Chapter 16: Performance measurement

Question 1

State

• The standard formula for calculating the money weighted rate of return
• The main advantages and disadvantages of using it to assess the investment manager’s performance

Answer 1

V₀(1+i)^T+Σ(1+i)^{T - t} = VT

• V₀, VT are market values of fund at beginning and end of period
• Ct is net cashflow into fund (excluding investmetn proceeds) at time t i is money weighted rate of return
• i is money weighted rate of return

+ Represents actual rate of return earned by the fund and so can be compared with actuarial assumptions

• Depends on timing and amounts of net cashflows into funds. If these outside manager’s control, then unfair to compare performance based on MWRR against other managers

Question 2

State a formula for the time weighted rate of return

State the main advantages and 2 disadvantages of TWRR

Answer 2

Question 3

Explain how the linked internal rate of return (LIRR) is calculated

List the circumstances under which it will give a close approxiation to the TWRR

Answer 3

Calculated by

• Determining fund at various dates throughout year
• calculating internal rate of return for each intervaluation period
• linking inter - valuation rates of return to get linked internal rate of return

Get close approximatioin to TWRR if

• Short intervaluation periods are used or
• Valuations occur close to dates of casfhlows or
• Cashflows are sall relative to size of the fund or
• Rate of return is very stable over each intervaluation period

Question 4

Give the two basic ways in which to compare the performance of a portfolio with an index

Outline how the performance of a portfolio can be compared against a notional fund

Answer 4

Two basic ways to compare performance of portfolio with index

• Compare actual value of portfolio at end of period with that would have achieved had inital value of portfolio and subsequent net new money been invested in same way as index
• Compare the time weighted return or (LIRR) from eah

High performance of portfolio can be compared against notional fund

• SImilar to assessing against a published index
• Difference is notional fund not based on particular market index, but definied in some other, predermined way
• need ot allow carefully for income, net new money, rebalancing, tax and expense

Question 5

Explain how to split the overall outperformance of an investment fund into sector selection and stock selection components

Answer 5

Sector selection and stock selection components

• r_AA = Return based on actual sectors and actual stocks
• r_AN = return based on actual sectors and notional stocks
• r_NN = return based on notional sectors and notional stocks

then

• stock selection component = r_AA - r_AN
• sector selection component = r_AN - r_NN
• Overall outperformance = (r_AA -r_{AN) +} (r_AN - r_NN) = r_AA - r_NN

Question 6

State the formula used to estimate

• The stock selection component attributable to equities
• the sector selection comoponent attributable to equities

Answer 6

Stock selection omponent attributable to equities

W_EA x (r_EA - r_EN)

Sector selection component attributable 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 equit returns
• r_NN is overall fund return based on notional stocks

Question 7

State the formula for the four risk adjusted performance measures

Answer 7

Treynor: T = (R_i - r)/ß_i

Sharpe S = (R_i - r)/σ_i

Jensen J = R_i - [r + ß_i (R_m - r)]

Pre-specified standard deviation P = R_p - [r +(R_m - r)σ_i/σ_m]

Question 8

Explain the circumstances in which the different risk adjusted measures are appropriate

Answer 8

Circumstances in which different risk - adjusted measures appropriate

• Measure incolving σ are based on capital market line, which applies only to efficient portfolios. So, should be used only when considering entire portfolio
• Measuring involving ß are based on security market line and so can be used in any circumstances ie entire portfolio or part of portfolio
• Jensen and pre-specified standard deviation measures are appropriate if required level of risk is pre-specified
• Unlinked Treynor and Sharpe measures, they cannot be used to compare two managers taking different levels of risk

Question 9

List the four main reasons for measing the investment performance of a portfolio

Answer 9

• To improve future performance
  
  • Data collected can be used to plannining future strategy
  • measuring performance will incenticise fund mangers
  • measuring performance will identify strengths and weakness
• To compare rate achieved against target rate
• to compare fund’s performance against
  
  • Others portfolios
  • index and or
  • Benchmark portfolio
• To appraise and remunerate investment managers

Question 10

List 6 main limitations and disadvantages of performance management

Answer 10

• Past performance maybe poor guide to future and it may not be easy to distinguish good luck from skill
• difficult to allow for risk
• frequency to allow for risk
• frequency - difficult to strike balance between assessing performance frequency enough to establish and correct problems, and avoiding spurious conclusions based on too short a measure period
• different funds may have different objectives and constraints, so comparisions between such funds may not be valid
• impact on fund manager behaviour - for example, frequent monitoring can encourage short term approach to investment
• cost of measuring performance

Question 11

State the main advantages and two main disadvantages of assessing performance relative to published indicies

Answer 11

Main advantages

• its relatively easy to do - by definition, data for published indicies is readily available and should be reliably accurate

Main disadvantages

• Available published indices might not be appropriate
• Cant attribute performance to stock and sector selection (as only one sector)

Question 12

Give two reasons for and two reasons against comparing invesetment performance relative to other portfolios

Answer 12

Reasons

• Appropriate if funds being compared have same objectives and same factors influencing investment strategy
• Gives indication of cost or benefit of following particular strategy, relative to that adopted by other funds

Reasons agaisnt

• Maybe inappropriate to compare performance of funds that have very different investment objectives or constraints (noting that these maynot by public knowledge)
• Relevant data may not be available

Question 13

State main advantages of assessing performance relative to a benchmarket portfolio

Answer 13

Main advantages of assessing performance

Benchmark portfolio

• Can be constructed to reflect objeectives of fund
• can be construsted in such a way that data necessary for comparisons easily obtained
• that reflects liabilities of funds avoids giving fund manger conflicting objectives

Can attribute performance to stock and sector selection