How to calculate standard deviation of a portfolio in excel?
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How to Calculate the Standard
Deviation of a Portfolio
The standard deviation of a portfolio
represents the variability of the returns of a
portfolio. To calculate it, you need some
information about your portfolio as a
whole, and each security within it.
Steps
Calculate the standard deviation of
each security in the portfolio. First
we need to calculate the standard
deviation of each security in the
portfolio. You can use a calculator or
the Excel function to calculate that.
Let's say there are 2 securities in
the portfolio whose standard
deviations are 10% and 15%.
Determine the weights of securities
in the portfolio. We need to know
the weights of each security in the
portfolio.
Let's say we've invested $1000 in
our portfolio of which $750 is in
security 1 and $250 is in security
2.
So the weight of security 1 in
portfolio is 75% (750/1000) and
the weight of security 2 in portfolio
is 25% (250/1000).
Find the correlation between two
securities. Correlation can be
defined as the statistical measure of
how two securities move with respect to
each other.
Its value lies between -1 and 1.
-1 implies that the two securities
move exactly opposite to each
other and 1 implies that they move
in exactly the same way in same
direction.
0 implies that there is no relation
as of how the securities move with
respect to each other.
For our example, let's take
correlation as 0.25 which means
that if one security increases by
$1, the other increases by $0.25.
Calculate the variance. Variance is
the square of standard deviation.
For this example, variance would
be calculated as (0.75^2)*(0.1^2)
+ (0.25^2)*(0.15^2) +
2*0.75*0.25*0.1*0.15*0.25 =
0.008438.
Calculate standard deviation.
Standard deviation would be square
root of variance.
So, it would be equal to
0.008438^0.5 = 0.09185 =
9.185%.
Interpret the standard deviation. As
we can see that standard deviation
is equal to 9.185% which is less than
the 10% and 15% of the securities, it is
because of the correlation factor:
If correlation equals 1, standard
deviation would have been 11.25%.
If correlation equals 0, standard
deviation would have been 8.38%.
If correlation equals 1, standard
deviation would have been 3.75%
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2
3
4
5
6
How to Calculate the Standard
Deviation of a Portfolio
The standard deviation of a portfolio
represents the variability of the returns of a
portfolio. To calculate it, you need some
information about your portfolio as a
whole, and each security within it.
Steps
Calculate the standard deviation of
each security in the portfolio. First
we need to calculate the standard
deviation of each security in the
portfolio. You can use a calculator or
the Excel function to calculate that.
Let's say there are 2 securities in
the portfolio whose standard
deviations are 10% and 15%.
Determine the weights of securities
in the portfolio. We need to know
the weights of each security in the
portfolio.
Let's say we've invested $1000 in
our portfolio of which $750 is in
security 1 and $250 is in security
2.
So the weight of security 1 in
portfolio is 75% (750/1000) and
the weight of security 2 in portfolio
is 25% (250/1000).
Find the correlation between two
securities. Correlation can be
defined as the statistical measure of
how two securities move with respect to
each other.
Its value lies between -1 and 1.
-1 implies that the two securities
move exactly opposite to each
other and 1 implies that they move
in exactly the same way in same
direction.
0 implies that there is no relation
as of how the securities move with
respect to each other.
For our example, let's take
correlation as 0.25 which means
that if one security increases by
$1, the other increases by $0.25.
Calculate the variance. Variance is
the square of standard deviation.
For this example, variance would
be calculated as (0.75^2)*(0.1^2)
+ (0.25^2)*(0.15^2) +
2*0.75*0.25*0.1*0.15*0.25 =
0.008438.
Calculate standard deviation.
Standard deviation would be square
root of variance.
So, it would be equal to
0.008438^0.5 = 0.09185 =
9.185%.
Interpret the standard deviation. As
we can see that standard deviation
is equal to 9.185% which is less than
the 10% and 15% of the securities, it is
because of the correlation factor:
If correlation equals 1, standard
deviation would have been 11.25%.
If correlation equals 0, standard
deviation would have been 8.38%.
If correlation equals 1, standard
deviation would have been 3.75%
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