Actuarial Investments

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Actuarial Investments

• Shane Whelan
• L527

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Performance Measurement Attribution
See also handout Return, Risk, Risk-Adjusted
Return Measures
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The Different Methods of Calculating Returns

• The Money-Weighted Rate of Return (MWRR)same as
  internal rate of return.
• Fundamental equation to solve for i
• So need to know
• Amounts dates of cashflows in and out
• Whether it is investment income flow or new
  money flows
• Taxsometimes non-trivial, e.g., CGT on unsold
  assets.
• Expenses, if performance quoted net of expenses.

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Basic Problems with MWRR

• Not good for comparing different fund managers as
  MWRR over 0-T is also, generally, a function of
  the amount and timing of net new money which is
  outwith the control of the fund manager.
• Example on board to illustrate.
• To estimate MWRR we recalculate from 0 to T1
  (cannot chain-link 0-T and T to T1)this is why
  it is called the money-weighted rate of return

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The Different Methods of Calculating Returns

• The time-weighted rate of return (TWRR)gives the
  (notional) return over the period on an
  investment at the start of the time period (i.e.,
  assuming no new money flows over the period).
• Linking the returns between periods when there is
  no cashflow
• TWRR Formula on Board with example.
• But, as defined on board, it is rather
  impractical to calculate. Now though we have
  daily valuations so this criticism not valid
  anymore.
• Hence get good approx. by calculating MWRR over
  intervals when it gives a good approx. to TWRR
  and then chain-linking.
• Especially good approx. when new money flows is
  small proportion of fund value and markets giving
  linear growth or mild growth in period.

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The Different Methods of Calculating Returns

• This approximation method is known as the linked
  internal rate of return (LIRR).
• Also something known as the holding period
  return, used to approx. TWRR, and calculated as
• This is not important it is an approx. to an
  approx.

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Uses of Performance Measurement

• To improve performance
• Incentise fund managers
• better set limitations on investment brief.
• To compare against some standard benchmark,
  competitor fund managers to make decision on its
  future management passive, change active fund
  manager. Hence identify strengths and weaknesses
  of current management process.
• To compare return with some target rate, e.g.,
  valuation rate of interest, interest on building
  society account, etc. May change contribution
  rate, investment vehicle, etc.
• Sundry other reasons renumerate fund managers,
  advertise performance track record, etc.

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Comparison of Portfolio with an Index

• Why should fund managers beat the market index?
• There are two ways to compare performance of fund
  with an index
• Compare the actual value of the portfolio at the
  end of period with the value that would have been
  achieved had the initial value of the portfolio
  and all subsequent new money flows had been
  invested in the same index.
• By calculating and comparing the time-weighted
  return from each.
• This later method allows comparison of many
  portfolios together and is the one almost
  universally used.

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Comparison of Portfolio Performance with
Benchmark Portfolio

• Now the performance of the portfolio is to be
  compared with a benchmark portfolio (or notional
  fund) which gives notional proportions invested
  in specified market indices (and usually
  rebalanced quarterly).
• Note that, in defining the benchmark, we
• Need to specify where re-investment of investment
  income is made.
• Need to specify the sectors where net new money
  flows come from/go to.

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Performance Attribution

• Two ways to outperform a set benchmark
• Stock selectionto outperform in each
  market/category against the set index.
• Strategy (or sector selection or asset
  allocation)to overweight the better performing
  sectors and underweight the worse ones.
• We must do a peformance attribution analysis to
  see where value is added.

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Example of Performance Attribution

• A pension fund sets its benchmark as 20 Irish
  equities, 50 overseas equities, 20 gilts and
  10 property, with an index assigned for each
  category. The benchmark is to be rebalanced
  quarterly. The actual and index performances are
  given below for a quarter.

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Example of Performance Attribution

• What is benchmark return?
• What was the total added value by the investment
  manager?
• How much of the value-added is due to stock
  selection? How much due to strategy?
• What action, if any, is warranted?
• If the trend in sector returns evident over the
  quarter persists for the next 12 quarters, what
  action (if any) is warranted?

