Chapter 16: Performance measurement (1) Flashcards
n) investment pf performance & the limitations of such pf measurement
State:
- the standard formula for calculating the MWRR
- The main advantage and disadvantages of using it to assess the investment manager’s performance
- And when it is a appropriate basis for comparison
Methods of calculating return
Formula:
v(0)(1+i) ^(1+T)+ sum_t(CF(t)(1+i)^(T-t) = v(T)
where:
- v(0) and v(T) are the market values of the fund at the beginning and end of period
- i is the MRR
- T is the valuation date
- CF(t) are net cash inflows at time t (excludes investment proceeds)
Advantages:
+ Represents the actual return achieved by fund
+ can be compared with actuarial assumptions to see if return achieved is higher or lower
disdvantages:
- depends on timing adn amounts of net cashflows into fund…
-if these are outside the manager’s control, then unfair to compare performance based on MWRR against other managers.
Appropriate when:
- no large CF in the valuation period
- rates of return during the period remain stable (ie.g., there are not great fluctuations in market values in the period)
n) investment pf performance & the limitations of such pf measurement
State:
- the standard formula for calculating the TWRR
- The main advantage and disadvantages of using it to assess the investment manager’s performance
- When will the MWRR and TWRR be similar
Methods of calculating return
Formula:
(1+i)^T = v(t1)/V(0) x v(t2)/v(t1) + CF(t1) x v(T)/v(tn) + CF(tn)
where:
- v(0) and v(T) are the market values of the fund at the beginning and end of period
- v(ti) is the market value of the fund just before a CF at time ti
- i is the MRR
- T is the valuation date
- CF(t) are net cash inflows at time ti (excludes investment proceeds)
Advantages:
+ it is not affect by the timing and size of net cashflows into the fund
disdvantages:
- requires knowledge of fund value at date of each cashflow
- does not give the actual return
similar when:
- CFs during the period are relatively small to funds involved
- rates of return during the period remain stable (ie.g., there are not great fluctuations in market values in the period)
n) investment pf performance & the limitations of such pf measurement
Explain how the linked internal rate of return (LIRR) is calculated.
List the circumstances under which it will give a close approximation to the TWRR.
Methods of calculating return
LIRR:
- determine the fund value at various dates throughout the year
- calculate the internal rate of return for eachh inter-valuation period.
- linking inter-valuation rates of return to get linked internal rate of return.
Close approximation when:
- short inter-valuation periods are used, or
- valuations occur close to dates of cashflows, or
- CF are small relative to size of the fund, or
- rate of return is very stablee over each inter-valuation period
n) investment pf performance & the limitations of such pf measurement
Give two basic ways in whch to compare the performance of a pf with an index.
Outline how the performance of a pf can be compared against a notional pf
Comparison of pf performance with an index and benchmark pf
Index
1. Compare actual value of the pf at the end of the period with the value of the index that would have been achieved if the initial value of the pf and susequent net new money where invested the same way as the index.
2. Compare TWRR return or (LIRR) from each.
Notional pf
- similar to assessing against a published index.
- Difference is that the notional pf not based on market value of index, but defined in some other, predetermined way (e.g., 50% in fixed interest index and 50% in equity index)
- need to allow carefully for net new money, income, rebalancing and tax and expenses
The meausures assume that the risk is identical between the actual pf and index or benchmark pf
n) investment pf performance & the limitations of such pf measurement
List Further information required to compare performance pf with index:
Comparison of pf performance with an index and benchmark pf
- timing and size of CF
- value of index at each CF date
- investment income that would have been earned by investing in the index
- taxation basis of the invetor –> tax that would have been incurred by investing to track index
- expenses that would have been incurred by investing in the index
- ‘riskness’ of the investment held by the investor
- appropriatness of the index
n.ii) Assess the performance of a portfolio
Explain how to split the overall performance of an investment fund into sector selection and stock selection componets.
investments sector selection and individual stock selection
- r_AA = based on the actual stocks and actual sector
- r_NN = return based on notional sectors and notional stocks
- r_AN = return based on actual sectors and notional stocks
then:
- sector selection = r_AN - r_NN
- stock selection = r_AA - r_AN
- total return = r_AA - r_NN
n.ii) Assess the performance of a portfolio
State the formulae used to estimate:
- stock selection component attributabble to equities
- sector selection component attributabble to equities
investments sector selection and individual stock selection
Stock selection to equities
w_EA x (r_EA - r_EN)
Sectorselection to equities
(w_EA - w_EN) x (r_EN - r_NN)
where:
- w_EA & w_EN are actual and notional equity weights
- r_EA & r_EN are actual and notional equity returns
- r_NN is overall fund return based on notional sectors and notional stocks
n.iv) Uses of risk-adjusted performance measures
State the formulae for the four risk-adjusted performacne measures.
