Ch 15 - Performance Measurement (1) Flashcards
When calculating rates of return, take extra care with:
The timing and size of all cashflows
Differentiating between investment income and new money
Tax and expenses
Merits of the money-weighted rate of return
Useful as an absolute measure of the achieved return (positive)
Affected by the timing and size of cashflows (negative) - Thus, not a good basis for comparing two different fund managers
Money-weighted rate of return - may be alright to compare two different fund managers if either of the following conditions hold:
No large cashflows (relative to the funds involved) in the valuation period
No great fluctuations in market values during the period (or rate of return is stable over the period)
TWRR and MWRR are similar when:
No large cashflows (relative to the funds involved) in the valuation period
No great fluctuations in market values during the period (or rate of return is stable over the period)
Merits of time-weighted rate of return
Not affected by the size or timing of cashflows - Therefore, can use as a basis for comparing different investment managers
Does not give the rate actually achieved
Impractical (think why for short answers like this)
Practical solution is to use the linked internal rate of return as an approximation for the TWRR. Conditions needed for the approximation to be good:
Rate of return is stable over each inter-valuation period
Small cashflows between periods relative to the size of the fund
Note:
LIRR and TWRR will be exact if the valuations occur on the same date as the cashflows!
Merits of the Linked Internal Rate of Return
Practical approximation for the TWRR
Does not give the rate of return actually earned on the assets over the period
Linked Internal Rate of Return
Determine the value of the fund at various dates throughout the year (e.g. monthly or quarterly intervals)
For each inter-valuation period, calculate the MWRR
Link the inter-valuation MWRRs together to get the LIRR for the year
Two basic ways in which to compare the performance of a portfolio with an index:
Compare the actual value of the portfolio with what would have been achieved had the money been invested in the same way in an index (gives us the notional value of the fund)
Comparing the TWRR from each (or the LIRR) OR EVEN IRR
Time-weighted rate of return formula
(1+i)^T = V(t1)/V(0) * V(t2)/[V(t1)+C(t1)] …V(T)/[Vtn)+C(tn)]
Money-weighted rate of return formula
V(0)(1+i)^T + sum(C(t)(1+i)^(T-t)) = V(T)
Treynor measure
[R(p) - r]/ beta(p)
Sharpe measure
[R(p) - r] / sigma(p)
Jensen measure
R(p) - R(b)
Where R(b) = r + beta(p)[R(m) - r] (the expected return on the benchmark)
Pre-specified standard deviation
R(p) - R(b)
Where R(b) = r + [R(m)-r]/(sigma(m) * sigma(p))
Beta formula
B = COV(Return on stock, Return on market) / Variance(Market return)
Where covariance = correlation coefficient * sigma(x) * sigma (market)
The main uses of performance measurement are to:
Improve future performance
Compare actual performance against target rates
Compare actual performance against a benchmark portfolio, index or other portfolios
Appraise and remunerate investment managers
The limitations of performance measurement include:
The past may be a poor guide for the future
Difficulty of allowing for risk
Possibility of spurious and/or misleading results if invalid comparisons are made or time periods that are too short are considered
Different funds may have differing objectives and constraints
Measurement may influence the actions of fund managers in ways that are inconsistent with the fund’s long-term objectives
It adds to the cost of investment
Merits of assessing a portfolio against an index
Easy to do
Data is readily available and is accurate
Published index may not be appropriate - Index is not consistent with the objectives (and constraints) of the investor
Merits of assessing a portfolio against other portfolios
Is appropriate if the funds being considered have the same objectives and the same factors influencing investment strategy
In practice there may be very few other funds that can be used for a valid comparison
Data from other funds may not be easily available
Overall, performance measurement relative to other portfolios is not ideal
Merits of assessing a portfolio against a benchmark portfolio
Can be constructed to reflect the objectives of the fund
Should also be constructed in such a way that the data necessary for comparisons is easily obtainable
By having a benchmark portfolio that reflects the liabilities of the fund, the danger of giving the fund manager conflicting objectives is also avoided
e.g. assessment encourages the fund manager to adopt a strategy that is not consistent with the objectives of the fund
