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Essential Performance Metrics to Evaluate
and Interpret Investment Returns
Alpha, beta, Sharpe ratio: these metrics are ubiquitous
tools of the investment community. Used correctly, they can
help investors better evaluate their investment decisions. Used
incorrectly, they may lead to erroneous conclusions.
Effectively evaluating an investment goes beyond observing short-term absolute
returns. Numerous measures can help decipher the full implications of various
investment choices by examining factors such as return, risk and performance
of the portfolio. This report identifies and explains popular performance metrics
and utilizes a hypothetical case study to illustrate evaluation techniques that may
help determine whether an investment manager has succeeded in effectively
implementing their investment objectives. Understanding the metrics in this
report will help to holistically interpret portfolio performance and will assist in
the manager evaluation and selection process. It is important to note that these
metrics are not an exclusive means for evaluating investment performance.
Other qualitative factors, such as an investor’s investment objectives and appetite
for risk and the manager’s investment technique and philosophy, should be
taken into consideration during the selection and evaluation process.
Each metric will be illustrated using the following hypothetical
case study assumptions:
▪▪ Two hypothetical managers, Manager A and Manager B, have similar investment styles and measure their performance against the same hypothetical benchmark.
▪▪ The risk-free rate of return is 3.00%.
▪▪ The most recent annual returns for each manager and the benchmark
are listed below.
Year
1
Benchmark
Manager A
Manager B
4.00%
5.00%
2.00%
2
20.00
15.00
28.00
3
-5.00
-2.00
-8.00
4
5.00
7.00
4.00
Please refer to opposite page for case study summary.
In the hypothetical above, all returns are provided gross of fees. It is important to remember that investment management fees would otherwise reduce the performance that
an investor would experience.
Case Study Summary
The metrics provide some valuable insight when evaluating both managers:
▪▪ Although Manager B produced a greater arithmetic return, Manager A
produced the greater geometric (compounded) return.
▪▪ Both managers provided positive excess return above the benchmark.
▪▪ Manager A was more consistent (less risky) than Manager B and the
benchmark, as evidenced by the lower standard deviation and beta.
▪▪ Manager A was more defensive (lower downside capture ratio), while Manager
B was more aggressive (higher upside capture ratio).
▪▪ Manager A was more successful in outperforming on a risk-adjusted basis,
measured by a positive alpha and higher Sharpe ratio.
▪▪ Manager A provides a greater probability of continuing to outperform the
benchmark, given the higher information ratio.
▪▪ The returns of the managers were highly correlated to the selected benchmark,
further validating their alpha and beta metrics.
Formula Key
ri : rate of return
ARi : interim active return
xi : interim return
ARavg : average active return
xavg : average of all returns
p : standard deviation of portfolio
n : number of years
m : standard deviation of market
Rp : return of portfolio
wfund, i : weight of asset i in the fund
Rf : risk-free rate of return
windex, i : weight of asset i in the index
Rm : return of market
COVp,m : covariance of portfolio and market
Rb : return of benchmark
COVA,B : covariance of portfolio A and portfolio B
n
∑ (a -a ) (b -b )
i
avg
i
avg
i=1
=
n-1
Conclusion
An enhanced understanding of performance metrics can help advisors evaluate different investment options for their clients, and, when used correctly, can
help them better communicate their recommendations and inspire investor
confidence. These metrics do not, however, provide a complete perspective alone,
and should be used in conjunction with a manager’s qualitative characteristics
(investment philosophy, process, portfolio holdings, etc.) in the evaluation and
selection process.
Metric
Measuring Returns
Arithmetic Mean Rp
Geometric Return Rg
Excess Return ER
Description
The arithmetic mean, or simple average, treats each year’s return as an
isolated event and excludes the impact
of compounding. The arithmetic mean
is calculated by summing the returns
for each time period, and dividing by
the number of periods.
