Alan Kring Productions in association with Emergent Light Studio presents the Illinois
State Collegiate Compendium, Academic Lecture in Business and Economics.
This is Business Finance, FIL 240 for Autumn semester 2023.
Today, the Capital Asset Pricing Model.
This is kind of a mathy thing, but none of the math really gets all that intense.
It's just one of those things where you have to have the formulas and the formulas are
just basically arithmetic, but the conceptual framework behind it actually can almost become
interesting in certain regards.
But first I'll look at the numbers and the numbers suck, really bad.
This was a bare day.
As you can see the Dow was down almost a percent.
The S&P 500 down more, a percent and a third.
And the NASDAQ down more than a percent and a half.
The typical risk return kind of thing.
It was a sour day on the street.
Part of that was this is a big earnings week.
You see companies estimate their earnings and then a while later, a few weeks or whatever
later, they actually say these were the earnings.
And so the question is, well did they beat their earnings estimate or did they fail to
even meet their earnings estimate?
Well it's a mixed bag right now.
For example, if you want to look at Tesla TSLA, it missed its earnings and the market
just potty trained that stock down four and three quarters percent for the day.
Now in the aftermarket it's recovering some of that as the diehard Tesla people think
they're getting a bargain and buying it back up in the aftermarket.
Also, some of the other financial, some of the banks didn't come in with earnings that
were up to expectations.
So that caused some concerns and that was one of the things that was rattling the market
a little bit today.
And then of course you have the issues, first of all the Middle East.
We're nowhere near a global war or anything like that, but at the same time it just isn't
quieting down.
And there's always a concern that someone's going to do something really stupid and cause
the whole shenanigans to turn ugly.
And that would of course, oil distribution would be disrupted and all that good stuff.
Not a lot of chance of it, but it still spooks the market a little bit, that kind of thing.
And there are other things that are concerning the market.
Notice that crude oil, it pushed up against its resistance at 88 and it came through a
little bit.
Notice how it spiked up there and it chickened out.
Went to like 89.50 and then it just dropped right back down, back through the resistance
and then it just kind of flopped around, moved up a little bit.
But that is what we would call a war premium.
Notice that it is not large at all, but there's a low probability of a premium so they do
it.
Yeah.
Oh, look at that.
What the heck?
Why does it do that?
Because I type it in the wrong place.
NFLX.
Holy shh.
Do you see that?
Did you know the aftermarket did that?
Holy cow.
Yeah.
That's the only thing that would do that.
Now if you look down here, they didn't show it, but see this is the earnings pattern.
Notice that they beat their earnings in third quarter last year and then they missed their
earnings a little bit there and then they hit their earnings, beat them and this time,
wow.
Blow out Q3 subscriber gains.
Most of that is the extra money I'm paying the damn service now.
That's where they got all that extra earnings.
But yeah, that's impressive.
Yeah, I was going to invest in it, but I decided to let other people do that one today.
I'm impressed though.
That's an awful heavy spike.
One day, if you bought at the bottom today, you would have earned 12.83%.
Boy would I like to have bought a couple of call options on that.
But notice that's a very expensive stock.
Anyway, that's more of those you got to have the money to do that kind of, play that kind
of a game.
But the whole big thing is subscriptions.
It's not quality of the shows.
They have great movies, but they have these subscriptions.
They apparently beat their subscription estimates by a mile.
It's also the competition.
There are other services out there that are offering shows.
Starting from the high end at Amazon, which Amazon is thinking of, well no, they're going
to charge a premium starting in January.
If you don't want ads in their movies, then you have to pay them extra money.
And then you have Hulu, you have lower end services.
And some people, you have niche services like Brit Box and things like that to some people.
And then you have the sort of quasi pirate services like Plex that some people have figured
out how to use.
Oh, is it me or does the water here smell bad?
Where did they get the water from?
Ass Lake?
Oh, so it collected all the bacteria and fungus in the pipes.
Oh well, meh, yellow and all that.
Okay.
Thank you for that one though.
That one was pretty impressive.
I mean, it always brings joy to my heart when I see someone, not me, making money on a day.
One thing I do want to point out though, S&P 500, look at the volume on those 500 stocks.
Typical day, vol is 3.7 billion.
Today only 2.4 billion.
Again, the investors are staying on the sidelines.
That's much weaker.
And some of my fellow, my former students who are now traders in Chicago and New York,
they've been sending me DMs on LinkedIn saying, you know, this is the beginning of the apocalypse
and all that.
