Universally Accepted Measures for Portfolio Performance Asst'Prof' Dr' Arnat Leemakdej Faculty of Co

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Universally Accepted Measures for Portfolio
PerformanceAsst.Prof. Dr. Arnat
LeemakdejFaculty of Commerce and
AccountancyThammasat Universitye-mail
arnat_at_velocall.comwebsite http//mif.velocall.co
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Outline

• Basic Concept of Performance Measurement
• Dollar Weighted Return
• Time Weighted Return
• Benchmark
• Risk
• Check basic concept
• Risk-adjusted Performance Measurement
• M-Square, T-Square
• Performance Attribution
• Q A

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Basic Concept
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Performance Evaluation

• We want to know whether a particular portfolio
  performance is abnormally high
• What is abnormal?
• Market adjusted, or market model adjusted
• Reward to risk measures such as the Sharpe ratio
• Complicated issue
• Many kinds of different benchmarks and measures
• Different measures may lead to different
  implications on performance evaluation

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Two ways of performance evaluation

• 1) Relative performance measures
• Compare with other benchmark with similar risk
  characteristics
• (Ex) high-yield bond portfolio
• growth stock portfolio
• 2) Risk-adjustment based on MV or CAPM
• Sharpe measure
• Treynor measure
• Jensen measure

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Sharpe Measure

• 1) Sharpe measure

rp - rf
s
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Treynor Measure

• 2) Treynor Measure

rp - rf ßp
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Jensens Alpha
3) Jensens Alpha
rp - rf ßp ( rm - rf)
a
p
p
rp Average return on the portfolio ßp
Weighted average Beta rf Average risk free
rate rm Avg. return on market index port.

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M2 Measure

• Attempt to resolve the difficulty in the
  interpretation of the Sharpe measure by
  translating it into a percentage term
• Developed by Modigliani and Modigliani
  (Modigliani-squared)
• Equates the volatility of the managed portfolio
  with the market by creating a hypothetical
  complete portfolio, rp, made up of T-bills and
  the managed portfolio
• M2 rp rm
• where rp is the return on the hypothetical
  portfolio
• If the risk is lower than the market, leverage is
  used and the hypothetical portfolio is compared
  to the market

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M2 Measure Example
Managed Portfolio Market
T-bill Return 35 28 6 Stan.
Dev 42 30 0 Hypothetical
Portfolios vol Markets vol 30/42 0.714 in
P (1-0.714)0.286 in T-bills rp (0.714)
(0.35) (0.286) (0.06) 26.7 ? Since this
return is less than the market by 1.3, the
managed portfolio underperformed
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T2 Measure

• Similar to the M2 measure, it converts the
  Treynor measure into percentage return basis
• Makes it easier to interpret and compare
• Equates the beta of the managed portfolio with
  the markets beta of 1 by creating a hypothetical
  portfolio made up of T-bills and the managed
  portfolio
• T2 Rp Rm
• where Rp is the excess return on the
  hypothetical portfolio
• If the beta is lower than one, leverage is used
  and the hypothetical portfolio is compared to the
  market

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T2 Example
Port. P. Market Risk Prem. (r-rf) 13
10 Beta 0.80 1.0 Alpha 5
0 Treynor Measure 16.25 10 Weight to
match Market beta w bM/bP 1.0 / 0.8 Adjusted
excess return RP w (RP) 16.25 TP2 RP -
RM 16.25 - 10 6.25
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Which Measure is Appropriate?

• It depends on investment assumptions
• 1) If the portfolio represents the entire
  investment of an individual, then total
  volatility matters
• Thus, Sharpe measure is appropriate, which can be
  compared to that of the market
• 2) If a portfolio is just one of a whole
  portfolio, then systematic risk matters
• Thus, use the Treynor or the Jensen a measure

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Limitations of the model-based performance
measures

• Assumptions underlying measures limit their
  usefulness
• Parameter stability
• When the portfolio is being actively managed,
  this stability requirement is not met
• Practitioners often use benchmark portfolio
  comparisons to measure performance

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Performance Attribution

• Decomposing overall performance into components
  that are related to specific elements of
  performance
• Asset allocation decision
• Market timing
• Up and Down Markets
• Security selection decision
• Sectors or industries
• Individual companies

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Decomposition of Performance Attribution

• Assume two broad asset markets, (1) stocks (2)
  bonds.
• Want to compare a managed portfolio return (rp)
  with a benchmark portfolio return (rm)
• rp rm (wp1rp1 wp2rp2) (wm1rm1 wm2rm2)
• (wp1 wm1)rm1 (wp2 wm2)rm2 ? asset
  alloc.
• wp1(rp1 rm1) wp2 (rp2 rm2) ? sec.
  selec.
• Difference in weights leads to asset allocation
  bets, and difference in returns within asset
  classes leads to security selection bets

