The
following provides
a brief description
of each statistic
used in our analysis
and gives the
formula used
to calculate
each. Annualized
statistics are
based on monthly
data, unless
Quarterly data
is specified.
Value
Added Monthly
Index (VAMI)  This index
reflects the
growth of a hypothetical
$1,000 in a given
investment over
time. The index
is equal to $1,000
at inception.
Subsequent monthend
values are calculated
by multiplying
the previous
month’s VAMI
index by 1 plus
the current month
rate of return.
Where
Vami 0=1000
and
Where R _{N}=Return for period N
Vami _{N}=( 1
+ R _{N }) ´ Vami _{N1
}
Compound
(Geometric) Average
Return  The
geometric mean
is the monthly
average return
that assumes
the same rate
of return every
period to arrive
at the equivalent
compound growth
rate reflected
in the actual
return data.
In other words,
the geometric
mean is the monthly
average return
that, if applied
each period,
would give you
a final Vami
(growth) index
that is equivalent
to the actual
final Vami index
for the return
stream you are
considering.
Annualized compound
quarterly and
annualized returns
are calculated
using the compound
monthly return
as a base.
Where
N=Number of
periods
Where
Vami _{0}=1000
Compound
Monthly ROR=( Vami _{N} ¸ Vami _{0} ) ^{1/ N}  1
Compound
Quarterly
ROR=( 1 + Compound Monthly ROR ) ^{3}  1
Compound
Annualized
ROR=( 1
+ Compound
Monthly ROR ) ^{12}  1
Standard
Deviation 
Standard Deviation
measures
the dispersal
or uncertainty
in a random variable
(in this case,
investment returns).
It measures the
degree of variation
of returns around
the mean (average)
return. The higher
the volatility
of the investment
returns, the
higher the standard
deviation will
be. For this
reason, standard
deviation is
often used as
a measure of
investment risk.
Where
R _{I}=Return
for period
I
Where
M _{R}=Mean
of return set
R
Where
N=Number of
Periods
_{N}
M _{R }=( S R _{I} ) ¸ N
^{I=1}
N
Standard Deviation=( S ( R _{I} 
M _{R} ) ^{2} ¸ (N  1) ) ^{½}
^{I=}
Annualized
Standard
Deviation
Annualized
Standard
Deviation=Monthly
Standard
Deviation ´ (
12 ) ^{
½}
Annualized
Standard
Deviation
* =Quarterly
Standard
Deviation ´ ( 4 )
^{
½}
*
Quarterly Data
M _{G} =
( S G _{I} ) ¸ N _{G}
^{I=1}
Downside
Deviation  Similar
to the loss standard
deviation except
the downside
deviation considers
only returns
that fall below
a defined Minimum
Acceptable Return
(MAR) rather
then the arithmetic
mean. For example,
if the MAR were
assumed to be
10%, the downside
deviation would
measure the variation
of each period
that falls below
10%. (The loss
standard deviation,
on the other
hand, would take
only losing periods,
calculate an
average return
for the losing
periods, and
then measure
the variation
between each
losing return
and the losing
return average).
Where
R _{I}=Return
for period
I
Where
N=Number of
Periods
Where
R _{MAR}=Period
Minimum Acceptable
Return
Where
L _{I}=R _{I}  R _{MAR }(
IF R _{I}  R _{MAR} < 0
)or 0 ( IF
R _{I}  R
_{
MAR ³
}
0
)
_{
N}
Downside
Deviation=(
(S ( L _{I }) ^{2} ) ¸ N ) ^{½}
I=1
Downside
Deviation =
( (S (
L _{I }) ^{2} ) ¸ N ) ^{½ }
^{ I }
Where
N_{L}=Number
of Periods
where R _{I}  M < 0
N
Sharpe
Ratio  A return/risk
measure developed
by William Sharpe.
Return (numerator)
is defined as
the incremental
average return
of an investment
over the risk
free rate. Risk
(denominator)
is defined as
the standard
deviation of
the investment
returns.