No one's investing.
I don't think it's that bad, but it is kind of spooky.
But anyway, going over here, you see the gold had a little bit of a run upward.
It's nowhere, oh, well, I want to look at gold.
Gold had a run upward of about one and a third percent.
It's not really that close to its resistance level at $2,000 an ounce, but still, that
is a lack of confidence when investors are going toward the metals.
Now over here with the 10-year bonds, just have a look at those puppies today.
The bonds, the ads off there, go over here to the bonds.
Okay, you've got the 10-year bond, price up, yield down.
So the price, I'm sorry, the yield up, price down.
So there are price going down, that's selling bonds.
Investors are getting out of the safety of bonds.
They're certainly not going to the riskier equities.
So uh-oh, gold.
That's that sequence of the flight to quality from stocks to bonds to get safety.
If bonds don't look safe, then bonds to gold, the safe harbor of gold.
And of course, the last round of that is if the gold's selling, then people are buying
bullets.
I recommend 556 rounds myself, just for the fun.
Now, notice that the euro and the pound both depreciated against the dollar modestly today.
Still the strength is in the American economy, not in Europe, not in London, in Great Britain,
and the Japanese yen, yep, it depreciated, it's backwards, it depreciated too.
So US, as bad as it might look in the stock market, it's still the currency that's showing
the strength in the global community.
Nikkei was all down, all through last night, and just barely eked out a tiny 1.01% return.
It came up above negatives, and ended the day just a tiny bit up.
That's not anything.
London, on the other hand, it just went down the whole day, it just kept flushing the toilet,
and by the end of the day, it was down more than 1%.
So there you go, there's the look at the world as it is today.
Let me see something, I'm dying, I can't stand it.
Netflix, I can't quit you.
Okay, right now in the aftermarket, that's still going to be a hell of a return.
But notice something, Netflix doesn't pay a dividend, so you're riding capital gain
the whole way through a year investment.
You're not going to get a check in the mail, so you just have to hope that price just keeps
going up and up and up.
And that's just the way those kinds of stocks are.
Their plow back ratio is 100%.
Every penny of that $9.39 per share they make, they plow it right back into the country.
The company's operations to keep that company growing.
So as long as they can get the subscribers and they can keep producing good television
series, and get some movies that were just out of first run, they are going to be fine.
I hope.
Now, let me take that off the table here and do something.
Now part of this sounds like it's kind of off the track,
but it really isn't, especially for your longer term.
Harkening back to your statistics course,
your sadistic course as it were, long ago,
and I won't assume that you remember a whole lot
from that course.
As you take more of your upper level courses,
you'll run into some of these statistics again,
and this is just one first shot
at your upper level use of statistics.
And I also get into, make sure you understand
that there is a difference between statistics
and the underlying probability theory.
One thing that is always of concern is that if numbers,
if you don't know what these numbers have
as their weaknesses and their strengths
from probability theory,
you can get into trouble using statistics.
That's why I bring up a few little points along here.
Now, measures.
In other words, what numbers are useful to us?
There's an old saying, make your statistics simple
or make them PhD level.
Don't play in the middle.
And these are all simple statistics,
and they are the ones that are mostly what we use.
We sometimes get into the heavy duty stuff,
or at least we think we do.
But first things first, central tendency.
Good grief.
Did that like hurt?
Sounded like a nose fart.
Okay, here we go, central tendency.
Where does the data want to show up?
It clusters around.
It's like you have a light outside at night,
and all of the moths, they tend to go to that light.
Sometimes you'll find one over here saying,
where the hell am I?
You'll find one over there, uh-oh, a bat's about to eat me.
But they tend to go toward that light.
And that's what data, we hope, does.
Now, some data just doesn't do that very much.
We can find a measure of central tendency,
but it really doesn't tell us
because the data's so scattered so evenly
that the central tendency measure doesn't usually work.
The big one is the mean,
or otherwise known as the average.
But the thing is that there are several of those.
But if you want a fancy formula,
one over n times the sum from i equals one to n,
that's the number of data points.
And let's talk about with stocks.
The return at period i,
the sum of the returns divided by the number of returns.
Nothing hard about that.
Add them up, divide by the number of data points.
However, even that one can have some different uses,
the different tricks on it.
One is the weighted average.
Where different data points have different weights.
I'll show you this in practice.
But the way you would do it is you would do the sum
from i equals one to n of the return to i
times the weight of that stock in the portfolio.
You say, well, where's the n?
Oh, it's actually right there.
