Homoskedastic

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