performance measurement Flashcards
1 Comparison between different methods of calculating return
1.1 The money-weighted rate of return (MWRR)
1.2 Time-weighted rate of return (TWRR)
. 1.4 Linked internal rate of return (LIRR)
The LIRR for a fund over a given year is found using the following process:
The money-weighted rate of return (MWRR)
The money-weighted rate of return (MWRR) is useful as an absolute measure of the achieved return. It can be compared with the actuarial assumptions underlying the fund to see whether the achieved return is higher or lower than that expected.
The standard formula for calculating the MWRR is:
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Cashflow v investment income
Cashflow in the above formula represents the excess of contributions received over claims and expenses paid. It is the money moving into (or out of) the fund.
Tax and expenses
For rates of return net of tax and expenses, VT and all disinvestments should be net of tax and expenses.
Basic problem with the MWRR
The money-weighted rate of return is not a good basis for comparing two different fund managers. The main reason for this is that the rate of return can be heavily influenced by the timing and size of cashflows. The payments into and out of a particular fund are not usually within the control of the investment manager, so rates of return influenced by cashflows are not very useful when comparing investment managers.
Fund Managers A and B are both given 10 million to invest. Both managers invest the whole 10 million in equities. Over the next six months the equity market is very sluggish, and the funds for both managers are still standing at 10 million. (There are no contributions to and no payments from either fund during the first six months. )
Then Manager A is asked to return 5 million to the trustees of the fund who need to make a large payment out. Meanwhile Manager B is given another 5 million to invest because the trustees of Fund B happen to have received a large payment into the fund. In the next six months, there is a strong bull market in equities and both Managers achieve a 50% return on their equity investments over the six-month period.
Calculate the annual money-weighted rate of return for each manager over the year described above. Comment on the results.
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Will money-weighted returns always give figures that are unsuitable for comparing different fund managers? Under what circumstances is the money-weighted rate of return least appropriate for comparison purposes?
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Time-weighted rate of return (TWRR)
The time-weighted rate of return overcomes the basic problem associated with money-weighted rates of return. Theoretically, it is usable as a basis for comparing different investment managers because the timing and size of cashflows will not distort the rates calculated.
It is calculated by
1. assessing the fund value at each time there is a cashflow in or out
2. calculating the return achieved for each period between cashflows
3. linking these returns together to give the time-weighted rate of return.
Note that the amount of money invested at each time will not affect the result.
Give a formula for the TWRR.
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Comparison of time-weighted return and money-weighted returns
The time-weighted rate of return and the money-weighted rate of return will be very similar when either the:
cashflows during the valuation period are small relative to the funds involved or
the rate of return is stable over the period.
When neither of these conditions hold, the two rates of return can be very different.
Impracticality of time-weighted rate of return
The problem with using the time-weighted rate of return in practice is the amount of data that is required: fund values are needed for every occasion on which there is a cashflow. This is often impracticable in practice. A practical compromise solution is to use the linked internal rate of return as an approximation for the time-weighted rate of return; this is often done using quarterly sub-intervals.
Linked internal rate of return (LIRR)
The LIRR for a fund over a given year is found using the following process:
1. Determine the value of the fund at various dates throughout the year (eg at monthly or quarterly intervals). 2. For each inter-valuation period, calculate the money-weighted rate of return. 3. Link the inter-valuation MWRRs together to get the linked internal rate of return for the year.
Under what conditions will the linked internal rate of return provide a very good approximation for the time-weighted rate of return?
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For each of the money-weighted rate of return, time-weighted rate of return and linked internal rate of return give one sentence summarising the main use and one sentence summarising the main weakness.
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How to do the assessment Comparison of portfolio performance with an index two basic ways in which to compare the performance of a portfolio with an index:
There are two basic ways in which to compare the performance of a portfolio with an index:
1. By comparing the actual value of the portfolio at the end of a defined period with the value that would have been achieved had the initial value of the portfolio and subsequent net new money been invested in the same way as the index.
2. By comparing the time-weighted return from each (or the linked internal rate of return as an approximation to the time-weighted rate of return).
In practice the method chosen and the type of return calculated will depend partly on the data available.