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Fourth Edition
Portfolio Performance
Evaluation
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Recent Mutual Fund Data
Mutual Funds in Morningstar Database: 17,212
 # of funds that have existed over 10 yrs: 2,073

In 10 yrs, 16.69% beat SP500 in avg return
and 71% in Sharpe Ratio
 10.6% beat the Value-Weighted NYSE
index in avg return and 56.73% in Sharpe
Ratio. Composite

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Mutual Funds

22% beat the SP 500 in any 5 of the past
years.

13.2% beat the Value-Weighted NYSE
index in any 5 of the past 10 years
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Hedge Funds?
Hedge Funds in TASS database: 1512
 93 have existed over 10 years
 41% and 31% beat the respective indices in
avg return
 75% and 69% beat the indices in Sharpe
ratio
 51% and 41% beat the indices in 5 or more
of the past 10 years.

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% of Pension Assets in Indices
Fourth Edition
Calpers ($155.3 billion)
NY Common Retirement ($146 billion)
NY Teachers' Retirement ($88 billion)
Penn Retirement System ($28 billion)
Wisconsin Retirement System ($67 billion)
93%
95%
75%
75%
70%
70%
55%
55%
35%
15%
-5%
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Abnormal or Exceptional Performance
What is abnormal?
Abnormal performance is measured relative to:




Benchmark portfolio
Market adjusted
Market model / index model adjusted
Reward to risk measures such as the Sharpe
Measure:
E (rp-rf) / p
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Factors That Lead to Abnormal
Performance

Market timing

Superior selection
- Sectors or industries
- Individual stocks
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Risk Adjusted Performance: Sharpe
1) Sharpe Index
rp - rf
p
rp = Average return on the portfolio
rf = Average risk free rate
=
Standard
deviation
of
portfolio
p
return
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M2 Measure
Developed by Modigliani and Modigliani
 Equates the volatility of the managed
portfolio with the market by creating a
hypothetical portfolio made up of T-bills
and the managed 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: return = 35%
standard deviation = 42%
Market Portfolio: return = 28%
T-bill return = 6%
standard deviation = 30%
Hypothetical Portfolio:
30/42 = .714 in P,
(1-.714) or .286 in T-bills
(.714) (.35) + (.286) (.06) = 26.7%
Since this return is less than the market, the managed portfolio
underperformed
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Risk Adjusted Performance:
Treynor
rp - rf
2) Treynor Measure
ßp
rp = Average return on the portfolio
rf = Average risk free rate
ßp = Weighted average
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Risk Adjusted Performance: Jensen
Jensen’s alpha
= rp - [ rf + ßp ( rm - rf) ]
p
p=
Alpha for the portfolio
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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Appraisal Ratio
Appraisal Ratio = ap / (ep)
Appraisal Ratio divides the alpha of the portfolio
by the nonsystematic risk
Nonsystematic risk could, in theory, be
eliminated by diversification
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Which Measure is Appropriate?
It depends on investment assumptions
1) If the portfolio represents the entire investment for
an individual, the Sharpe ratio should be compared
to the Sharpe ratio for the market.
2) If many alternatives are possible, use the Jensen
aor the Treynor measure
The Treynor measure is more complete because it
adjusts for systematic risk
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Limitations

Assumptions underlying measures limit their
usefulness

When the portfolio is being actively managed,
basic stability requirements are not met

Practitioners often use benchmark portfolio
comparisons to measure performance
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Performance Attribution
Decomposing overall performance into
components
 Components are related to specific elements of
performance


Example components
- Broad Allocation
- Industries
- Up and Down Markets
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Process of Attributing Performance
to Components
Set up a ‘Benchmark’ or ‘Bogey’ portfolio

Use indexes for each component

Use target weight structure
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Process of Attributing Performance
to Components

Calculate the return on the ‘Bogey’ and on the
managed portfolio

Explain the difference in return based on
component weights

Summarize the performance differences into
appropriate categories
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Complications to Measuring
Performance

Two major problems
- Need many observations even when portfolio

mean and variance are constant
Active management leads to shifts in
parameters making measurement more difficult
To measure well
- You need a lot of short intervals
- For each period you need to specify the makeup
of the portfolio
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Managing funds against benchmark:
Market Timing Example
Adjusting portfolio for up and down
movements in the market

In Low Market: adopt low ßeta strategy

In a High Return Market: load on ßeta!
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Example of Market Timing
rp - rf
* *
* *
*
*
*
*
* **
* *
* * *
** *
*
*
* *
rm - rf
Steadily Increasing the Beta
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