You see this simple formula,
one over n is the weight of each one in the portfolio.
So a simple average is just a very basic application
of a weighted average.
Now let me show you this in practice.
Pull up an Excel sheet here and do it again.
Okay, the stock, the return, and the weight.
So you could have stock A, stock B, and stock C.
And I'm showing you this in Excel to show you,
and I think I've shown you this formula, this trick before,
but it's a really sweet little thing.
Return to stock A, let's say is 7.6%.
The return to stock B is 13.9%.
And the return to stock C is 11.4%.
And let's say the weight of A in the portfolio is 0.4.
The weight of B in the portfolio is 0.5.
And the weight of C in the portfolio is 0.1.
The sum of those would be 1.5.
And the weight of C in the portfolio is 0.5.
The weight of C in the portfolio is 0.1.
The sum of those would be 100%.
Now, then, the weighted average.
Watch how I do this.
I'm gonna show you how to do this.
So you can see here, you can see the column of returns,
comma, by the column of weights.
And there's your Uncle Bob.
11.13%.
And you could do it the other way.
This times this, plus this times this, plus this times this,
and you get the same number.
Some product just takes that pain out of it.
That's all it does.
And you'll find that that's useful in your homework.
And there will be other classes.
You'll probably find some product to be one of those little go-tos.
Yeah?
You wanna see it?
Click on what?
Oh, down right there.
Click on the one over here.
Oh, let me show you.
This one?
Oh, yeah.
Watch.
Sum product.
Now, sum product actually has some really sophisticated uses, too,
and I don't even know all I can do.
But you take the sum product, and you say,
I want you to take each cell in this column,
comma, times its associated cell in this column.
So it's B2, colon, B4, comma, C2, colon, C4.
Boom.
It's a nice little formula.
It's a nice little Excel formula.
Like I said, I saw someone using it in some bizarre, complicated way,
and I didn't quite get it, what he was doing.
But yeah, for us, you'll find that this is really useful
the next week or the week after that for some problems
where you calculate the weights by your given stock prices.
So then you have the overall price of what's your portfolio,
of your portfolio.
So you take each of the prices divided by the total value,
and that makes the weight,
and the sum product can do that really cleanly for you.
But that's next week. Don't worry about it.
Okay, so that's weighted average.
It's much more useful for a lot of data.
But then there's another one.
It's called the moving average.
I'm going to put it over here.
The moving average.
Now the moving average actually takes a subset of the data.
Suppose that you had one, two, three, four, five, six, seven, eight
up through today, last eight days of data.
Now a simple average would just take,
add those data values up, divide by eight.
A moving average says, okay, let's do an eight-day moving average.
So the first for today, you get the average.
And then tomorrow a new data point comes in,
so you drop the oldest and find that average.
And then the next day a new data point comes in,
so this time you drop what is again the oldest data point,
and you put in that one.
Now that would be an eight-day moving average.
You could do a three-day, a four-day.
You see what this does is this doesn't hold on to old data.
It keeps refreshing and dumping off the oldest data.
And in my business, in stocks, currencies,
we have different ones that tell us different things.
Like for example, in currencies you'll have a 120-day moving average.
Then you'll also have a 60-day moving average,
a 30-day moving average, a 15-day moving average.
And each of them tells you a little bit different story
about what's happening with the data.
So these moving averages are actually pretty popular,
especially when there is new data coming in.
You don't really want to see there's a trade-off.
If you have a long moving average, like that eight-day,
that's taking account of things that have happened
for the last eight days.
But it's a three-day, well that would take only what's happened
over the last three days.
The trade-off is that the three-day is a more current moving average.
But it also has that at the expense of older data
that might have some use in it.
You know, I take your moving average of your weight, okay,
for the last 60 days, okay.
So every day I drop the weight to your 61 days earlier.
Well, you're saying, well that's nonsense, okay.
Let's take a five-day, every five days.
I drop the oldest one every day of five days.
Well, what I'm doing is I'm sacrificing what might be useful information
about cycles in your weight behavior.
I wouldn't see those anymore with the shorter moving average.
The data is fresher, it's more current,
but at the same time it is giving up some information.
Like, who knows, every 40 days you decide to gain 30 pounds
and then you lose it two days later after your pizza festivities are over.
Something like that.
That's a terrible example.
Okay, now there's also another version of moving average.
It's the weighted moving average where you would take like,
okay, let's say a three-day moving average.
Well, the most recent day you give like 60% weight.
And then the day before that, let's say you give 30% weight.
