Two Returns From the Same Investment

Time-weighted return measures how an investment performed over a period while removing the effect of money added or withdrawn, so it shows how well the portfolio or manager did. Dollar-weighted return, also called money-weighted return, takes the timing and size of cash flows into account, so it shows how well the investor actually did with the money they put in.

The two can differ sharply. An investor who adds money just before a fall and stops adding before a rise can earn a much lower dollar-weighted return than the fund’s time-weighted return, even though they held the same fund.

Fund managers are judged on time-weighted return because they do not control when clients add or withdraw money. Investors care about dollar-weighted return because it reflects what happened to their own money. For the full route from the exam to a career explaining these results to clients, our complete guide to how to become an investment adviser representative covers every step.

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The Starting Point: Holding Period Return

Both measures build on the holding period return, the simplest measure of performance. It equals the ending value minus the beginning value, plus any income received, all divided by the beginning value.

A share bought for $50 that pays a $2 dividend and is sold for $55 has a holding period return of 55 minus 50 plus 2, divided by 50, or 14 percent. This works well for a single investment with no money added or withdrawn.

Once cash flows happen in the middle of a period, a single holding period return no longer tells the whole story. The Series 65 Exam Preparation course at FRC covers holding period, time-weighted and dollar-weighted returns together, because the exam often asks which one fits a given situation.

How Time-Weighted Return Works

Time-weighted return splits the overall period into sub-periods at each cash flow and calculates the return for each sub-period separately. The sub-period returns are then linked together by multiplying one plus each return and subtracting one.

Because each sub-period return is calculated before new money arrives or after money leaves, the size of the account at any moment has no effect on the result. Each period counts equally, regardless of how much money was invested during it.

For a period longer than a year, the linked return is usually annualised by taking the appropriate root. This produces a geometric average return, which is the standard way funds and managers report performance.

How Dollar-Weighted Return Works

Dollar-weighted return is the internal rate of return of all the investor’s cash flows. It is the single rate that makes the present value of all money invested equal to the present value of all money taken out, including the final value of the account.

Because it is calculated from the investor’s actual cash flows, periods when more money was invested have a bigger effect on the result. Good returns earned on a large balance raise the dollar-weighted return more than the same returns earned on a small balance.

Dollar-weighted return is therefore a measure of the investor’s experience. It combines the performance of the investments with the effect of the investor’s own decisions about when to add or withdraw money.

Time-Weighted and Dollar-Weighted Return Compared

Worked Example: Poor Timing

An investor buys one share of a fund for $100. A year later the share is worth $120, and she buys a second share; at the end of the second year, the share price has fallen to $108.

Step one: the time-weighted return links a 20 percent gain in year one with a 10 percent loss in year two, so 1.20 times 0.90 is 1.08, an 8 percent cumulative return or about 3.9 percent a year. Step two: for the dollar-weighted return, she invested $100 and then $120 and ended with two shares worth $216, so her cash flows are minus 100, minus 120 and plus 216.

Step three: the internal rate of return of those cash flows is about minus 1.3 percent a year. The fund earned a positive return, but she lost money, because she invested more just before the fall.

Worked Example: Good Timing

A second investor buys one share for $100. A year later the price has fallen to $80 and he buys another share; by the end of the second year the price has risen to $104.

Step one: the time-weighted return links a 20 percent loss with a 30 percent gain, so 0.80 times 1.30 is 1.04, about 2.0 percent a year. Step two: his cash flows are minus 100, minus 80 and plus 208 for the two shares.

Step three: the dollar-weighted return is about 9.7 percent a year, far higher than the time-weighted return. Buying more when the price was low raised his personal return well above the fund’s.

Study Performance Measurement With FRC

Performance questions on the exam test both the calculations and the judgment of which measure fits the situation. Our Series 65 course explains each return measure with worked examples and links them to the risk-adjusted measures advisers use every day.

Consider studying with FRC for every exam on your route. Explore our USA exam courses, from the SIE through the Series 7, Series 63 and Series 65.

To take advantage of the membership, explore FRC Professional Membership, which gives you a verified Digital Profile that shows employers your real-time course progress, together with the Video Resume. Current offers are on our membership deals page.

