

Investment
Analysis & Portfolio Management
(FIN630)
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Lesson
# 39
EVALUATION
OF INVESTMENT PERFORMANCE
Framework
for Evaluating Portfolio
Performance:
When
evaluating a portfolio's performance,
certain factors must be considered.
Assume that
in
early 2004 you are
evaluating the Go Growth
mutual fund, a domestic
equity fund in the
category
of large growth (it
emphasizes largecapitalization growth
stocks). This fund
earned
a total return of 20 percent
for its shareholders for
2003. It claims in an
advertisement
that it is the #1 performing
mutual funds in its
category. As a shareholder,
you
are trying to assess Go
Growth's performance.
SOME
OBVIOUS FACTORS TO CONSIDER IN
MEASURING PORTFOLIO
PERFORMANCE:
Differential
Risk Levels:
Based
on our discussion throughout
this text of the riskreturn
tradeoff that underlies
all
investment
actions, we can legitimately say
relatively little about Go
Growth's performance.
The
primary reason isthat
investing is always a twodimensional
process based on both
return
and risk. These two factors
are opposite sides of the
same coin, and both must
be
evaluated
if intelligent decisions are to be made.
Therefore, if we know nothing
about the
risk
of this fund, little can be
said about its performance.
After all, Go Growth's
managers
may
have taken twice the
risk of comparable portfolios to
achieve this 20percent
return.
Given
the risk that all
investors face, it is totally inadequate to
consider only the
returns
from
various investment alternatives.
Although all investors
prefer higher returns, they
are
also
risk averse. To evaluate portfolio
performance properly, we must
determine whether
the
returns are large enough
given the risk involved. If
we are to assess
portfolio
performance
correctly, we must evaluate
performance on a riskadjusted
basis.
Differential
Time Periods:
It is
not unusual to pick up a
publication from the popular
press and see two
different
mutual
funds of the same typefor
example, smallcapitalization growth
funds or balanced
fundsadvertise
themselves as the #1 performer. Each of
these funds is using a
different
time
period over which to measure
performance. For example, one
fund could use the
10
years
ending December 31, 2003, whereas
another fund uses the
five years ending June
30,
2003.GoGrowth
could be using a oneyear
period ending on the same
date or some other
combination
of years. Mutual fund
sponsors may emphasize different
time periods in
promoting
their performance. Funds can also
define the group or index to
which
comparisons
are made.
Although
it seems obvious when one
thinks about it, investors
tend not to be careful
when
making
comparisons of portfolios over
various time periods. As with
the case of
differential
risk,
the time element must be
adjusted for if valid
performance of portfolio results is to
be
obtained.
Appropriate
Benchmarks:
A
third reason why we can say little
about the performance of Go
Growth is that it's
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percent
return given its, risk, is
meaningful only when compared to a
legitimate alternative.
Obviously,
if the averagerisk fund or
the market returned 25
percent in 2003, and Go
Growth
is an averagerisk fund, we would
find its performance
unfavorable. Therefore, we
must
make relative comparisons in performance
measurement, and an important
related
issue
is the benchmark to be used in
evaluating the performance of a
portfolio.
It is
critical in evaluating portfolio
performance to compare the returns,
obtained on
the
portfolio being evaluated
with the returns that
could have been obtained
from a
comparable
alternative. The measurement process
must involve relevant and
obtainable
alternatives;
that is, the benchmark
portfolio must be a legitimate
alternative that
accurately
reflects
the objectives of the
portfolio being
evaluated.
An
equity portfolio consisting of Standard
& Poor's Composite 500 Index
(S&P
500)
stocks should be evaluated relative to
the S&P 500 index or other
equity portfolios
that
could be constructed from
the Index, after adjusting
for the risk involved. On
the
other
hand, a portfolio of smallcapitalization
stocks should not be judged against
the
benchmark
of the S&P 500. Or, if a
bond portfolio manager's
objective is to invest in
bonds rated A or
higher, it would be inappropriate to
compare his or her
performance
with
that of a junk bond
manager.
It
may be more difficult to
evaluate equity funds that
hold some midcap and
small
stocks
while holding many S&P 500 stocks.
Comparisons for this group can be
quite
difficult.
Constraints
on Portfolio Managers:
In
evaluating the portfolio manager
rather than the portfolio
itself, an investor
should
consider
the objectives set by (or
for), the manager and any
constraints under which he
or
she
must operate. For example if a
mutual fund's objective is to
invest in small
speculative
stocks
investors must expect the
risk to be larger than that
of a fund invested in S&P 500
stocks
with substantial swings in
the annual realized
returns.