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Asset allocation vs. Selection

• (1) (2)
  (3) (4) (5)(3)(4)
• Portfolio Benchmark Excess
  Index contribution to
• Market weight weight weight
  return performance
• Stocks 0.7 0.6
  0.1 5.81 0.581
• Bonds 0.07 0.3
  -0.23 1.45 -0.3335
• Cash 0.23 0.1
  0.13 0.48 0.0624
• Contribution of asset allocation 0.3099
• (1) (2)
  (3) (4) (5)(3)(4)
• Portfolio Benchmark Excess
  Portfolio contribution to
• Market return return
  return weight performance
• Stocks 7.28 5.81
  1.47 0.7 1.03
• Bonds 1.89 1.45
  0.44 0.07 0.03
• Contribution of selection within markets 1.06

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Lure of Active Management

• Are markets really efficient?
• Some managers outperform the market for extended
  periods, and investors are willing to pay for
  expensive analysis
• The abnormal performance may not be too large,
  but it is too large to be attributed solely to
  noise
• Markets are nearly efficient
• Evidence of anomalies exists
• Turn of the year effect, small firm effect,
  momentum effect
• ? The evidence suggests that there is some role
  for active management

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Market Timing

• What is market timing?
• Adjust the portfolio weights according to a
  forecast of the market movements for next period
• (EX) Shift between stocks, bond, and money
  market instruments
• Results higher returns, lower risk (downside is
  eliminated)
• With perfect ability to forecast, the portfolio
  return behaves like an option
• The value of perfect market timing ability is
  equivalent to the value of a call option

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Rate of Return for a Perfect Market Timer
rf
rM
rf
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How to judge timing ability?

• Need long horizon to judge the ability
• Judge proportions of correct calls
• Bull markets and bear market calls
• See if managers adjust portfolios for up and down
  movements in the market
• Low Market Return ? low ßeta
• High Market Return ? high ßeta

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Example of Market Timing
Steadily increasing the beta as the market
moves up
rp - rf




















rm - rf



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Style Analysis

• Introduced by Bill Sharpe
• Explain percentage returns attributable to style
  investment
• Size effect
• Value vs. growth
• Momentum
• Style Analysis has become popular with the
  industry

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Morning Stars Risk Adjusted Rating

• Similar to mean Standard Deviation rankings
• Companies are put into peer groups
• Stars are assigned
• 1-lowest
• 5-highest
• Highly correlated to Sharpe measures

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Active portfolio management

• Concentrate funds in undervalued stocks, sectors,
  or industries
• Active selection procedure results in taking some
  unsystematic risk
• Balanced funds in an active portfolio and in a
  passive portfolio
• Some portion based on passive strategy, and the
  rest based on active strategy
• (Ex) Treynor/Black model

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Treynor-Black Model

• Model used to combine actively managed stocks
  with a passively managed portfolio
• Optimal combination of active and passive
  portfolios can be determined, based on a
  reward-to-risk measure that is similar to the the
  Sharpe Measure
• Assumptions
• Analysts have a limited ability to find a select
  number of undervalued securities
• Portfolio managers can estimate the expected
  return and risk for the actively-managed
  portfolio as well as the broad market portfolio
  (passively managed)

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Reward-to-Variability Measure
Passive Portfolio Squared Sharpe ratio

2
-
rf
rm
ù
é
E
(
)
2
S
ú
ê

m
s
û
ë
m
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Appraisal Ratio
Active Portfolio Squared Abnormal return
2
ù
é
aA
ú
ê
seA
û
ë
aA
Alpha for the active portfolio
Unsystematic standard deviation for active
seA
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Combined portfolios Squared Sharpe ratio
(
)
2
2
ù
é
ù
é
-
rf
rm
E
a
A
2
S
ú
ê
ú
ê


P
s
s
û
ë
û
ë
eA
m
CML
CAL
E(r)
P
A (active)
M (market passive)
Rf
s
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Summary Treynor-Black Model

• Sharpe ratio can be increased by active
  management with added ability to pick stocks
• Slope of new CAL gt CML
• (rp-rf)/sp gt (rm-rf)/sp
• P is the portfolio that combines the passively
  managed portfolio with the actively managed
  portfolio
• The combined efficient frontier has a higher
  return for the same level of risk

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QA

• Why dont we use target price analyzed by
  analyst rather than historical price to compute
  expected return ?