Bm410: Investments
Performance Evaluation
and Active Portfolio
Management
Or figuring out if you or your manager is good or just lucky!
Objectives

A. Understand active portfolio management
and performance evaluation
 B. Understand how to calculate risk adjusted
rates of return
 C. Decompose returns into components
attributable to asset allocation and securities
selection
A. Active Portfolio Management and
Performance Evaluation

Why are these two topics so important?
• Active Portfolio Management and Performance
Evaluation are very difficult tasks and are critical
to investing
• Very few have done it well
• They are very complicated subjects
• Theoretically correct measures are difficult to
construct
• Different statistics or measures are appropriate
for different types of investment decisions and
portfolios
Active Portfolio Management and
Performance Evaluation (continued)
 How

are these topics viewed?
• Academics and industry view them from different
areas
• Industry and academic measures are different-sometimes extremely different, with different
results
The key area is measuring performance
• Most performance measurement is for a buy and
hold strategy, or at best, a steady state
• Active management complicates this process,
for it is by definition changing
Active Portfolio Management and
Performance Evaluation (continued)


The nature of active management leads to very
challenging measurement problems
• Remember, managers may be buying and selling at
any point in time
• What are asset classes?
What about risk?
• Risk is more complex than just variance or standard
deviation
• Is it upside or downside?
Active Portfolio Management (continued)
 What
is Active Portfolio Management?
• The process of using current, historical, and
publicly available data to actively manage a
portfolio in an effort to:
• Earn investment returns in excess of the
manager’s specified benchmark (or benchmark,
bogey, target) after all costs, including
transactions costs, taxes, management, and other
fees
• Earn consistent excess returns period after
period--and not just from luck
Active Portfolio Management (continued)

Are markets totally efficient?
• This is a critical question
• Some managers outperform the market for
extended periods, but not others. Why?
• While the abnormal performance in some
instances may not be large, it is too large to be
attributed solely to noise
• Evidence remains that anomalies, such as the
turn of the year, exist
• The evidence suggests that there is a role for active
portfolio management in inefficient markets
• It even suggests there is a role in efficient markets
Active Portfolio Management (continued)

What are abnormal returns?
• Abnormal returns are investment returns which,
after fees and transactions costs, are in excess of:
• A specified benchmark portfolio
• Can be a specified index (S&P 500, sector,
or another real or proxy portfolio)
• A market proxy adjusted for risk
• A market model / adjusted index model
• A reward to risk measure, such as the Sharpe
Measure:
E (rp-rf) / sp
Active Portfolio Management (continued)

What major factors lead to abnormal returns?
• 1. Superior Market timing (or asset allocation)
• Shifting assets between a poor-performing asset
class and a better performing asset class to
outperform a specified benchmark which
includes both asset classes
• 2. Superior selection (or stock or asset selection_
• Picking sectors, industries, or companies within
a specified benchmark which outperform that
specified benchmark
1. Superior Market Timing Ability


What is superior market timing ability?
• A process where the manager gains abnormal
returns from adjusting the portfolio for movements
in the market
• The manager shifts among stocks, money
market instruments and bonds based on their
expectations for returns from each asset class
What are the results of superior market timing?
• Higher returns with lower risk
• With perfect forecasting abilities, the portfolio
behaves like an option
• However, no one has perfect forecasting abilities
Superior Market Timing (continued)

With perfect market timing ability (PMTA)
• What would your actions have been since 1970-2002?
• Switch to T-Bills in 73, 74, 77, 78, 81, 90, 00, 01, 02
• No negative returns or losses
• Average S&P500 Return: 10.8% PFA 16.7%
• Standard Deviation
17.5%
11.0%
• Results with perfect timing?
• You would have had a 54% increase in mean return
• You would have a 37% lower standard deviation of
returns
Superior Market Timing (continued)

With imperfect forecasting ability
• How would you judge performance?
• Long horizon necessary to judge the ability
• Judge proportions of correct calls
• Judge both bull markets and bear market calls
• What is the evidence from the real world: “Market
Timing Also Stumps Most Pros”
• By the time there is enough information to judge
to value added, most portfolio managers have
retired, written books, or gone back to being
teachers
2. Superior Selection Ability


