STAT2032 Chap.5 Investment Performance
Investment Performance
A fund history can support different return measures because external cash flows change whose experience is being measured. Money-weighted return solves one equation of value using the dates and sizes of contributions and withdrawals, so it reflects the investor's exposure.
Time-weighted return splits the record whenever new money crosses the boundary, calculates clean segment growth and links the factors, so it isolates the investment manager's path. The chapter concentrates on classifying flows correctly, avoiding double counting of income already inside fund values, and explaining why both answers can be valid.
Classification comes first.
A contribution or withdrawal crosses the boundary between investor and fund and changes capital under management. Interest, dividends and price movements that remain inside the portfolio are already embedded in the observed fund value. Entering them again as external flows counts them twice.
A chronology should therefore record value immediately before each external flow, the amount crossing the boundary and value immediately after it. Those two sides close one time-weighted segment and open the next.
MWRR weights market experience by the amount of money exposed at each date.
A large contribution before a strong return gives that interval more influence; the same contribution after the rise cannot benefit from it. TWRR removes this timing effect by multiplying clean segment factors. Neither measure is universally superior. MWRR answers what the dated investor cash flows earned, while TWRR answers how the underlying fund path compounded independently of external timing.
When no external flow occurs, both collapse to the same opening-to-closing return, which is a useful boundary check.
What this chapter covers
- 01
External and internal cash flows
- 02
Money-weighted return equations
- 03
Time-weighted segment returns
- 04
Linking growth factors
- 05
Investor and manager perspectives
- 06
Income and cash-flow classification
Worked example · free
Measure one fund path in two ways
- 1The first clean segment return is 10600/10000 - 1 = 6%.
- 1Immediately after the contribution, the second segment begins at $12,600.
- 1The second segment return is 13800/12600 - 1 = 9.5238%.
- 1Link the factors: 1.06 times 1.095238 minus one = 16.0952%.
- 2For MWRR, solve 10000(1+i) + 2000(1+i)^(1/2) = 13800.
Key terms
- External cash flow
- Money contributed to or withdrawn from the fund across the measurement boundary by the investor.
- Money-weighted return
- The yield solving an equation of value for the investor's dated contributions, withdrawals and ending value.
- Time-weighted return
- The linked growth rate across subperiods separated at external cash-flow dates.
- Linking factor
- The product of one plus each clean subperiod return before subtracting one for the total return.
Investment Performance FAQ
Which return measures manager performance?
Time-weighted return is designed to remove the effect of external contributions and withdrawals that the manager does not control. It splits the measurement period at those flows and links the clean growth factors. Money-weighted return can still be the right measure for the investor, because it reflects how much money was exposed during each part of the path.
Why must the record be split at an external flow?
Without a split, the contribution or withdrawal would be mixed with investment gain and distort the growth rate. Value the segment ending immediately before the flow, adjust the fund for the external amount, and begin the next segment immediately after it. The flow changes capital under management, not the return earned inside either clean segment.
Do dividends count as external cash flows?
It depends on whether they cross the measurement boundary. Dividends retained inside the fund are already included in the observed fund value and should not be entered again. A distribution paid out to the investor crosses the boundary and belongs in the investor's dated cash flows. State the treatment rather than assuming from the word dividend alone.
When will the two return measures agree?
They agree when external-flow timing has no weighting effect, including the simple case with no contributions or withdrawals during the measurement interval. They may also coincide by numerical chance. Agreement does not make the definitions identical, so the answer should still identify whether the purpose is investor experience or underlying fund performance.
Exam move
Take a fund chronology and label every event as external contribution, external withdrawal or internal investment movement before calculating anything. Build the time-weighted solution as a sequence of segment opening values, closing values and growth factors. Then write the money-weighted equation from the investor's perspective with a consistent sign convention and fractional exponents for dates.
Compare the answers by changing only the timing of a contribution; TWRR should preserve the underlying path, while MWRR changes because capital was exposed differently. Practise explaining the purpose of each measure in one sentence. Inspect dividend and fee language carefully to decide whether the amount is already reflected in fund values or crosses the investor boundary.
The most important check is conceptual: new money must not be counted as investment gain.
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