CFA Program Level I

Money-weighted vs time-weighted return: CFA Level I explained

A time-weighted return links the returns of the sub-periods between external cash flows, so it removes the effect of when the client added or withdrew money. A money-weighted return is the internal rate of return of all the cash flows, so it reflects their timing and size. Use time-weighted to judge a manager who does not control the cash flows.

The two definitions

The GIPS standards define a time-weighted return as a method of calculating period-by-period returns that reflects the change in value and negates the effects of external cash flows. A money-weighted return reflects the change in value and the timing and size of external cash flows.

An external cash flow is capital that enters or leaves the portfolio. Dividend and interest income are not external cash flows.

To compute a time-weighted return, value the portfolio just before each external cash flow, compute each sub-period's return, then link them: (1 + R1)(1 + R2)...(1 + Rn) - 1. To compute a money-weighted return, find the discount rate at which the present value of all cash flows, including the ending value, is zero. That is the internal rate of return.

Worked example

A client invests 100,000 at the start of year 1. At the end of year 1 the portfolio is worth 110,000, and the client then adds 100,000, making 210,000. During year 2 the portfolio falls 5% to 199,500.

Time-weighted: year 1 return = 110,000 / 100,000 - 1 = 10%. Year 2 return = 199,500 / 210,000 - 1 = -5%. Linked two-year return = 1.10 x 0.95 - 1 = 4.5%. Annualized: 1.045^0.5 - 1 = 2.23% a year.

Money-weighted: solve 100,000(1 + r)^2 + 100,000(1 + r) = 199,500. With x = 1 + r, x^2 + x - 1.995 = 0, so x = (-1 + √8.98) / 2 = 0.99833 and r = -0.17% a year. Check: 100,000 x 0.99833^2 + 100,000 x 0.99833 = 199,500.

The manager earned positive returns in a time-weighted sense, but the client's money-weighted return is slightly negative, because the larger amount was invested in the year the portfolio fell. The client chose that timing, so the time-weighted figure is the fair measure of the manager.

What the GIPS standards require

The GIPS standards are voluntary ethical standards for presenting investment performance, based on fair representation and full disclosure. A firm that claims compliance must apply them firm-wide.

A firm must present time-weighted returns unless it controls the external cash flows into the portfolios and the composite or pooled fund is closed-end, fixed-life, fixed-commitment, or holds illiquid investments as a significant part of its strategy. Only then may it present money-weighted returns.

For time-weighted returns, portfolios must be valued at least monthly and on the date of every large cash flow, which each firm defines per composite. Periodic and sub-period returns are linked geometrically. Money-weighted returns must be annualized since inception and use daily external cash flows.

Where the exam catches people

Believing the money-weighted return is better for judging a manager: it includes the client's timing decisions, so the time-weighted return is used when the client controls cash flows.
Believing a time-weighted return averages the sub-period returns: it links them geometrically, (1 + R1)(1 + R2) - 1.
Believing dividends received are external cash flows: under the GIPS standards, dividend and interest income are not external cash flows.
Believing GIPS firms may choose money-weighted returns freely: they must present time-weighted returns unless they control the cash flows and the fund meets one of the listed characteristics.
Believing the two measures always agree: they match only when there are no external cash flows during the period.

Written from CFA Institute's documentation

2020 GIPS Standards for Firms (CFA Institute, PDF)

Try 3 questions on this

Pick an answer to see why each option is right or wrong.

Dana Kowal invests USD10,000 in a fund at the start of year 1. At the end of year 1 her account is worth USD12,000, and she then adds USD10,000. At the end of year 2 the account is worth USD21,525. Her annual money-weighted rate of return is closest to:
Right. In the game that’s Renown for your Quantitative Methods building.
Not that one: A is right. In the game your Quantitative Methods building would lose a little Renown, and this question would come back later.
The answerA.5.00%A money-weighted return is the internal rate of return: the rate r at which the net present value of the cash flows is zero. Cash flows: −10,000 at time 0, −10,000 at time 1, +21,525 at time 2.Your answerB.8.36%8.36% links the two yearly returns geometrically, which is a time-weighted return and removes the effect of the USD10,000 addition. The money-weighted return reflects that the larger balance earned the year-2 loss, so it is lower, at 5.00%.Your answerC.8.92%8.92% is the simple average of +20.00% and −2.16%. A money-weighted return is the single rate that sets the NPV of all the cash flows to zero, 5.00% here.
Show the full explanation and doc quotes
At r = 5%: 10,000 × 1.05² + 10,000 × 1.05 = 11,025 + 10,500 = 21,525, so the NPV is zero and the money-weighted return is 5.00%.
Written from www.gipsstandards.org/standards/gips-standards-for-firms/gips-standards-handbook-for-firms/
A portfolio managed by Westbury Capital is worth USD50.0 million at the start of a year. On 30 June it is worth USD55.0 million just before the client adds USD5.0 million. At year end it is worth USD57.0 million. The portfolio's time-weighted return for the year is closest to:
Right. In the game that’s Renown for your Quantitative Methods building.
Not that one: A is right. In the game your Quantitative Methods building would lose a little Renown, and this question would come back later.
The answerA.4.50%The contribution is a large external cash flow, so the year splits into two sub-periods. First half: 55.0 / 50.0 − 1 = 10.00%. The second half starts at 55.0 + 5.0 = 60.0, so its return is 57.0 / 60.0 − 1 = −5.00%.Your answerB.5.00%5.00% is 10.00% + (−5.00%). Sub-period returns compound: the second-half loss applies to a value that already includes the first-half gain, so the returns are multiplied as (1.10)(0.95) − 1, giving 4.50%.Your answerC.14.00%14.00% is 57.0 / 50.0 − 1, which treats the client's USD5.0 million deposit as if the manager had earned it. A time-weighted return removes the effect of external cash flows.
Show the full explanation and doc quotes
Linking geometrically: (1 + 0.10) × (1 − 0.05) − 1 = 1.045 − 1 = 4.50%.
Written from www.gipsstandards.org/wp-content/uploads/2021/03/2020_gips_standards_firms.pdf
A client of Harrow Asset Management decides alone when to add money to or take money out of her equity portfolio, and she made a large addition just before a market fall. The firm wants a return measure that reflects the manager's investment decisions over the year. Which measure is most appropriate?
Right. In the game that’s Renown for your Quantitative Methods building.
Not that one: C is right. In the game your Quantitative Methods building would lose a little Renown, and this question would come back later.
Your answerA.Time-weighted return, because it counts dividend income as an external cash flowDividend and interest income are not external cash flows under the GIPS glossary; external cash flows are capital entering or leaving the portfolio. The time-weighted return is right here because it neutralises the client's additions and withdrawals.Your answerB.Money-weighted return, because it reflects the timing and size of the client's cash flowsThe money-weighted return reflects when and how much money the client added or removed. Her large addition just before the fall would lower the figure for reasons outside the manager's control.The answerC.Time-weighted return, because it removes the effect of the client's cash flowsA time-weighted return measures period-by-period changes in value while stripping out the effect of external cash flows. The client, not the manager, chose when money came in, so a measure of the manager's decisions should exclude that timing.
Show the full explanation and doc quotes
The money-weighted return builds the timing and size of those flows into the result.
Written from www.gipsstandards.org/wp-content/uploads/2021/03/2020_gips_standards_firms.pdf