UNDERSTANDING COMMON
PORTFOLIO STATISTICS
The charts used throughout this manual are for illustrative purposes only and
do not represent the actual performance of any specific investment.
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Alpha
Alpha
6
5.49
5
Alpha, %
Measures risk-adjusted performance, factoring in the
risk due to the specific manager rather than the overall
market. A high value for alpha implies that the manager
has performed better than would have been expected,
given its beta (volatility). In contrast, a negative alpha
indicates the manager has underperformed, given the
expectations established by beta.
4
3
2
1
Why it’s important
Alpha can be used to directly measure the value added
or subtracted by a manager. Alpha depends on
two factors: (1) the assumption that market risk, as
measured by beta, is the only risk measure necessary;
and (2) the strength of the linear relationship between
the manager and the index, as it has been measured by
R-squared. In addition, a negative alpha can sometimes
result from the additional expenses that are present in a
manager’s returns as compared to the benchmark index.
0
–1
–0.32
5 Years
Portfolio A: 5.49%
Has shown a very high positive alpha, indicating the manager
has added more return than its beta implies.
Portfolio B: –0.32%
Has provided a negative alpha, showing that the manager’s
returns have been lower than its beta would imply.
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Batting Average
The batting average of a manager versus a benchmark
is the ratio between the number of periods when the
manager outperformed the benchmark and the total
number of periods.
’12
Batting Average
’11
’10
’09
Why it’s important
Batting average shows consistency of outperformance.
For example, this manager outperformed the benchmark
in 7 out of 10 periods. So the batting average for the
manager would be 70%. Ideally you want a manager
that has a batting average greater than 50%.
’08
’07
’06
’05
’04
’03
–10
–5
0
5
10
15
20
25
30
Excess Return, %
Benchmark: Russell 1000® Growth Index. The Russell 1000 Growth Index
contains those securities in the Russell 1000® Index with a greater-thanaverage growth orientation. Companies in this index tend to exhibit
higher price-to-book ratios, lower dividend yields, and higher forecasted
growth rates. These indexes are unmanaged. An investment cannot be
made directly in an index.
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Beta
Why it’s important
Beta can be used to show how sensitive a manager
is to movements in the market. It is important to note
that a low beta for a manager does not necessarily
imply that the manager has a low level of volatility.
A low beta signifies only that the manager’s marketrelated risk is low. (Standard deviation is a measure of
a fund’s absolute volatility.) R-squared is a necessary
statistic to factor into the equation because it reflects
the percentage of a manager’s movements that are
explained by movements in its benchmark index, and
thus whether it is an appropriate benchmark.
Beta
1.5
1.37
1.05
1.0
Beta, %
Shows the volatility of a manager as compared to the
volatility of the benchmark; specifically, the performance
the stock, fund, or portfolio has experienced in a given
period of time as the index moved 1% up or down. A beta
above 1 is more volatile than the index, while a beta below
1 is less volatile.
0.5
0.0
5 Years
Portfolio A: 1.05%
n Taking on 5% more volatility than the index.
n If the index goes up by 1%, this manager is likely to go up by 1.05%.
n If the index goes down by 1%, this manager is likely to go down 1.05%.
Portfolio B: 1.37%
n Taking on 37% more volatility than the index.
n If the index goes up by 1%, this manager is likely to go up by 1.37%.
n If the index goes down by 1%, this manager is likely to go down 1.37%.
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Correlation
1
A statistical measure of how two assets move together
and is bounded by +1 and –1. A correlation of +1
indicates that the assets are perfectly positively
correlated and move in tandem—when one goes up, the
other also goes up. A correlation of –1 indicates the two
assets are perfectly negatively correlated and move in
opposite directions.
