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Portfolio Standard Deviation - Meaning, Formula, Examples, How to Calculate? - YouTube
Channel: WallStreetMojo
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hello everyone hi welcome to the channel
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till the end and also if you are new to
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by clicking the bell icon today we have
a topic with ours is called portfolio
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standard deviation now see portfolio
standard deviation it measures the
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expected variability in the rate of
return of the portfolio and it is
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determined based on the standard
deviation of the return of each asset in
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the portfolio you well this is just a
dialog box that's written but we will
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try and get incorporated with the whole
concept unit very detailed format so
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portfolio standard deviation now see
portfolio standard deviation is the
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standard deviation of the the rate of
return on the investment portfolio
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and is used to measure the inherent
volatility of an investment so it
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measures the investment risks okay and
it helps the analyzing the stability of
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the return of the portfolio so portfolio
standard deviation is calculated based
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on the standard deviation of the return
of each asset is the portfolio so the
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proportion of the each asset in the
overall portfolio that has the
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respective weights in the total
portfolio and also the correlation
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between each pair of the asset in the
portfolio let's do some interpretation
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part of the standard deviation of the
portfolio see this helps in determining
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the risk of the investment that is what
we call as the expected the returns so a
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high portfolio standard deviation
highlights that you know the portfolio
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risk the portfolio risk is high and
return is more volatile in nature as
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such you know the unstable as well so
portfolio with a low standard deviation
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the low SD the portfolio with the low
standard deviation implies that you know
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less volatility and more stability in
terms of the returns of the portfolio
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and it is very useful financial metric
when comparing different portfolios
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we'll go with an example part or to get
more insight see let's say there's a guy
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called John John had planned to invest a
certain amount of money let's say in
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let's say John plans to invest a certain
amount of money every month in one of
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the two funds which he is shortlisted
for the investment purpose drop down
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some particular details let's say the
average return for last 3 years fund
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A and fund B over here it comes down to
12% over here 12% and the standard
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deviation has 814 so assuming the
stability of the return is the most
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important for John while making the
investment and keeping one or the other
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factors as constant we can easily see
that both the funds are having in the
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average rate of return
closely standing at 12% okay so you know
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fund a has standard deviation of let's
say 8 DSD standing at 8 which means it's
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average it and can vary between 4%
to 28% right by adding
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and subtracting it from the average it
and on the other hand let's say fun B if
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you see here a standard deviation of 14
which means that a return can vary
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between -2 to 26% by adding and
subtracting 14 from the average return
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if you - here from 14
that is you know you need to deduct that
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way so does based on on his risk
appetite if John wishes to avoid
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excessive exist volatility will prefer
investment in fund compared to fund B
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as it offers you know the same average
return with a less amount of volatility
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and more stability on the returns for
you see 1212 but you know as HD less is
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these more here but the standard
deviation of the board for is important
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as it helps you know analyzing the
contribution of individual assets there
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are two the portfolio standard deviation
and is impacted by the correlation with
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other assets in the portfolio and its
proportion of the weight in the
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portfolio okay now how to calculate the
portfolio standard deviation okay we'll
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try and understand this first we'll try
and not down some some things you know
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portfolio standard deviation calculation
you know it's a multi-step process and
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involves the like you know the formula
basically so assuming that you know the
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portfolio comprises of two assets only
the standard deviation of the two asset
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portfolio can be computed using the
portfolio standard deviation formula let
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me show you that this is the formula
that you can use the standard deviation
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of the portfolio there is a weight into
standard deviation of a then weight into
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standard deviation that is
multiplication of B plus 2 into weight
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of a into weight of B into either you
can multiply covariance over here or
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correlation into this is the covariance
of a and B into standard deviation of a
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into standard deviation of B so find the
standard deviation of each of the
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portfolio find the weight of the each
portfolio which we require here okay and
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weight of each asset in the overall
portfolio and define the correlation
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between them that is over here okay
correlation of the assets in the above
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case between the assets in the portfolio
and correlation can vary between minus 1
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to plus 1 so apply the values in the
above-mentioned to derive the standard
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deviation formula of the two asset
portfolio
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so let's understand the portfolio
standard deviation calculation of the
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three portfolio of the three as a
portfolio with the help of an example
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now calculating the portfolio standard
deviation of the d3 asset portfolio is
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will go something
now this multi-step process how does
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exactly works we'll try and understand
this in a very detail format over here
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there are three stocks you know flame
this is let's say this is flame
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international okay it's considering you
know a portfolio comprising of three
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stocks let's say A B and C and this is
the brief Details of weights all they're
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gonna invest the expected return they
are expecting the and the standard
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deviation the correlation between a and
B a and C and B and C is available with
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us so now for a three asset portfolio
this can be computed by weight of a into
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standard deviation of a weight of B into
standard deviation of B rate of C into
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standard deviation of C plus it remains
the same - into W into WB into
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covariance this is covariance of a and B
into standard deviation of a and B plus
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2 into W a in to see here the second one
into the correlation of a and C that is
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point 3 multiplied by standard deviation
of a and C and then it goes with a B and
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C that is weight of B weight of C +
sorry you multiply that with the
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correlation point - 1 5 and then the
standard deviation of B and C that is 13%
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and 15% so this is how
you are going to compute your entire
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value where you over here W a again I
repeat and W B W C are the weights of
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stock ABC respectively in the portfolio
this k a k b and Casey are the standard
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deviation that is you know Sigma over
here of ABC and this RK a and RK c are
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the correlation sorry not the covariance
correlation between stock a and stock V
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and a and C and B and C respectively
okay so if you compute over here the
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hole
it should come closely around 15 to 18%
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from the number it looks like so
we know we see that you know standard
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deviation of portfolio is closely around
15 to 18% despite you know the
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individual asset in the portfolio there
is there is having different level of
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standard deviation that is stock a
24 stock B 18 and stock C 15%
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due to the correlation between
them in the portfolio so after taking
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the example I want to finally conclude
on this particular topic C standard
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deviation of portfolio is important too
and undoubtedly which helps in matching
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the risk helps in matching the risk
level of the portfolio with clients risk
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appetite and its measures measures the
total risk in the portfolio comprising
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of both systematic and unsystematic risk
now a larger standard deviation implies
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that you know more volatility and more
dispersion in the returns and does you
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know more risky in the nature so it
helps in measuring the what we call as
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consistency in which the returns are
generated and is a very good measure to
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analyze the performance of the mutual
fund and also the hedge funds returns
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consistent however I know it is
persistent in order to load that you
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know the standard deviation is based out
of the
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historic data and past results may be
predicted for the future results but
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they may also change over time and
therefore we know it can alter the
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standard deviation so one should be more
careful before making any investment
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decisions based on the same so that's it
for this particular topic after
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discussing all the data regarding
meaning interpretation a short example
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we had gone a stepwise calculation of
two standard deviation in three stocks
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that is two stocks in three stocks
calculation so that's it for this
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particular topic if you have learned and
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