Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Chapter 24
Portfolio Performance
Evaluation
Irwin/McGraw-Hill
24-1
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Introduction





Complicated subject
Theoretically correct measures are difficult to
construct
Different statistics or measures are appropriate
for different types of investment decisions or
portfolios
Many industry and academic measures are
different
The nature of active management leads to
measurement problems
Irwin/McGraw-Hill
24-2
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Dollar- and Time-Weighted Returns
Dollar-weighted returns
 Internal rate of return considering the cash
flow from or to investment
 Returns are weighted by the amount
invested in each stock
Time-weighted returns
 Not weighted by investment amount
 Equal weighting
Irwin/McGraw-Hill
24-3
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Text Example of Multiperiod Returns
Period
Action
0
Purchase 1 share at $50
1
Purchase 1 share at $53
Stock pays a dividend of $2 per share
2
Stock pays a dividend of $2 per share
Stock is sold at $108 per share
Irwin/McGraw-Hill
24-4
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Dollar-Weighted Return
Period
Cash Flow
0
-50 share purchase
1
+2 dividend -53 share purchase
2
+4 dividend + 108 shares sold
Internal Rate of Return:
 51
112
 50 

1
(1  r ) (1  r ) 2
r  7.117%
Irwin/McGraw-Hill
24-5
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Time-Weighted Return
53  50  2
r1 
 10%
50
54  53  2
r2 
 5.66%
53
Simple Average Return:
(10% + 5.66%) / 2 = 7.83%
Irwin/McGraw-Hill
24-6
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Averaging Returns
Arithmetic Mean:
Text Example Average:
n
rt
r
t 1 n
(.10 + .0566) / 2 = 7.81%
Geometric Mean:
Text Example Average:
1/ n


r   (1  rt )  1
 t 1

n
Irwin/McGraw-Hill
24-7
[ (1.1) (1.0566) ]1/2 - 1
= 7.83%
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Comparison of Geometric and
Arithmetic Means
Past Performance - generally the geometric
mean is preferable to arithmetic
 Predicting Future Returns- generally the
arithmetic average is preferable to
geometric
- Geometric has downward bias

Irwin/McGraw-Hill
24-8
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Abnormal Performance
What is abnormal?
Abnormal performance is measured:
 Benchmark portfolio
 Market adjusted
 Market model / index model adjusted
 Reward to risk measures such as the Sharpe
Measure:
E (rp-rf) / p
Irwin/McGraw-Hill
24-9
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Factors That Lead to Abnormal
Performance
Market timing
 Superior selection
- Sectors or industries
- Individual companies

Irwin/McGraw-Hill
24-10
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
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
Irwin/McGraw-Hill
24-11
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
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

Irwin/McGraw-Hill
24-12
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
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
Irwin/McGraw-Hill
24-13
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Risk Adjusted Performance:
Treynor
rp - rf
2) Treynor Measure
ßp
rp = Average return on the portfolio
rf = Average risk free rate
ßp = Weighted average
Irwin/McGraw-Hill
24-14
for portfolio
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Risk Adjusted Performance:
Jensen
3) Jensen’s Measure
= 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.
Irwin/McGraw-Hill
24-15
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
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
Irwin/McGraw-Hill
24-16
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Which Measure is Appropriate?
It depends on investment assumptions
1) If the portfolio represents the entire investment for
an individual, Sharpe Index compared to the
Sharpe Index 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 risk
Irwin/McGraw-Hill
24-17
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
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

Irwin/McGraw-Hill
24-18
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Market Timing
Adjusting portfolio for up and down
movements in the market
 Low Market Return - low ßeta
 High Market Return - high ßeta
Irwin/McGraw-Hill
24-19
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Example of Market Timing
rp - rf
* *
* *
*
*
*
*
* **
* *
* * *
** *
*
*
* *
rm - rf
Steadily Increasing the Beta
Irwin/McGraw-Hill
24-20
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Performance Attribution
Decomposing overall performance into
components
 Components are related to specific elements of
performance
 Example components
- Broad Allocation
- Industry
- Security Choice
- Up and Down Markets

Irwin/McGraw-Hill
24-21
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Process of Attributing Performance
to Components
Set up a ‘Benchmark’ or ‘Bogey’ portfolio
 Use indexes for each component
 Use target weight structure
Irwin/McGraw-Hill
24-22
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
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 or selection
 Summarize the performance differences into
appropriate categories

Irwin/McGraw-Hill
24-23
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Formula for Attribution
n
n
i 1
i 1
rB   wBi rBi & rp   w pi rpi
n
n
i 1
i 1
rp  rB   w pi rpi   wBi rBi 
n
 (w
i 1
r  wBi rBi )
pi pi
Where B is the bogey portfolio and p is the managed portfolio
Irwin/McGraw-Hill
24-24
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
Contributions for Performance
Contribution for asset allocation
(wpi - wBi) rBi
+
Contribution for security selection
=
Total Contribution from asset class wpirpi -wBirBi
Irwin/McGraw-Hill
24-25
wpi (rpi - rBi)
 The McGraw-Hill Companies, Inc., 1999
Bodie
Kane
INVESTMENTS
Marcus
Fourth Edition
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
Irwin/McGraw-Hill
24-26
 The McGraw-Hill Companies, Inc., 1999