × 1.10 is still 0.99. Yet the investor now has a $900 gain over the $20,000 contributed. Solving $10,000 × x² + $10,000 × x = $20,900 gives x = (√9.36 − 1) / 2, approximately 1.029706. The annual money-weighted return is about positive 2.9706%.

Both examples have the same two investment returns and the same scheduled contribution amounts. What changes is which return happens when more capital is invested. This is a diagnostic exercise, not evidence that an investor could forecast the better sequence. Use it to check your interpretation of a performance report, not to invent a market-timing rule from two imagined years.

Keep the measurement boundary consistent

Write down exactly what the account includes. If it includes securities and its cash balance, selling a holding and leaving the proceeds inside that account changes the composition rather than adding outside money. A transfer from a separate bank account crosses the measurement boundary. A dividend retained within the measured account belongs in its investment result; do not also classify the same cash as a new personal contribution.

The boundary matters when aggregating accounts. A transfer from Account A to Account B is external to each account viewed separately but internal to a combined A-plus-B portfolio. Mark both sides with a matching transfer identifier so consolidation does not manufacture a deposit or withdrawal. Keep the original records even when the combined report nets the movement to zero.

Fees require equal care. The SEC's investor bulletin explains that expenses reduce both portfolio value and the capital left earning returns. Decide whether the report is before or after specified fees and make that label visible. An expense paid from inside the account should not be silently reclassified as a personal withdrawal to make a net-of-fee return look stronger.

For a small hypothetical fee check, start with $1,000, earn $100, and deduct a $10 fee at the period's end. The ending $1,090 implies a 9% net return, compared with 10% before that fee. If the quoted ending value already includes the deduction, subtracting $10 again double counts it. This simplified timing assumption is explicit; actual charges may occur throughout the period.

Build a report another reader can reproduce

Use a ledger with one row per valuation or external flow. Include the date, event description, amount, whether it crosses your chosen boundary, and the account value immediately before and after a contribution or withdrawal when available. Keep supporting statements or exported records attached to the rows. Missing valuations should remain marked as missing; a monthly closing balance cannot establish an exact intramonth path.

Then present four outputs together: opening and closing values, net external contributions, the dollar investment result, and the named return measure with its period. For the first example, the compact report reads: opening $10,000; closing $18,900; deposits $10,000; investment loss $1,100; cumulative time-weighted return negative 1%; annual money-weighted return approximately negative 3.7126%.

When comparing a benchmark, match dates, currency, income treatment and fee basis. Do not compare a cumulative account number with an annual benchmark number just because both carry a percent sign. Finally, write one sentence explaining the difference between saving and investment performance. A reproducible report helps assess the history; it cannot establish that the same return will recur or tell you which security to purchase next.