It is
imperative to recognize the
importance of the investment
policy statement pursued,
by
a
portfolio manager in determining the
portfolio's results in many
cases he investment
policy
determines the return and/or
the risk of the portfolio.
For example, Brinson,
Hood,
and
Bee bower found that
for a sample of pension plans
the asset allocation
decision
accounted
for approximately 94 percent of
the total variation in the
returns to these funds.
In
other
words, more than 90 percent
of the movement in a fund's
returns, relative to
the
market
returns, is attributable to a fund's
asset allocation
policy.
If a
portfolio manager is obligated to operate
under certain constraints
these must be taken
into
account. For example, if a
portfolio manager of an equity fund is
prohibited from
selling
short, it is unreasonable to expect the
manager to protect the portfolio in
this manner
in a
bear market. If the manager is
further prohibited from
trading in options and futures
the
only
protection left in a bear
market may be to reduce the
equity exposure.
Other
Considerations:
Of course,
other important issues are
involved in measuring the
portfolio's performance,
including
evaluating the manager as opposed to
the portfolio itself if the
manager does not
have
full control over the
portfolio's cash flows. It is essential
to determine how well
diversified
the portfolio was during the
evaluation period, because,
diversification can
reduce
portfolio risk.
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All
investors should understand
that even in today's
investment World of
computers
and
databases, exact, precise
universally agreedupon methods of
portfolio evaluation
remain
an elusive goal. One popular
press article summarized the
extent of the problem
by
noting
that "most investors ...
don't have the slightest
idea how well their
portfolios are
actually
performing." This article
suggests some doityourself
techniques as well, as
some
"storebought
solutions" and discusses some
new trends in the money
management industry
10
provide investors with
better information.
Investors
can use several "wellknown,
techniques to assess, the
actual performance of a
portfolio
relative to one or more alternatives. In
the final analysis, when
investors are
selecting
money managers to turn their
money over to, they
evaluate these managers
only
on
the basis of their published
performance statistics. If the
published "track record"
looks
good,
that is typically enough to
convince many investors to
invest in, a particular
mutual
fund.
However, the past is no guarantee of an
investment manager's future.
Shortterm
results
may be particularly
misleading.
Return
and Risk Considerations:
Performance
measurement begins with portfolio
valuations and transactions
translated
into
rate of return. Prior to 1965,
returns were seldom related
to measures of risk. In.
eval
uating
portfolio performance, however,
investors must consider both
the realized return
and
the risk that was assumed.
Therefore, whatever measures or
techniques are used
these
parameters must be incorporated
into the analysis.
MEASURES
OF RETURN:
When
portfolio performance is evaluated,
the investor should be
concerned with the
total
change in
wealth. A proper measure of
this return is the total
return (TR), which
captures
both
the income component and the
capital gains (or losses)
component of return. Note
that
the
Performance Presentation Standards
require the use of total
return to calculate
performance.
In
the simplest case, the
market value of a portfolio can be
measured at the beginning
and
ending
of a period, and the rate of return can
be calculated as
Rp=VE VB /
VB
Where
VE is the ending
value of the portfolio and VB is its beginning
value.
This
calculation assumes that no
funds were added to or
withdrawn from the portfolio
by
the
client during the measurement
period. If such transactions
occur, the portfolio return
as
calculated,
Rp may not be an accurate measure of
the portfolio's performance.
For example,
if
the client adds funds close
to the end of the measurement period,
would produce
inaccurate
results, because the ending
value was not determined by
the actions of the
portfolio
manager. Although a close approximation of
portfolio performance might
be
obtained
by simply adding any
withdrawals or subtracting any
contributions that are
made
very
close to the end of the measurement
period, timing issues are a
problem.
DollarWeighted
Returns:
Traditionally,
portfolio measurement consisted of calculating
the dollarweighted rate of
return
(DWR), which is equivalent to
the internal rate of return
(IRR) used in several
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financial
calculations. The IRR measures
the actual return earned on
a beginning portfolio
value
and on any net contributions
made during the period.
The DWR equates all
cash
flows,
including ending market
value, with the beginning
market value of portfolio.