What is superior selection ability?
• The ability of a manager to build an investment
portfolio which generates abnormal returns through
buying undervalued stocks, sectors or industries and
selling overvalued stocks, sectors or industries
Does this require total active management?
• A portfolio manager might balance funds in both an
active portfolio and in a passive portfolio
• The goal is to overweight/buy actively managed
funds when they outperform the benchmark, and
run passively when actively managed funds underperform
Questions
 Any
questions on active management?
B. Calculate Risk-adjusted Performance



How do you determine whether a portfolio
manager is generating abnormal returns?
• Is it just returns?
Should you also be concerned about risk?
• It is not just returns that matters—they must be
adjusted for risk.
There are a number of recognized performance
measures available:
• Sharp Index
• Treynor Measure
• Jensen’s Measure
Risk Adjusted Performance:
Sharpe

Sharpe Index
• A ratio of your “excess return” divided by your
portfolio standard deviation
rp – rf
sp
• rp = Average return on the portfolio
• sp = Standard deviation of portfolio return
• The Sharpe Index is the portfolio risk premium
divided by portfolio risk as measured by standard
deviation
Risk Adjusted Performance:
Treynor

Treynor Measure
• This is similar to Sharpe but it uses the portfolio
beta instead of the portfolio standard deviation
rp – rf
ßp
rp = Average return on the portfolio
rf = Average risk free rate
ßp = Weighted average b for portfolio
• It is the portfolio risk premium divided by portfolio
risk as measured by beta
Risk Adjusted Performance:
Jensen

Jensen’s Measure
• This is the ratio of your portfolio return less CAPM
determined portfolio return
• ap = rp - [ rf + ßp (rm – rf) ]

ap = 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.
It is portfolio performance less expected portfolio
performance from CAPM
Risk Adjusted Performance (continued)

Which Measure is Appropriate? Are there
some general guidelines?
• Generally, if the portfolio represents the entire
investment for an individual, Sharpe Index
compared to the Sharpe Index for the market is best
• If many alternatives are possible, or this is only part
of the portfolio, use the Jensen a or the Treynor
measure.
• Of these two, the Treynor measure is more
complete because it adjusts for risk
Risk Adjusted Performance (continued)

Are their limitations of risk adjustment
measures?
• Yes, very much so. The assumptions underlying
measures limit their usefulness
• Know the key assumptions and be careful!
• When the portfolio is being actively managed, basic
stability requirements are not met
• Be careful
• Practitioners often use benchmark portfolio
comparisons and comparisons to other managers to
measure performance
• This is largely because they are easier
Risk Adjusted Performance Problem
 Consider
the following data for a particular
sample period:
Portfolio P
Market
• Average return
35%
28%
• Beta
1.2
1.0
• Standard Deviation
42%
30%
 Calculate the following performance measures for
P and the market: Sharpe, Jensen (alpha), and
Treynor. The T-bill rate during the period was 6%.
By which measures did P outperform the market.
Answer
•
• Average return
• Beta
• Standard Deviation
Portfolio P Market
35%
28%
1.2
1.0
42%
30%
Sharpe = (rp – rf )/ sd
• Portfolio (35-6)/42 = .69
• Market (28-6)/30 = .73
Jensen = rp – [rf + ßp (rm – rf)]
• Portfolio alpha = 35 – [6 + 1.2 (28-6) = 2.6%
• Market alpha = 0
Answer
•
• Average return
• Beta
• Standard Deviation
Portfolio P Market
35%
28%
1.2
1.0
42%
30%
Treynor = (rp – rf )/ ßp
• Portfolio (35-6)/1.2 = 24.2
• Market (28-6)/1.0 = 22.0
 The portfolio outperformed the market in terms
of the Jensen’s alpha and the Treynor measure,
but not the Sharpe ratio.
Questions
• Any questions on risk-adjusted performance
measures?
C. Portfolio Attribution and
Decomposing Portfolio Returns

What is Portfolio Attribution?
• Portfolio attribution is the process of decomposing
portfolio returns into components, generally
attributable to asset allocation and securities
selection (although other components can be added
as well)
 What is the importance of these components?
• These components are related to specific elements
of portfolio performance
 What are examples of some of these components?
• Broad Allocation, security choice, industry, trading,
etc.
Portfolio Attribution (continued)