The geometric average treats returns
as part of a continuous, single
experience and includes the impact
of compounding. The geometric or
time-weighted return is measured
by linking periodic returns through
multiplication.
Excess return measures the amount by
which an investment outperforms its
respective benchmark. Excess return is
the unadjusted, or absolute, difference
between the manager’s results, measured
arithmetically, and the benchmark returns,
both positive and negative.
What it
Measures
The average return over an
investment period.
The compounded return over an
investment period.
The manager’s return compared to the
benchmark over an investment period.
How to
Interpret
All else equal, a higher arithmetic
return is better.
All else equal, a higher geometric
return is better.
A positive excess return indicates the manager outperformed
the benchmark;
a higher excess return is better.
Important
Considerations
Often the starting point for evaluating
performance, this is likely to be the return investors calculate by themselves.
The arithmetic mean is an input to
calculate other ratios, such as Sharpe
ratio and Alpha, described later.
Most money managers report their
returns using the geometric average
because it reflects the actual growth or
reduction of dollars in a portfolio more
accurately than the arithmetic mean.
The geometric average will always be
expressed as a lower percentage than
the arithmetic average, assuming a varied return sequence and a time period
greater than one year.
While the metric can be useful as a
functional screening tool, it ignores
an important issue — the level of risk
assumed to achieve those results.
Formula
r1 + r2 + ... +rn
n
1
[(1+r1)(1+r2)...(1+rn)] n -1
Case Study
Benchmark: 6.00%
Manager A: 6.25%
Manager B: 6.50%
Benchmark: 5.63%
Manager A: 6.08%
Manager B: 5.72%
Refer to case study
assumptions and
summary sections for
additional information.
Manager B earned a higher
arithmetic return.
Manager A earned a higher
geometric return.
Rp - Rb
Manager A: 0.25%
Manager B: 0.50%
Both managers provided excess
return, but Manager B had higher
excess return.
Measuring Risk
Measuring Risk-Adjusted Returns
Standard
Deviation 
Beta β
Alpha 
Sharpe Ratio SR
Standard deviation indicates the
consistency of a manager’s returns.
It is a measure of total volatility,
both systematic (market related) and
non-systematic (security specific).
It is calculated by selecting a series
of returns; finding the difference or
variance around the mean of those
returns; summing the squared deviations from the mean; and dividing by
the number of observations (minus
one degree of freedom for a sample).
Beta is a measure of sensitivity to
the market benchmark. It measures
the volatility of a security or portfolio
relative to the market as a whole
(systematic risk only). It is calculated
as the covariance between a portfolio and the market divided by the
market variance.
Jensen’s alpha is the portfolio’s
risk-adjusted performance or “value
added” by a manager. Alpha is the
incremental return between a manager’s actual results and the expected
results, given the level of risk.
The Sharpe ratio measures the efficiency of a portfolio. It quantifies the
return received in exchange for risk
assumed. It is calculated by taking the
return of a portfolio above a risk-free
rate divided by the portfolio standard deviation.
The overall volatility of the manager
relative to its average return.
The volatility of the manager relative
to the overall market.
The manager’s return in excess of
what would be forecasted by the
portfolio’s market exposure.
The efficiency of the portfolio,
defined as the return net of cash per
unit of volatility around a portfolio’s
average return.
A lower standard deviation indicates
more consistent performance and
lower risk; a higher standard deviation indicates less consistency and
higher risk. The greater the standard deviation, the more varied the
return sequence.
A beta of 1.0 indicates that a manager
would respond similarly to the market.
A beta greater than 1.0 indicates that
a portfolio would be more responsive
to movements in the market, while
a beta below 1.0 indicates a more
muted response.
A positive alpha indicates that a selected portfolio has produced returns
above the expected level at the same
level of risk, and a negative alpha suggests the portfolio underperformed
given the level of risk assumed.
The higher the Sharpe ratio, the better.
Standard deviation is the expected
variance of future returns on either
side of the average, based on behavior
of past performance, and does not
differentiate between returns above or
below the mean.