2
Fund 1
3
Fund 2
0.19
Fund 3
0.63
0.07
Fund 4
0.66
0.28
0.93
Fund 5 –0.08
0.51
–0.38 –0.18
Fund 6 –0.08
0.53
–0.37 –0.18
0.97
Why it’s important
Fund 7 –0.03
0.59
–0.32 –0.13
0.95
0.93
When creating a portfolio, correlation can tell you how the
managers within the portfolio will perform together over
time. Portfolios that contain low-correlated managers will
tend to be less volatile and have lower risk.
Fund 8 –0.15
0.47
–0.42 –0.24
0.94
0.96
0.86
Fund 9 –0.02
0.35
–0.17 –0.06
0.64
0.65
0.63
0.65
0.43
–0.08
0.61
0.60
0.65
0.48
Fund 10
0.16
High
.70 to 1.0
4
5
0.09
Moderate
.11 to .69
6
7
None
.10 to –.10
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8
9
Moderate Neg
–.11 to –.69
10
0.25
Highly Neg
–.70 to –1.0
Duration
Measures the approximate price volatility of a bond or
bond portfolio for a small change in interest rates. For
example, if a bond portfolio has a duration of 5, for a
1% change in interest rates up or down, the bond price
will fall or rise by approximately 5%.
Duration
Bond Portfolio A*
6.2
Bond Portfolio B
4.5
Bond Portfolio C
3.1
*Bond Portfolio A’s higher duration implies more
price volatility for a change in interest rates.
Why it’s important
In changing interest-rate environments, duration can alert
an investor to how much volatility his or her portfolio will
experience, allowing the investor to make changes to his
or her investments accordingly.
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Information Ratio
Is determined by taking the annualized excess return over a
benchmark and dividing it by the standard deviation of excess
return (tracking error). This measure relates the magnitude
and consistency with which an investment outperformed its
benchmark. The higher the information ratio, the better.
Why it’s important
Information Ratio
Manager A
–0.30
Manager B
0.60
Manager C*
1.20
*Manager C’s higher information ratio shows that
the manager consistently added more return per
unit of risk.
The information ratio is a risk-adjusted measure, which
captures excess or active returns and relates them to excess or
active risk. The information ratio is used as a way to compare
more- and less-aggressive managers at the same time.
A convenient way to think of the information ratio is as a
measure of how well one was rewarded for each incremental
“unit” of risk. The information ratio can be a very valuable tool
in evaluating a manager’s ability to add incremental value relative
to incremental risk. This tool is only valuable, however, when
the benchmark is carefully chosen and appropriate.
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R-squared
Reflects the percentage of a manager’s movements
that can be explained by movements in its benchmark
index. Values range from 0 to 100, where 0 indicates no
correlation and 100 indicates perfect correlation. An
R-squared measure of 35, for example, means that only
35% of the manager’s movements can be explained by
movements in the benchmark index.
R-Squared
Manager A*
95
Manager B
75
Manager C
66
*Manager A’s high R-squared gives greater
confidence in any alpha and beta calculations.
Why it’s important
R-squared can be used to ascertain the significance of
a particular alpha or beta. The higher the R-squared, the
more confidence we have in the values for alpha and
beta. Ideally you want to choose a benchmark that has
an R-squared of 85% or higher to your manager.
On the other hand, an R-squared value that is close to
0 indicates that alpha and beta are not particularly
useful because the manager is being compared against
an inappropriate benchmark.
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Risk/Return Chart
A Risk/Return chart shows the relationship between
the return of a manager and its associated risk as
represented by standard deviation.
Risk/Return: 3 Years
Manager
16
Total Annualized Return, %
Why it’s important
The ideal plot in this chart is in the upper left corner,
indicating that the manager outperformed the benchmark
with less risk. The same chart can be drawn to compare
a manager to the median of its peer group.
Benchmark
14
12
10
8
6
4
2
0
0
2
4
6
8
10
12
14
16
Total Annualized Std Dev, %
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18
20
22
Sharpe Ratio
A risk-adjusted measure developed by William F. Sharpe,
calculated using standard deviation and excess return
to determine reward per unit of risk—the higher the
Sharpe ratio, the better the manager’s historical riskadjusted performance.