Because
the
DWR is affected by cash
flows to the portfolio it
measures the rate of return to
the
portfolio
owner. Thus, it accurately
measures the investor's
return. However because
the
DRW
is heavily affected by cash
flows, it is inappropriate to use
when making comparisons
to
other portfolios or to market
indexes, a key factor in
performance measurement. In
other
words,
it is a misleading measure of the
manager's ability, because
the manager does not
have
control over the timing of
the cash inflows and
outflows. Clearly, if an investor
with
$1,000,000
allocates these funds to a
portfolio manager by providing half at
the beginning
of
the year and half at
midyear, that portfolio
value at the end of the year
will differ from
another
manager who received the
entire $1,000,000 at the
beginning, of the year. This
is
true
even if both managers had
the same two 6month
returns during that
year.
TimeWeighted
Returns:
In
order to evaluate a manager's
performance properly, we should
use the timeweighted
rate of
return (TWR). TWRs are
unaffected by any cash flows
to the portfolio;
therefore,
they
measure the actual rate of
return earned by the
portfolio manager.
We
wish to determine how well
theportfolio manager performed
regardless of the
size or
timing of the cash flows.
Therefore, the timeweighted rate of
return measures the
compound
rate of growth of the portfolio
during the evaluation
period. It is calculated by
computing
the geometric average of the
portfolio subperiod returns.
That is, we calculate
the
geometric mean of a set of return
relatives (and subtract out
the 1.0).
Which
Measure to Use:
The
dollarweighted return and,
the timeweighted return, can
produce different results,
and
at
times these differences are
substantial. In fact, the
two will produce identical
results only
in
the case of no withdrawals or
contributions during the
evaluation period and with
all
investment
income being reinvested. The
timeweighted return captures the rate of
return
actually
earned by the portfolio manager, whereas
the dollarweighted return captures
the
rate of
return earned by the
portfolio owner.
For
evaluating the performance of
the portfolio manager, the
timeweighted return
should
be
used, because he or she
generally has no control
over the deposits and
withdrawals made
by
the clients. The objective
is to measure the performance of
the portfolio manager
independent
of the actions of the
client, and this is better
accomplished by using the
time
weighted
return.
RISK
MEASURES:
Why can we
not measure investment
performance on the basis of a
properly calculated rate
of
return measure? After all
rankings of mutual funds are
often done this way in the
popular
press,
with oneyear, threeyear, and sometimes
fiveyear returns shown. Are
rates of return,
or
averages, good indicators of
performance?
Differences
in risk will cause portfolios to respond
differently to changes in the
overall
market
and should be accounted for in
evaluating performance.
We
now know that the
two prevalent measures of
risk used in investment
analysis are total
risk
and nondiversifiable or systematic risk.
The standard deviation for a
portfolio's set of
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returns
can be calculated easily with a
calculator or computer and is a measure
of total risk.
As we
know from portfolio theory,
part of the total risk can
be diversified away.
Beta,
a relative measure of systematic
risk, can be calculated with
any number of
software
programs,
However, we must remember
that Betas are only
estimates of systematic
risk.
Betas
can be calculated using weekly,
monthly, quarterly, or annual
data, and each will
produce
a different estimate. Such variations in
this calculation could
produce differences in
rankings
which use beta as a measure
of risk. Furthermore, betas can be
unstable, and they
change
over time.
RiskAdjusted
Measures of Performance:
Based
on the concepts of capital market
theory, and recognizing the
necessity to incorporate
return
and risk into the analysis,
three researchers William Sharpe,
Jack Treynor, and
Michael
Jensen developed measures of
portfolio performance in the
1960s. These
measures
are often referred to .as
the composite (riskadjusted')
measures of portfolio
performance,
meaning that .they
incorporate 'both realized
return and risk into
the
evaluation.
These measures are often
still used, as evidenced by
Morningstar, perhaps
the
bestknown
source of mutual fund information,
reporting the Sharpe ratio
explained below.
The
Sharpe Performance Measure:
William
Sharpe, whose contributions to portfolio
theory have been previously
discussed,
introduced
a riskadjusted measure of portfolio
performance called the
rewardtovariability
ratio
(RVAR) based on his work in
capital market theory. This
measure uses a
benchmark
based
on the expost capital market
line. This measure can be
defined as:
RVAR
= [TRp  RF] / SDp
=
excess return / risk
TRp =
the average TR for portfolio
p during some period of
time
RF = he
average riskfree rate of return
during the period
SDp =
the standard deviation of return
for portfolio p during the
period
TRp
RF = the excess return
(risk premium) on portfolio
p
The
Treynor Performance
Measure:
At
approximately the same time
as Sharpe's measure was developed
(the mid1960s), jack
Treynor
presented a similar measure
called the rewardtovolatility
ratio (RVOL) like
Sharpe,
Treynor sought to relate the
return on a portfolio to its
risk. Treynor,
however,
distinguished
between total risk and
systematic risk, implicitly
assuming that
portfolios
are
well diversified; that is,
he ignored any diversifiable
risk. He used as a benchmark
the
ex post
security market line.
