Covariance
Categories: Metrics
Covariance is a way to determine how two investments are linked, in terms of whether they both grow (or lose value) at the same time...or whether one investment grows in value while the other loses value.
A positive covariance between two investments means they’ll both grow (or lose value) more or less linearly together. A negative covariance means that, as one investment grows in value, the other will lose value, also more or less linearly. A zero covariance means, well...just that they don’t follow a linear pattern and/or don’t always increase or decrease together, or that they head in opposite directions.
Investors almost always want a portfolio without a bunch of investments that all have a positive covariance with each other. Because if one heads south, they all probably will. That’s bad. A well-diversified portfolio will have a decent amount of negative covariance pairs to protect the whole shooting match from tanking at once if that particular market (or markets) tank.
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Finance: What is co-variance?8 Views
Finance allah shmoop what is co variance while co variance
is a way to tell if two investments will both
head to millionaire acres together or to the poor house
together or if one is headed to millionaire acres while
the other is headed Teo you know the poor house
three choices there that's where co variance comes in and
it basically comes in these three flavors Positive co variance
which means the investments both either grow in value or
both lose value typically in a linear fashion that's positive
co variance They're like tied together Negative cove arians means
that as one investment grows well the other loses like
loses value also typically in a linear fashion you know
kind of graphically linear and then you have zero co
variance which means well we're just sure that whatever their
relationship is it almost certainly isn't a linear one They're
just not really varying together They may both grow together
but in a non linear kind of curvy almost random
fashion they may head opposite directions but they probably won't
do it in a straight line of kind of way
right Well co variances used to help investors make sure
their portfolios are adequately diversified after all if our when
one or more markets do crash again it'd be nice
if our net worth wasn't also completely totally changed right
Kind of kind of want to hedge your bets there
a little bit So let's pretend we have a portfolio
in which all the investments are in companies that make
different kinds of hand held tech like smartphones and tablets
and smart watches and you know adult aides of different
flavors and forms So these investments in our portfolio will
almost all certainly have a positive co variance with each
other like they all kind of have the same buyers
and sellers and appetites and market swings And then the
surgeon general one day determines that the radiation from handheld
tech causes monster ism The value of our portfolio will
hit rock bottom fast stirred on an album of spoken
word poetry by vladimir putin if instead we had paid
attention to all that positive co variance data and try
to get some investments with negative co variance is well
we might not be looking through the want ads and
selling plasma every day to pay for food a portfolio
With a number of pairs of investments with negative co
variances would mean that while some of our tech stocks
might have plummetted our monster defense stocks might have skyrocketed
All right So how do we calculate co variance Well
they're two ways First we can use the co variance
formula which has us take one investments returns subtract the
mean return from each of those returns And repeat that
for the other investments multiplying all the pairs together to
sum up those values Wait can we just do this
step by step All right let's do that that way
Yeah There we go So let's take the returns from
two different investments Read from the same time period We'll
need to find the means The averages of investment one
and investment to well to get that for investment one
an average Well we'll add up the returns of five
point one five point three five hundred francs having and
if i had a total of twenty seven point two
by five giving us an average there Five point four
for for investment too We had three point three of
your own and these are like percent returns on bonds
Or something like that That's A kind of think about
a total seventeen point nine five by five and we
get three point five eight Right now we subtract the
mean from each individual return So for investment one that
means subtracting the mean of five point four four from
each data point you get five point one five point
three five point four five seven five seven Not to
be mean But that means we also need to subtract
the mean of investment to which was that three point
five eight from each of those data points and so
on And get what we mean here that's How it
should look so next up multiply the matched pairs of
points like negative zero point three four times negative zero
point two eight and then negative point one four times
Negative point one eight and so on All right time
to some All those values to get point o nine
five two plus point two five two plus uh negative
went for a a aa plus Pulling on three One
two and five seven two gives us point two oh
four There we go What We finish up dividing that
Some by one last the number of hairs of data
points So we'll divide by point two Oh four There
that thing will divide that by four Which gives us
a cove Arians finally of point Oh five one What
the hell does that mean Well that positive cove arians
means that in general as investment one gains value in
general so too does investment to or that in general
as investment one loses value so too does investment to
meaning they're pretty correlated So it's not a huge issue
to have some investments with positive co variances but the
entire portfolio i probably shouldn't be made up of positive
cove Arians pairs of investments maybe kick in a few
investments to the curb in favor of some that produced
negative co variances Good idea no matter how attached you
are to a particular investment or sector of the economy
Well now that we've used the actual co variance formula
what are other ways we can do A ploy to
find co variance Well we can calculate the correlation coefficient
a k a the r value r r squared value
of the data points And then multiply that value by
both the standard deviation of the ecs data and the
standard deviation of the wide data Okay well the individual
standard deviations and our values can be quickly calculated using
technology like a graphing calculator website er's frenchie or something
like that using a graphing calculator on those same returns
from investments one into from before while we found our
to be point nine o two one exit standard deviation
to be point two six eight and wise standard deviation
be point two one six eights is just different Pairs
of investments Like a bond portfolio How correlated worthy Well
when we multiply point nine o two one by point
two six away and then by point two one six
eight we get a co variance love wait for it
point oh five one yeah we've seen that number before
And we're not in the matrix Alright again a positive
cove Arians means that the two investments will probably either
both grow in value over same time period or probably
lose value together over the same time period They may
grow or lose value of different race but whatever direction
one goes in well the other follows Think about him
Like penguins were kind of you know sniffing each other
well A negative co variance will mean that is one
investment gains value than the everyone loses value and that's
Good Sometimes people call that ej that's kind of a
good thing to have stabilized Report Follow at least in
the short term a well diversified portfolio should have enough
pairs of investments or combinations of investments that have negative
co variances so that they protect you in the really
ugly scenarios Right now we just have to figure out
who's going to clean up the office before the boss 00:06:41.797 --> [endTime] gets back