Risk-adjusted performance measures
- Treynor ratio
T = (R_p - r)/ beta
- measures the reurn in excess over the risk free per unit of systematic risk
- narrow risk than Sharpe as it considers only non-diversifiable risk
- Sharpe ratio
S = (R_p - r)/s.d
- measures excess returns per unit of total risk (systematic and not systematic)
Both not useful on standalone basis and the higher the better when compare with other pfs
- Jensen (alpha)
j = R_p - [ r + Beta_p(R_m - r)]
- measure how actual return deviates from the return predicted by a benchmark model (CAPM)
- J> 0 outperforming and j<0 underpeforming the benchmark
- values can be used to rank pfs
- it is representation of the maximum an investor should pay for active management
- pre-specified standard deviation
P = R_p - [ r + (R_m - r)*s.d_p/s.d_m)
n.iv) Uses of risk-adjusted performance measures
Explain the circumstances in which the different risk-adjusted measures are appropriate.
Risk-adjusted performance measures
- Measures involving s.d are based on the capital marekt line, which applies only to efficient pfs. So, should be used only when considering entire pf.
- Measures involving beta are based on the security market line and so can be used in any circumstance, ie., entire pfs or part of the pf
- Jense and pre-specified standard deviation measures are appropriate if required level of risk is pre-specified
- Unlike the Treynor and Sharpe measures, they cannot be used to compare two managers taking different levesl of risk.
n.v) Discuss value of pf measurement and its limitations
List the four main reasons for measuring the investment performance of a pf.
Uses of performance measurement
- to improve future performance
- data collected can be used for planning future strategy
- measuring performance can incentivise managers
- measuring performance will identify strengths and weaknesses - to compare rate achieved against target rate, e.g., rate assumed in actuarial valuation, premium rates
- to compare fund’s performance against:
- other portfolios
- index and/or
- benchmark pfs - to appraise and remuerate investment managers.
n.v) Discuss value of pf measurement and its limitations
List the six main limitations and disadvatages of performance measure.
Limitations of performance measurement
- past performance may be a poor guide for future performance and may not be use to distinguish from luck.
- Difficult to allow for risk
- frequency - difficult to strike balance between assessing performance frequently enough to establish and correct problems, and avoiding spurious conclusions based on too short a measurement period.
- different funds may have different objectives and constraints (tax position), so comparison between such funds may be invalid
- impact on fund manager behaviour - for example, frequent monitoring can encourage shor-term approach to investment.
- cost of measuring performance
n.iii) assessing pf performance relative to published indices, other pfs
State the main advantage and two main disadvantages of assessing performance relative to publishsed indices.
Relative merits of different ways of assessing pfs
Advantage:
it’s relatively easy to do - by definition, data for published indices should be readily available and should be reliably accurate.
disadvantages
- available published indices may not be appropriate (no single index which is consistent with the objective)
- Can’t contribute performance to stock and sector selection (as only one sector)
n.iii) assessing pf performance relative to published indices, other pfs
Give two reaons for and against comparing investment performance relative to other pfs.
Relative merits of different ways of assessing pfs
For
1. Appropriate if fund being compared have the same objectives and factor influencing the investment stategy.
2. Gives indication of the benefit or cost of adopting particular strategy relative to that adopted by other funds.
Against
- May be in appropriate to compare performance of funds that have very different investment objectives and constraints (noting that these may not be public knowledge)
- Relevant data may not be available
n.iii) assessing pf performance relative to published indices, other pfs
State the main advantages of assessing performance relative to a benchmark pf.
Relative merits of different ways of assessing pfs
- Benchmark pf:
- Can be constructed to reflect objectives of the fund
- can be constructed in such way that data necessary for comparisons is easily obtained
- reflect liabilities of the fund avoids giving fund manager conflicting objectives. - Can attribute performance to stock slection and sector selection