In
measuring portfolio performance,
Treynor introduced the
concept of the
characteristic
line
which was used to partition a
security's return into its
systematic and nonsystematic
components.
It is used in a similar manner
with portfolios, depicting
the relationship
between
the returns on a portfolio and those of
the market. The slope of the
characteristic
line
measures the relative
volatility of the fund's
returns. As we know, the slope of
this line
is
the beta coefficient, which
is a measure of the volatility
(or responsiveness) of the
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portfolio's
returns in relation to those of the
market index.
Characteristic
lines, can be estimated by regressing each
portfolio's returns on the
market
proxy
returns using either raw
returns for the portfolios
and raw proxy returns or
excess
portfolio
returns and excess1 market proxy it turns
where the riskfree rate has
been
subtracted
out: The latter method is
theoretically better and is used
here.
Treynor's
measure relates the average
excess return on the
portfolio during some
period
(exactly
the same variable as in the
Sharpe measure) to its systematic
risk as measured by
the
portfolio's beta. The
rewardtovolatility ratio
is:
RVOL =
[TRp  RF] / βp
=
Average excess return on
portfolio p
βp =
the beta for portfolio
p
In
this case, we are
calculating the excess
return per unit of systematic
risk. As with RVAR,
higher
values of RVOL indicate
better portfolio performance.
Portfolios can be ranked on
their
RVOL, and assuming that the
Treynor measure is a correct
measure of portfolio
performance,
the best performing
portfolio can be determined.
Comparing
the Sharpe and Treynor Measures:
Given
their similarity, when
should RVAR or RVOL be used,
and. why? Actually,
given
the
assumptions underlying each measure,
both can be said to be correct.
Therefore, it is
usually
desirable to calculate both measures
for the set of portfolios
being evaluated.
The
choice of which to use could
depend on the definition of
risk. If an investor thinks
it
correct
to use total risk, RVAR is
appropriate; however, if the
investor thinks that it
is
correct
to use systematic risk, RVOL
is appropriate.
What
about the rankings of a set
of portfolios using the two
measures? If the portfolios
are
perfectly
diversified that is, the
correlation coefficient between
the portfolio return and
the
marketreturn
is l.0 the rankings will be
identical. For typical
large, professionally
managed
portfolios, such as broadbased
equity mutual funds, the
twomeasures often
provide
identical, or almost identical,
rankings.
As
the portfolios become less
well diversified, the
possibility of differences in
rankings
increases.
This leads to the following
conclusions about these two
measures: RVAR takes
into
account how well diversified
a portfolio was during the measurement
period.
Differences
in rankings between the two
measures can result from
substantial differences in
diversification
in the portfolio. If a portfolio is
inadequately diversified, its
RVOL ranking
can be
higher than its RVAR
ranking. The nonsystematic
risk would not affect
the RVOL
calculation.
Therefore, a portfolio with a Jaw
amount of systematic risk and a
large amount
of
total risk could show a
high RV0L value and a low
RVAR; value. Such a
difference in
ranking
results from the substantial
difference in the amount of
diversification of the
portfolio.
This
analysis leads to an important
observation about the Sharpe
and Treynor measures.
Investors
who have all (or
substantially all) of their
assets in a portfolio of securities
should
rely
more on the Sharpe measure,
because it assesses the
portfolio's total return in
relation to
total
risk, which: includes any
unsystematic risk assumed by
the investor. However
for
those
investors, whose portfolio
constitutes only one (relatively)
small part of their
total
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assets
that is, they have
numerous other assets
systematic risk may well be
the relevant risk.
In
these circumstances, RVOL Is
appropriate, because it considers only
systematic or non
diversifiable
risk.
Measuring
Diversification:
Portfolio
diversification is typically measured by
correlating the returns on
the portfolio
with
the returns oh the market
index, this is accomplished as
part of the process of
fitting a
characteristic,
line whereby the'
portfolio's returns are
regressed: against the
market's
returns.
The square of the
correlation coefficient produced as a
part of the analysis,
called
the
coefficient of determination, or R2, is used to, denote the
degree of diversification.
The
coefficient,
of determination indicates the
percentage of the variance in
the portfolio's
returns
that is explained by the
market'sreturns. If the fund is
totally diversified, the R2 will
approach
1.0, indicating that the
fund's returns are
.completely explained by the
market's
returns:
The lower the coefficient of
determination, the less the
portfolio returns are
attributable
to the market's returns.
