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Principles of finance ah la shmoop what is the relationship

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between expected return and standard deviation Tohave a cranky disposition

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about long term investing like given off the vibe that

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you know mr market better than mr market knows himself

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you need the math and the stats tio you know

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back up your crankiness and it's good to be cranky

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all the investing yet says they're cranky Warren buffett is

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like king crank but one of the things you need

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to be cranky about and understand is how standard deviation

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helps you know what the real risks are when you

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invest your cash or at least the theoretical mathey notion

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of that Because in real world when we doubt warren

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buffett does a lot of this kind of math but

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he knows how to do it in a pinch So

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anyway how do you quantify those risks when you put

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your dollars toe work That's what this notion is all

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about and how does calculating a standard deviation help with

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that notional investing or theoretical investing The standard deviation of

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how a stock could perform versus it's expected return gives

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us an idea of how risky it is to invest

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In that stock or at least the math of that

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risk And yes i'll be it with like a million

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asterisks here but but but but but but but just

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looking at history of stock prices to predict some future

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price well is right up there with the crystal ball

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and astrology method of investing So view This math exercises

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just a second set of copilot eyes on investing in

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the real world Curl up and die Ah hair salon

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franchise that's relatively new it's a new hypo through the

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market it's been analyzed by the quote experts unquote and

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has produced this table of expected returns That's what the

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experts produced when they only looked at trailing close of

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day stock prices over the last year and change no

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idea how they got this table All we're saying is

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that there was a dartboard and some darts and ah

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a blindfold This table represents the three ways things could

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go for investors investing in curl up and die The

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most likely case according to the experts or stock brokers

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out there for curl up and die is that it

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returns twelve percent in a year on an investment made

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in the stock at this price right now Well this

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is estimated to happen with a seventy five percent probability

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on either side of that outcome are less likely outcomes

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curl up and die could return just nine percent on

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an investment with a fifteen percent probability on that return

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Or it could return sixteen percent on an investment with

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a ten percent probability And yes these air insane Numbers

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like there's 0 chance it could lose money like really

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but yeah we're just doing this for illustrative purposes on

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lee So how can we use that information This probability

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table to determine how risky investing in curl up and

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die is And yes this notion of risk is totally

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made up here It's not reflective of real life in

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the university Our lawyers made us say that All right

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well the fundamentals of the company i eat what they

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produce how big their market is how well they're doing

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in that market how talented they are how hungry they

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are how fast their revenues air growing along with our

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profit margins has a million times more to do with

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stock prediction than these standard dev Cal Kes But you'll

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get asked about them all the time when you host

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cocktail parties for that greater south milwaukee cardiologists investment club

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So anyway yeah you better know how to dance the

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dance All right here we go We need to calculate

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the weighted standard deviation of the investment returns which we

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find by subtracting each possible return from the most likely

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case return which is twelve percent Our worst case scenario

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is that we only make nine percent So if we

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get point o nine minus most likely return of well

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percent and that's point one too which is a negative

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point Oh three for our first count there all right

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And then the second thing is our most likely case

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minus the most likely case Right So that zero in

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the best case scenario of positive sixteen percent return our

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point one six minus that point one too Now that

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gives us point Oh four And now we square those

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differences All right so negative point Oh three squared is

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point o o nine Well zero squared at least in

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california is zero and then there's a point oh four

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square there which is point oh one six Next we

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multiply by the probability that each return could happen Take

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the worst case probability of fifteen percent there point one

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five times the point O o nine giving us point

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o o one three five then the most likely case

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probability of seventy five percent or point seven Five times

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the zero which is wait for it Yes zero And

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then the best case probability of point one or ten

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percent times the point of all one sixth giving us

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point a one six and then we add up the

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values of that point Oo one three five and zero

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and point owen six giving us point triple zero two

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nine five All right lastly who we square the root

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that value gets too are weighted standard deviation here which

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is point o one seventy or one point seven Two

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percent So by itself the weighted standard deviation doesn't tell

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us anything but in comparison to other waited standard deviations

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While we can get an idea for how risky the

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investment is how does the value of the standard deviation

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of the possible returns on investment help Well in general

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a stock that has a lower waited standard deviation unexpected

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returns than other stocks is more stable less volatile This

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stock will likely have returns that won't vary from boom

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to bust and everywhere in between So what makes a

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stock less volatile Well things like having a ton of

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cash on the balance sheet and no debt paying a

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hefty dividend Yeah that'll stabilize you real quick look att

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and t stock for the last decade It pays a

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big dividend and male pretty much goes nowhere having stable

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reliable growing earnings Yeah that'll do it for you and

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not trading in an astronomically high price to earnings ratio

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that will stabilize you stuff like that Well the savvy

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investor doesn't get much from just knowing the standard deviation

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of expected returns on just one stock The magic happens

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when we compare the standard deviations of other stocks to

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help us manage risk that is a given stock is

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usually evaluated relative to something and that something is usually

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the overall market like the s and p five hundred

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and nasdaq or something of similar ilk Well here are

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the projections of two different investments using standard deviations which

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one is probably the less risky we need to subtract

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the most likely expected return from each outcome For car

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lotta's customs We're going to be subtracting the most likely

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return of point one three from each of the three

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cases of point Oh seven there and point one three

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and point two one for zaza pizza will be taking

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point one five away from the three cases of point

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Oh four point one five and point one seven and

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note how ridiculous It is that there's No way we

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lose money in any of these investments were geniuses We'll

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square all those differences for carla's Customs will be squaring

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Negative point Oh six zero and point six giving us

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a point Zero zero three six zero in point zero

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zero three six again for zaza pizza will square negative

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point one one zero and point to giving us a

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point One two one zero and point well four and

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will multiply those answers by their probabilities So for carla's

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customs well that'll be pointed all three six point two

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zero and point oo three sixteen point oh eight Oh

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there we go for zaza pizza will not be point

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a one to one times at point one three thing

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and zero and point oh four times Point two Now

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we sum them Add them all up for carl otto

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were adding point oo seven nine to zero and this

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thing to a date there to get point triple zero

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eight to eight for the pizza joint We're adding and

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double zero One five seven three zero and that an

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eight Eight and we get point Oh one six six

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one of yeah Finally here at the end of all

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things or at least this problem we square the root

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answers giving us point Oh two eight six four Car

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lotte and point oh four Eight for zaza What does

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this tell us Carla's customs has awaited standard deviation Unexpected

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returns of two point eight Six percent whiles oz pizza

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has awaited standard deviation of four point Oh eight percent

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Well if your goal is to keep the risk low

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or rather the volatility low well then you'd go with

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carla does because it has a meaningful e less beta

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or volatility attached to it then za Alright Well the

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standard deviation of the expected returns is a way to

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measure the risk of a particular investment compared to another

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investment The lower the standard deviation in comparison others well

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less risky The investment likely is to calculate standard deviation

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We take the the most likely return and subtracted from

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each possible return square Those differences multiply them by how

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likely they are to happen Add them up and then

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square the root some well Standard deviation of expected returns

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shouldn't be the only tool in your investment toolbox when

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it comes to determining risk But if you want to

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sit at the adult table when its investment time and

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at least talk to talk well it's a tool you 00:08:24.166 --> [endTime] don't need to be familiar with

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