Aggressive investors may choose
portfolios with higher betas, while defensive investors may focus on lower
beta investments.
For a given level of risk, a higher value
added by a manager is desirable.
It helps equalize returns of managers within the same asset class so
they can be compared on a riskadjusted basis.
n
∑ (x -x )2
i avg
i=1
n-1
Benchmark: 10.36%
Manager A: 6.99%
Manager B: 15.26%
Manager A was more consistent (less
risky) than both Manager B and the
benchmark, as measured by a lower
standard deviation.
COVp,m
m2
RP - [Rf+βp(Rm-Rf)]
Manager A: 0.67
Manager B: 1.47
Manager A: 1.25%
Manager B: -0.90%
Manager A was more defensive; Manager B was more aggressive.
Manager A outperformed on a riskadjusted basis indicated by a higher,
positive alpha. Manager B underperformed on a risk-adjusted basis
indicated by a negative alpha.
Rp- Rf
p
Benchmark: 0.29
Manager A: 0.46
Manager B: 0.23
Manager A had a more efficient portfolio than Manager B.
Measuring Performance Com
R-Squared R2
Active Share AS
Tracking Error TE
R-squared, also referred to as the coefficient of
determination, represents the dependence of one
variable (the manager’s return) on another variable
(the benchmark return). It is calculated by squaring
the correlation coefficient between the manager
and the benchmark. Alternately, R-squared can be
calculated by squaring beta, multiplying this term
by the market variance and dividing by the manager’s variance.
Active share measures the percentage of the manager’s portfolio holdings that are different from the
benchmark. It is calculated using the weight of each
stock held by the manager relative to the weight of
each stock in the benchmark. For a manager that
never shorts stock and never buys on margin, active
share will be between 0% and 100%.
Tracking error measures active risk or the variability
of a portfolio’s return compared to the benchmark.
It is calculated as the standard deviation (consistency) of the active return, or alpha.
The percentage of a manager’s return directly attributable to the benchmark.
The degree to which the manger is selecting stocks
that are different from its benchmark.
The volatility of the manager relative to its
benchmark return.
Many research professionals agree that an Rsquared above .70 indicates a “good fit” between
the manager and benchmark, validating the benchmark as suitable.
Higher active share implies a greater amount of
positions that are different from the benchmark,
interpreted as a greater degree of stock picking.
For an index or a passive manager, tracking error
should be close to zero, while active managers, especially those that have produced significant excess
return, usually have higher tracking errors.
R-squared is used to select an appropriate benchmark. It helps identify the percentage of a manager’s return that is specifically attributable to
underlying benchmark volatility. The residual is
active manager risk that may improve or reduce a
manger’s results based on their skills. A strong Rsquared also provides confidence that the alpha and
beta of the portfolio are reasonably accurate.
A manger can only outperform a benchmark by taking positions that are different from the benchmark.
Some amount of positive active share is a necessary but not sufficient condition for outperforming
the benchmark.
Investors can eliminate active risk by simply indexing their portfolios.
ß2x m2
p
2
Manager A: 0.98
Manager B: 0.99
Both Manager A and Manager B have a good fit with
the benchmark.
n
½ ∑ │wfund, i-windex, i│
i=1
Manager A: 65%*
Manager B: 80%*
* Because calculation of active share requires analysis of portfolio and benchmark holdings, which
are not included in the case study, these results
are estimated.
Manager B engaged in a greater degree of stock
picking relative to the benchmark than Manager A.
Tracking error by itself is not necessarily good or
bad. It can help identify the extent the investment
experience may vary from the benchmark. A high
tracking error may be useful in identifying potential style drift.
n
∑ (AR - AR )2
i
avg
i=1
n-1
Manager A: 3.59%
Manager B: 5.07%
Manager B’s portfolio was more varied compared
with the benchmark than Manager A’s portfolio.
mpared to a Benchmark
Information Ratio IR
Capture Ratio CR
Correlation Coefficient ρ
The information ratio provides guidance regarding a manager’s ability to persistently produce
returns above the benchmark. It is calculated
by the excess return in the numerator divided
by the tracking error, or consistency of excess
return, in the denominator.
