Workstation Calculation Guide - Morningstar

20 Correlation
Correlation coefficient measures the extent to which the returns of a fund and a benchmark are
related. Values vary between 1 and –1. A correlation of 1 would indicate a perfect positive
correlation, i.e., a fund’s returns move exactly in line with its benchmark. A correlation of -1 would
indicate a perfect negative correlation, i.e., a fund’s returns move in the exact inverse of its
benchmark.
where
r xy
xy
n
n
2
n
xi
xi
i1
i1
x
,
n(
n 1)
x
2
y
y
n
n
i1
n
2
y
i
i
n(
n 1)
1
2
y
i
21 Correlation (Bull)
Bull correlation measures the relationship between a fund and positive market movements.
xy
r xy
, where y i is positive.
See Item 11 for and , and Item 12 for .
x
y
x
y
xy
22 Correlation (Bear)
Measures the relationship between a fund and negative market movements.
xy
r xy , where y i is negative.
See Item 11 for and , and Item 12 for .
x
y
x
y
xy
23 Covariance
A measure of how much the fund and its benchmark move together. A positive covariance shows
that the returns of a fund and its benchmark move in the same direction. A negative covariance
shows that the returns of a fund and its benchmark move in opposite direction.
xy
1
n 1
n
i1
x
xy
y
i
i
24 Down-Down Periods
It’s the percentage of the total number of observations where a negative return was followed by
another negative return. Note: The divisor is the number of observations minus 1.
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