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Performance Attribution

• Let the benchmark be bi, i.e., the proportion in
  ith sector is given by bi and ?bi1. Assume
  benchmark is only rebalanced at end of period.
• Let the index performance of sector i be indi and
  the fund performance within that sector be fundi.
• Then the benchmark returnrB((?bi(1
  indi))-1).100
• Let the actual return of the fund be rF (in
  terms) over the period .
• Then the outperformance of the benchmark is
• Outperformance rF-rB
• Attribution of outperformance
• Stock selection (?bi(1 fundi)-?bi(1
  indi)).100 (?bi(1 fundi)-1).100- rB
• StrategyrF- ?bi(1 fundi)

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Limitations of Performance Measurement

• Past (relative) performance is a very poor guide
  to future (relative) performance.
• Not easy to distinguish skill from luck as return
  series are noisy.
• Must standardise in some way for risk.
• Not so obvious how (see later and handout).
• Cost must balance cost with benefits. Property
  portfolios are particularly expensive to value
  and, in any event, what conclusions can be made
  from quarterly performanace evaluation?
• Care must be used in comparing like-with-like.
• Funds have different objectives and constraints.
• Impact on fund manager behaviour short-termism.

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Relative Merits of Different Ways of Assessing
Portfolios

• With published indices
• Easy to do
• But is there an appropriate index?
• Performance relative to other portfolios
• Good measure of cost involved by following
  strategy/management structure if compared with
  funds with similar investment constraints.
• Care to compare like-with-like.
• More expensive generally than with (1)
• Performance relative to benchmark portfolio
• Can blend advantages of each above to form ideal
  compromise.

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Risk-adjusted Performance Measures

• Risk-adjusted performance measures are not used
  extensively in UK but are more common in the US.
• It is (theoretically) bizarre to measure return
  (or outperformance) without paying some attention
  to risk.
• One problem with risk measures is that they only
  allow for risk defined in terms of variance of
  returns and do not allow for actuarial risk or
  downside risk.
• See handout, Overview of Return, Risk,
  Risk-Adjusted Measures.

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4 Possible Risk-adjusted Performance Measures

• The Treynor Measure
• The Sharpe Measure
• The Jensen Measure
• Pre-specified Standard Deviation

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When apply each measure?

• Where portfolio represents the investor total
  wealth then use standard deviation as measure of
  risk. This gives added return per unit of risk.
• If only part of portfolio then use the beta of
  the portfolio. This gives the added return per
  unit of systematic risk.

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Thoughts on Risk-Adjusted Returns

• Clearly sound idea in theory. However practical
  implementation might be premature
• Is s.d. an adequate measure of risk?
• Arguably only to first order approximation.
• Does the beta of CAPM adequately account for
  cross-sectional differences in return?
• No says Hawawini Keim (2000) The Cross Section
  of Common Stock Returns A Review of the Evidence
  and Some New Findings. In Security Market
  Imperfections in World equity Markets, Keim, D.
  Ziemba, W. (Editors), Cambridge University Press.
• If so, can it be measured to the accuracy
  required for our comparison purposes?
• Arguably no.
• Is the risk-free rate to our investors the
  short-term interest rate?
• Arguably no, it is the matching asset a
  liability unit.

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Review of Performance Measurement The Different
Methods of Calculating Returns

• The money-weighted return and showed to calculate
  it.
• Why the money-weighted return is not appropriate
  as a tool to compare fund managers.
• The time-weighted return and approximations to
  the time-weighted return
• LIRR
• Holding period return.
• Comparison of fund return with index or benchmark
  return.
• Performance attribution
• Stock selection
• Strategy or asset allocation.
• Risk measures and risk-adjusted return measures.

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CompletesPerformance Measurement Attribution
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CompletesPerformance Measurement