Where
R _{I}=Return
for period
I
Where
M _{R}=Mean
of return
set R
Where
N=Number
of Periods
Where
SD=Period
Standard
Deviation
Where
R _{RF}=Period
Risk Free
Return
_{ N}
M _{R }=( S R _{I} ) ¸ N
^{I=1}
N
SD=( S ( R _{I}  M _{R} ) ^{2} ¸ (N  1) ) ^{½}
^{
I=1}
Sharpe
Ratio=( M _{R}  R _{RF} ) ¸ SD
Annualized
Sharpe
Ratio
Annualized
Sharpe=Monthly
Sharpe ´ (
12 )
^{
½}
Annualized
Sharpe
* =Quarterly Sharpe ´ ( 4 )
^{
½ }* Quarterly Data
Sortino
Ratio  This
is another
return/risk
ratio developed
by Frank Sortino.
Return (numerator)
is defined
as the incremental
compound average
period return
over a Minimum
Acceptable
Return (MAR).
Risk (denominator)
is defined
as the Downside
Deviation below
a Minimum Acceptable
Return (MAR).
Where
R _{I}=Return
for period
I
Where
N=Number
of Periods
Where
R _{MAR}=Period
Minimum
Acceptable
Return
Where
DD _{MAR}=Downside
Deviation
Where
L _{I}=R _{I}  R _{MAR }(
IF R _{I}  R _{MAR} < 0
)or 0 (
IF R _{I}  R
_{
MAR ³
}
0
)
_{
N}
DD _{MAR}=( (S ( L _{I }) ^{2} ) ¸ N ) ^{½}
I=1
Sortino
Ratio=( Compound Period Return  R _{MAR} ) ¸ DD _{MAR}
Annualized
Sortino
Ratio
Annualized
Sortino=Monthly
Sortino ´ (
12 )
^{
½}
Annualized
Sortino* =Quarterly Sortino ´ ( 4 )
^{
½ }
*
Quarterly
Data
Calmar
Ratio  This
is a return/risk
ratio. Return
(numerator)
is defined
as the Compound
Annualized
Rate of Return
over the
last 3 years.
Risk (denominator)
is defined
as the Maximum
Drawdown
over the
last 3 years.
If three
years of
data are
not available,
the available
data is used.
ABS is the
Absolute
Value.
Sterling
Ratio  This
is a return/risk
ratio. Return
(numerator)
is defined
as the Compound
Annualized
Rate of Return
over the
last 3 years.
Risk (denominator)
is defined
as the Average
Yearly Maximum
Drawdown
over the
last 3 years
less an arbitrary
10%. To calculate
this average
yearly drawdown,
the latest
3 years (36
months) is
divided into
3 separate
12month
periods and
the maximum
drawdown
is calculated
for each.
Then these
3 drawdowns
are averaged
to produce
the Average
Yearly Maximum
Drawdown
for the 3year
period. If
three years
of data are
not available,
the available
data is used.
Where
D1 Calmar
Ratio =
Compound
Annualized
ROR ¸ ABS (Maximum Drawdown)
=
Maximum
Drawdown
for first
12 months
Where
D2 = Maximum
Drawdown
for next
12 months
Where
D3 = Maximum
Drawdown
for latest
12 months
Average
Drawdown
= ( D1
+ D2 +
D3 ) ¸ 3
Sterling
Ratio =
Compound
Annualized
ROR ¸ ABS ( (Average Drawdown  10% ))
Drawdown  Drawdown
is any losing
period during
an investment
record. It
is defined
as the percent
retrenchment
from an equity
peak to an
equity valley.
A Drawdown
is in effect
from the
time an equity
retrenchment
begins until
a new equity
high is reached.
(i.e. In
terms of
time, a drawdown
encompasses
both the
period from
equity peak
to equity
valley (Length)
and the time
from the
equity valley
to a new
equity high
(Recovery).
Maximum
Drawdown is simply
the largest
percentage
drawdown
that has
occurred
in any investment
data record.