The capture ratio is presented as two numbers,
up-capture and down-capture. The downside
capture ratio measures, on an absolute basis,
how much of a benchmark’s decline was captured by the portfolio. Downside capture ratio is
calculated by dividing the portfolio performance
by the benchmark performance during periods
when the benchmark performance is negative.
Upside capture ratio is similarly defined as
the percentage portfolio return divided by the
market return when the market rises.
Correlation measures the relationship or
association that two variables have to each
other. It is calculated as the covariance between
two investments divided by the product of their
standard deviations.
A manager’s ability to add incremental value
relative to incremental risk.
The degree of under- or outperformance by a
manager compared to the benchmark.
The direction and degree of linear relation
between two investments.
A higher information ratio is desirable.
Defensive portfolios would typically have downside capture ratios of less than 1.0. Aggressive
portfolios would typically have upside capture
ratios greater than 1.0.
A high association between two variables means
they tend to move in the same direction and a
low association means they tend to diverge. A
correlation of 1.0 represents perfect correlation,
a correlation of -1.0 represents perfect negative
correlation, and a correlation of 0.0 offers no
predictive value.
Some consider this metric a more sophisticated
Sharpe ratio. Ideally, a manager would seek to
add excess return in a consistent manner so
that returns do not swing too far from their
benchmark in any given period. The information
ratio can be used to compare managers across
asset classes.
Capture ratios do not incorporate risk; they
simply measure the under- or outperformance of
a portfolio compared to
the benchmark.
Blending assets that do not move in tandem
may help reduce a portfolio’s overall volatility.
The correlation coefficient between two assets
helps to determine the potential benefits of
diversification.
Rp- Rb
TE
Manager A: 0.069
Manager B: 0.0986
Manager B’s higher information ratio indicates a greater consistency in outperforming
the benchmark.
Up
(Down) =
Capture
Manager returns
when benchmark is
positive (negative)
covA, B
A x B
Benchmark
returns when
positive (negative)
Manager A: 0 .40 downside;
0.93 upside
Manager B: 1 .60 downside;
1.17 upside
Manager A was more defensive (lower downside
capture ratio), while Manager B was more aggressive (higher upside capture ratio).
Correlation A, B : 0.97
Manager A and Manager B have high positive
correlation, indicating the portfolios tend to
move in tandem.
DISCLOSURES
This report is provided for educational and informational purposes only. The statements contained herein are based upon the opinions of Nuveen Investments Wealth Management
Services. All opinions and views constitute our judgments as of the date of writing and are subject to change at any time without notice. This information contains no investment recommendations and should not be construed as specific tax, legal, financial planning or investment advice. Please note that this information should not replace a client’s consultation with a
professional advisor regarding their tax situation. Clients should consult their professional advisors before making any tax or investment decisions. Information was obtained from third
party sources, which we believe to be reliable but not guaranteed.
Hypothetical examples are shown for illustrative and educational purposes only. All indices are unmanaged and unavailable for direct investment. Index returns include reinvestment
of dividends and do not reflect investment advisory and other fees that would reduce performance in an actual client account. Different benchmarks and economic periods will produce
different results. Other methods may produce different results, and the results for the individual portfolios and for different periods may vary depending on market conditions and the
composition of the portfolio. Past performance is no guarantee of future results. All investments carry a certain degree of risk and there is no assurance that an investment will provide
positive performance over any period of time. Since no one manager is suitable for all types of investors, it is important to review investment objectives, risk tolerance, tax objectives and
liquidity needs before choosing an investment style or manager. Securities offered through Nuveen Securities, LLC, an affiliate of Nuveen Investments, Inc.
© 2016 Nuveen Investments, Inc.
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