This indicates that other
factors, which could have
been
diversified
away, are being allowed to
.influencethe portfolio's
returns.
Jensen's
Differential Return
Measure:
A
measure related to Treynor's
RVOL is Jensen's differential
return measure (or
alpha).
Jensen's
measure of performance like
Treynor's measure is based on
the capital asset
pricing
model
(CAPM). The expected return
for any security (i)
or, in this case, portfolio
(p) is
given
as;
E
(Rpt) = RFt + βp
(E (RMt) RFt)
Problems
with Portfolio
Measurement:
Using
the three riskadjusted
performance measures just
discussed to evaluate portfolios
is
not
without problems. Investors
should understand their
limitations, and be guided
accordingly.
First,
these measures are derived
from capital market theory
and the CAPM and are
therefore
dependent on the assumptions involved
with this theory. For
example, it the
Treasury
bill rate is not a satisfactory
proxy for the riskfree
rate, or if investors
cannot
borrow
and lend at the riskfree rate
this will have an impact on
these measures of
performance.
An
important assumption of capital
market theory that directly
affects the use of
these
performance
measures is the assumption of a
marker portfolio that can be
proxied by a
market
index. We have used the
S&P 500 Index as a market proxy, as
is often. However,
there
are potential
problems.
Although
a high correlation exists
among most of the commonly
used market proxies
this
does
not eliminate the problem
that some may be efficient
but others are not.
According to
Roll,
no unambiguous test of the CAPM
has yet been conducted.
This point should be
kept
in
mind when we consider
performance measures based on
the CAPM, such as the
Treynor
and
Jensen; measures.
The
movement to global investing
increases the problem of
benchmark error. The
efficient
frontier
changes when foreign securities
are added to the portfolio.
The measurement of
beta
will be affected by adding foreign
securities. Given that a
world portfolio is likely
to
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have
a smaller variance than the
S&P 500 Index, any measure of
systematic risk is likely
to
be
smaller.
A
long evaluation period is
needed to determine successfully
performance that is
truly
superior.
Over short .periods, luck
can overshadow all else, but
luck cannot be expected to
continue.
According to some estimates, the
number of years needed to make such
an
accurate
determination is quite
large.
OTHER
ISSUES IN PERFORMANCE
EVALUATION:
Monitoring
Performance:
Portfolio
evaluation of managed portfolios
should be a continuing process.
The results of
the
portfolio must be calculated
using some of the techniques
discussed above. In
addition,
a
monitoring process should
evaluate the success of the
portfolio relative to the
objectives
and
constraints of the portfolio's
owners.
Performance
Attribution:
Most
of this chapter has considered
how to measure a portfolio
manager's performance.
However,
portfolio evaluations also to concern
with the reasons why a manager
did better or
worse
than a properly constructed
benchmark with complete
risks adjustment. This part
of
portfolio
evaluation is called performance
attribution, which seeks to
determine, after the
fact,
why a particular portfolio had a given
return over some specified
time period and,
therefore,
why success or failure
occurred.
Typically,
performance attribution is a topdown
approach; it looks first at
the broad issues
and
progresses by narrowing the
investigation its purpose is to decompose
the total
performance
of a portfolio into specific
components that can be associated
with specific
decisions
made by the portfolio
manager.
.
Performance
attribution often begins with,
the policy statement that
guides the management
of
the portfolio; the portfolio
normally would have a set of
portfolio weight to be used.
If
the
manager uses a different set,
this will account for some
of the results. In effect, we
are
looking
at the asset allocation
decision. If the manager chooses to
allocate portfolio
funds
differently
than the weights that
occur in the benchmark
portfolio, what are the
results?
After
this analysis performance
attribution might analyze sector
(industry) selection and
security
selection. Did the manager
concentrate on or avoid certain sectors,
and if so what
were
the results? Security
selection speaks for
itself.
Part of
this process involves
identifyinga benchmark of performance to
use in comparing
the
portfolio results. This
bogey is designed to measure
passive results, ruling out
both asset
allocation
and security selection decisions. Any
differences between the
portfolio's results
and
the bogey must be
attributable to one or more of these
decisions made by the
portfolio
manager.
Another
way to think about
performance attribution is to recognize
that performance
different
from a properly constructed
benchmark comes from one of
two sources, or both:
1.
Market timing
2.
Security selection
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Techniques
are available to decompose
the performance of a portfolio
into these two
components.
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