Arithmetic and Geometric Averages

When returns over several periods are averaged, the method matters. The arithmetic average simply adds the returns and divides by the number of periods, while the geometric average reflects compounding and shows the actual rate at which money grew.

Worked example: a fund gains 50 percent in year one and loses 50 percent in year two. Step one: the arithmetic average is 50 plus minus 50, divided by 2, or 0 percent. Step two: $100 grows to $150 and then falls to $75, so the geometric average is the square root of 0.75 minus 1, or about minus 13.4 percent a year.

The geometric average is always lower than or equal to the arithmetic average, and the gap widens as volatility rises. Time-weighted returns use geometric linking, which is why they describe what really happened to each dollar invested from start to finish.

Worked Example: A Withdrawal Halfway Through the Year

A client starts the year with $100,000. The portfolio gains 10 percent in the first six months, reaching $110,000, and the client then withdraws $50,000, leaving $60,000; in the second half, the portfolio falls 20 percent to $48,000.

Step one: the time-weighted return links the two halves, 1.10 times 0.80, giving 0.88, a loss of 12 percent for the year. Step two: the dollar-weighted return uses the cash flows of minus $100,000 at the start, plus $50,000 at mid-year and plus $48,000 at the end, and the rate that balances them is about minus 2.7 percent.

Step three: the client’s own result was much better than the portfolio’s, because half the money was taken out before the loss. The portfolio’s manager is still judged on the 12 percent loss, because the timing of the withdrawal was the client’s decision, not the manager’s.

Estimating Dollar-Weighted Return Without Software

Calculating an internal rate of return by hand requires trial and error, so practitioners often use an approximation called the Modified Dietz method. It divides the investment gain by the average capital invested, weighting each cash flow by how long it was in the account.

Using the withdrawal example, the gain is the ending value of $48,000, minus the starting value of $100,000, plus the $50,000 withdrawn, which equals minus $2,000. The average capital is $100,000 minus half of the $50,000 withdrawal, or $75,000, so the estimate is minus $2,000 divided by $75,000, or about minus 2.7 percent, very close to the exact answer.

On the exam, you are more likely to be asked which measure applies than to calculate an internal rate of return. Knowing that dollar-weighted return responds to the size and timing of cash flows is usually enough.

Why Managers Are Judged on Time-Weighted Return

A fund manager cannot control when investors buy or sell fund shares. If managers were judged on dollar-weighted returns, a manager could look skilful or poor simply because of when clients happened to add money.

For this reason, the Global Investment Performance Standards, a voluntary framework widely used by investment firms, require time-weighted returns for most portfolios. Fund performance in prospectuses and factsheets is also presented on a time-weighted basis, which allows funds to be compared fairly.

Time-weighted returns are also the starting point for the risk-adjusted measures used to judge managers. Our comparison of Sharpe ratio vs Treynor ratio shows how those returns are adjusted for risk, and our article on alpha vs beta shows how they are compared with what the market risk would predict.

Why Investors Should Also Look at Dollar-Weighted Return

For an individual client, dollar-weighted return answers the question that matters most: how much did my money actually earn? It reflects regular contributions, lump-sum additions, withdrawals and the effect of buying or selling at the wrong time.

Studies of fund investors have repeatedly found that average investor returns trail the funds they own, because money tends to flow in after strong performance and out after losses. The gap between a fund’s time-weighted return and its investors’ dollar-weighted return is sometimes called the behaviour gap.

Advisers can help close that gap. Encouraging steady contributions, rebalancing rather than chasing performance and avoiding panic selling during downturns can make a larger difference to a client’s dollar-weighted return than choosing a slightly better fund.

Performance Reporting Rules for Advisers

Investment advisers who advertise performance must follow the SEC’s marketing rule. Among other requirements, an adviser that shows gross performance must also show net performance after fees with equal prominence, and performance for portfolios must generally cover one, five and ten-year periods, or the period since inception if shorter.

Advisers must also avoid presenting performance in a way that is misleading, such as cherry-picking favourable periods or showing results for only the best-performing accounts. State regulators apply similar standards to state-registered advisers.