Sharpe ratio is a measure of investment efficiency
expressed as the amount of return earned per unit
of associated risk. It can be used to compare two
managers directly on how much excess return each
manager achieved for a certain level of risk.
■ 5th to 25th Percentile
■ 25th Percentile to Median
■ Median to 75th Percentile
■ 75th to 95th Percentile
2
Sharpe Ratio
Why it’s important
Sharpe Ratio, Morningstar Large Blend Universe
Manager A
S&P 500 Index
1
0
–1
3 Years
5 Years
Manager A
S&P 500 Index
Morningstar Large Blend Universe Median
3 Years
1.65
1.30
1.23
5 Years
0.34
–0.04
–0.07
Example: As you can see, Manager A has achieved more return per unit
of risk than the S&P 500 Index and the Morningstar Large Blend category
median. The S&P 500 is a weighted, unmanaged index, comprised of
500 stocks, which serves as a broad indicator of stock price movements.
An investment cannot be made directly in an index.
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Standard Deviation
The statistical measurement of dispersion of returns
spread around their historical average, or in other words,
how widely a stock or portfolio’s returns varied over a
certain period of time.
Why it’s important
Investors use the standard deviation of historical
performance to try to predict the range of returns that
are most likely for a given investment. When
a stock or portfolio has a high standard deviation,
the predicted range of performance is wide, implying
greater volatility.
Standard
Deviation
Avg Annual
Return
Predicted
Return
Range
(3-Year)
(3-Year)
Manager A
11%
10%
–1% to 21%
Manager B*
20%
10%
–10% to 30%
*Although both managers returned an average of 10% per year, Manager B
exhibited more volatility.
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Style Charts
Style charts are typically used to show where a manager
lies on the value-to-growth and small- to large-cap
spectrums. You will often see a style chart on which
four to six style reference indexes are plotted, with the
value-oriented ones on the left and the growth-oriented
on the right, small cap at the bottom, and large cap at
the top.
In this illustration you can see the style movement of
two managers across the style spectrum. The smaller
plots represent earlier points in time, the large more
recent. As you can see, the triangular-shaped manager
has exhibited style drift from small cap to large cap.
The circular-shaped manager has been style-consistent
over time, with the plots tightly grouped together. When
building a portfolio, style consistency is an important
consideration.
36-month moving average
Lg Value
Lg Growth
Sm Value
Sm Growth
Small - Large
Why it’s important
Style
Value - Growth
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Tracking Error
Is a measure of how closely the manager follows the
index, and is measured as the standard deviation of the
difference between the manager and index returns.
Why it’s important
The sophisticated investor is concerned with both relative
and absolute performance. A tool such as tracking error
can be used to provide an acceptable range of relative
performance when evaluating a manager. Style bets,
security selection, transaction costs, and fees may cause
high tracking error. An active manager whose sector and
security selection deviates widely from the index may
exhibit high tracking error. A passively managed index
fund is expected to replicate the returns of an index
and should have a low tracking error.
Tracking Error
Manager A*
4.2
Manager B
8.7
Manager C
10.5
*Manager A has exhibited lower volatility relative
to the benchmark.
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Up Market/Down Market Capture Ratio
Shows what portion of market performance was
captured by a manager in up and down markets. An
up market is defined as periods when the benchmark
return is positive and a down market is defined as
periods when the benchmark return is negative.
The ideal plot in this chart is in the upper left
corner, indicating that the manager outperformed the
benchmark in both up and down markets, capturing
more than 100% of performance in positive periods and
less than 100% in negative periods.
Manager
Benchmark
140
Up Mkt Capture Ratio, %
Why it’s important
Up/Down Capture: 3 Years
120
100
80
60
40
20
0
0
10
20
30 40 50 60 70 80
Down Mkt Capture Ratio, %
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90 100 110
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0207214-00004-00 PI1574 Expiration 05/31/2018