How do you determine portfolio attribution?
• 1. Set up a ‘Benchmark’ or ‘Bogey’ portfolio which
includes all relevant asset classes
• Use indexes for each component
• Use target weight structure
• 2. Compare your portfolio returns in each asset
class to the benchmark returns of each index
• 3. Calculate your attribution
Portfolio Attribution (continued)


Why is it important to attribute performance to
the portfolio’s components?
• It can explain the difference in return based on
component weights or selection
• It can summarize the performance differences into
appropriate categories
What happens if you don’t perform portfolio
attribution?
• You will not know why you are performing as you
are?
• You will not know how to improve
Portfolio Attribution Problem

Consider the following information regarding the
performance of a money manager during a recent
month. The equity index is the S&P500, Bonds the
Salomon Brothers Index, and cash is the Lehman Cash.
•
•
Asset Class Actual Actual
Return Weight
Benchmark
Weight
Benchmark
Return
• Equity Fund 2.0% .70
.60
2.5%
• Bond Fund 1.0% .20
.30
1.2%
• Cash Fund
0.5% .10
.10
0.5%
a. What was the managers return in the month? What
was the over/underperformance?
Answer
Asset Class Actual Actual Benchmark Benchmark
Return Weight Weight
Return
Equity
2.0% .70
.60
2.5%
Bonds
1.0% .20
.30
1.2%
Cash
0.5% .10
.10
0.5%
a. What was the managers return in the month? What
was the over or underperformance?
The managers return was (2.0%*.7) + (1.0%*.2) +
(.5%*.1) or 1.65%.
The index return was (2.5%*.6) + (1.2%*.3) +
(.5%*.1) or 1.91%. the total underperformance
was .26% for the portfolio or 1.65%-1.91%.
Portfolio Attribution Problem
Asset Class Actual Actual Benchmark Benchmark
Return Weight Weight
Return
Equity
2.0% .70
.60
2.5%
Bonds
1.0% .20
.30
1.2%
Cash
0.5% .10
.10
0.5%
b. What was the contribution of security selection to
relative performance?
c. What was the contribution of asset allocation to relative
performance? Confirm that the sum of selection and
allocation contributions equals her total excess return
relative to the bogey.
Answer Part B
b) What was the contribution of security selection to
relative performance?
(1)
(2)
(1*2)
Market Diff. Ret. Man. Port. Wgt. Contribution
Equity -0.5%
.70
-0.35%
Bonds -0.2%
.20
-0.04%
Cash
0.0%
.10
0.00%
Contribution of Security Selection
-0.39%
(1) Fund return less index return (2.0%-2.5%)
(2) Actual weight of the managed portfolio
(1*2) Contribution of asset class security selection
to the portfolio
Problem Part C
c. What was the contribution of asset allocation to relative
performance? Confirm that the sum of selection and
allocation contributions equals her total excess return
relative to the bogey.
(3)
(4)
(3*4)
Market Excess Weight Index-BM Contribution
Equity 10%
.59%
0.059%
Bonds -10%
-.71%
0.071%
Cash
0%
-1.41%
0.000%
Contribution of Asset Allocation
0.130%
(3) Weight of actively managed fund less benchmark weight (- is
underweight)
(4) Asset class return less total portfolio return (equity is 2.50-1.91 or
.59%, bond is 1.20-1.91=-.71)
(3*4) Contribution of the asset class to the total portfolio
Overall Attribution Results
•
The actively managed portfolio under
performed the benchmarks by .26% or 26 basis
points (1.65%-1.91%). This underperformance
was a combination of a -.39% contribution to
security selection and a .13% contribution from
asset allocation.
• While the manager picked the asset classes that
performed the best, she didn’t do as well
picking the stocks. She needs to work on stock
selection or just index that part of the portfolio
construction process.
Portfolio Attribution Summary



Performance Evaluation and Active Portfolio
Management are very difficult tasks
• Very few have done it well
Active management is a difficult topic
• While some active managers have proven their
ability to deliver consistent excess returns, the
numbers are few
Finding adequate statistics to evaluate performance is
critical
• Understand the assumptions on which the statistics
are based
Questions

Any questions on portfolio attribution?
Review of Objectives

A. Do you understand the importance of
performance evaluation and active portfolio
management?
 B. Do you understand how to calculate risk
adjusted rates of return?
 C. Do you understand how to decompose
returns into components attributable to asset
allocation and securities selection?