Clear client reports often show both measures. The time-weighted return shows how the strategy performed, and the dollar-weighted return shows how the client’s own account grew, helping the client see the effect of their contributions and withdrawals.

The Memory Aid

Remember “time judges the manager, dollars judge the investor”: time-weighted return measures the portfolio’s performance, dollar-weighted return measures the investor’s experience.

For the calculations, remember “link the periods” for time-weighted return and “find the IRR” for dollar-weighted return.

For timing, remember “more money before gains lifts dollars, not time”: good timing raises dollar-weighted return but leaves time-weighted return unchanged.

Exam Traps to Avoid

The first trap is using dollar-weighted return to judge a fund manager. Managers do not control client cash flows, so time-weighted return is the right measure.

The second trap is assuming the two measures must be close. They can differ widely, and can even have opposite signs, when large cash flows happen before big market moves.

The third trap is averaging returns arithmetically to describe growth over time. The geometric average, used in time-weighted returns, reflects compounding. The fourth trap is forgetting that dollar-weighted return is the internal rate of return of the investor’s cash flows.

A Client Scenario

A client is disappointed that her account grew by much less than the 9 percent a year her fund’s factsheet shows for the past five years. Over that period she invested a large lump sum near a market peak, then sold part of her holding during a sharp fall and reinvested after the market had already recovered.

The adviser explains that the factsheet shows the fund’s time-weighted return, which ignores when she added or withdrew money. Her dollar-weighted return, calculated from her actual cash flows, is about 4 percent a year, and the difference comes mainly from the timing of her purchases and sales.

The adviser recommends investing future savings monthly through automatic contributions and agreeing a rebalancing plan in advance, so that market swings do not drive decisions. The discussion and the plan are documented in the client’s file.

The Dictionary as a Video Library

The FRC dictionary is a study tool, not just a glossary. Every entry pairs a written explanation with deep-dive video, on-page quizzes and interactive flash cards, so you can read a concept, watch it explained and test yourself in one place.

Rules are covered in the same depth: open a rule and you will find the full explanation alongside video walk-throughs of how it applies in practice. Use the dictionary to explore the performance and risk terms in this article as their own explanations, videos and quizzes.

Practice Questions to Test Yourself

Question one: Which return measure removes the effect of deposits and withdrawals? Time-weighted return.

Question two: A share bought for $40 pays a $1 dividend and is sold for $45. What is the holding period return? 15 percent, because 45 minus 40 plus 1, divided by 40, is 0.15.

Question three: An investor adds a large sum just before a strong rally. Which return will be higher for that period, time-weighted or dollar-weighted? Dollar-weighted, because more money was invested during the strong period.

Question four: A fund returns plus 25 percent and then minus 20 percent. What is its geometric average annual return? 0 percent, because 1.25 times 0.80 equals 1.00.

Question five: Which measure do the Global Investment Performance Standards require for most portfolios? Time-weighted return.

Turn Analytical Skill Into Career Evidence

Explaining why a client’s result differs from a fund’s published return is one of the most common and important conversations in advice. FRC’s Digital Profile shows employers the courses you are actively studying and the progress you have earned through assessed learning, verified by FRC, and a QR code on your resume takes them straight to it.

The FRC Video Resume lets a hiring manager hear you before the interview. Walking through the difference between time-weighted and dollar-weighted returns shows the clarity that client-facing roles demand.

Related Questions

Regular payroll contributions are one of the simplest ways to smooth the timing of cash flows, as explained in What Is a 401(k)?. For how much a portfolio’s returns typically vary from year to year, see Standard Deviation vs Beta.

Key Points to Retain

Time-weighted return links the returns of each sub-period between cash flows, removing the effect of deposits and withdrawals, and is the standard measure of a portfolio or manager’s performance. Dollar-weighted return is the internal rate of return of the investor’s actual cash flows, reflecting both the investments’ performance and the timing of the investor’s decisions.

The two can differ widely, and good timing raises dollar-weighted return while poor timing lowers it. Geometric averages reflect compounding and are used in time-weighted returns, and advisers presenting performance must follow the SEC’s marketing rule, including showing net performance after fees.

For the role the exam leads to, read our guide to what an investment advisor representative is.