And then the day before that, the oldest day, you give 10% weight too.
So it has a trailing off effect.
So you're using older data, but you're giving it less weight,
less seriousness in the overall average.
So that's a weighted moving average.
Those are quite popular in not just in stocks,
but also in some kinds of businesses too.
Weighted moving averages of cash flows,
weighted moving averages of costs and things like that.
So that we are recognizing older data as telling us something,
but we're not giving it a lot of weight in the final story
of the moving average that we're using.
So there's that.
Now, there is another measure of central tendency.
It is not a formula.
Well, I guess you could write it as a formula.
But it's more of a metric that we really should pay attention to,
especially comparing it to the mean.
This one is called the median.
50% of the data is above,
and 50% of the data is below.
The median has one very desirable feature.
It is robust to the size of the data points.
Let me show you what I mean.
Forever in all kinds of subjects,
we assume a normal distribution of data, the bell curve.
Even if it's not normally distributed,
they say, well, if you collect enough data,
then it becomes a normal, we can have large numbers and all that.
Bullshit. It actually doesn't.
And that's an unfortunate thing,
especially in a subject like education.
Let me show you something.
See, here, the average is also the 50-50 point.
The median is the mean in a symmetric normal distribution,
or in any symmetric distribution.
But what if you have data,
which mostly is clustering up here,
but you have this long tail of low scores on a midterm?
Well, see, that would mean that your average
is going to be sensitive to these low scores impacting on it.
And so your average is going to look very low
because of all these people over here that didn't do so well.
The same is true on the other side.
You can have data where most people are down here.
And then you have the few really bright students in the class
who get the 98s and the 100s.
Well, they are going to have a disproportionate impact on the average.
But it doesn't matter for the median.
The median just says half here, half here.
The classic story is the professor,
well, that test could have been that hard
because I got one person who got 100.
Everyone else got a low score, but one person got 100.
So that 100 skews the story of what the data is trying to tell us.
And so the median is actually quite useful
for our purposes in a lot of different subjects.
Like, for example, the average on this midterm
was a – it came out to be a 75.5.
The median came out to be a 78.
Well, what would that tell me?
Ah, the average was dragged down by –
that I looked at the data.
There were some – there were a couple of zeros.
How do you – 10 percent?
So a couple of 18 percent.
Those very low scores made the average look lower
than what the other – what the data was saying.
Actually, it was about 50, 50 at 78 percent.
But if you look at the average, it was lower than that
because of some low data points.
I've had it go the other way, too.
I've got a couple of people ace an exam.
Everyone else just didn't do so well.
So this high 100 and a 99, they skewed the data upward
a little bit.
And so it looked like the average wasn't as bad –
what it's telling me that it was better,
the performance on the exam, than it really was.
This happens in all kinds of situations.
In human behaviors, in human behaviors,
in testing of failure rates, it's rather surprising.
When you've got – you don't – you think the data is
normally distributed, okay?
But there are – the outliers are actually kind of
important to the process.
So you want to look at the average and the median
and see if they're telling you something
because they're different, okay?
So that's central tendency.
Let me get that off the board here.
And now we get to the other important aspect of this –
risk.
As I've said before, the classic measure of risk
is the standard deviation.
And that is the 1 over n minus 1, if it's a sample,
times the sum from i equals 1 to the number of data points
of the data point – each data point –
minus the average of the data points, squared.
And then you take the square root of that mess.
Now for the population, you use n, not n minus 1.
Notice that as the sample size increases, n minus 1
and gets closer and closer to n, so the sample standard
deviation approaches the population standard deviation.
Just kind of a side point there.
That's the measure of central tendency.
However, that doesn't do us a lot of good.
By the way, why does this square come in?
Because we want data points below the average
and data points above the average, not to cancel each other out.
So we square, and that way they're always going to be some positive.
Okay.
That one isn't the only one.
The one that is our friend is beta.
That measures only one part of the risk.
The systematic risk.
The risk that cannot be canceled out by the volatility
of other things in the portfolio.
Now if you want to know, there is a formula for beta.
And I'll just give it to you.
Beta of a stock is going to be the correlation coefficient
of that stock with the market portfolios
times the standard deviation of that stock
divided by the standard deviation of the market portfolio.
Now, why am I showing you this?
First of all, notice this.
Beta is our favored measure because we can use it
to compare stocks to things that are important,
like the market portfolio.
Suppose that you had a risk-free portfolio, just T-bills, okay?
Well, the standard deviation of the T-bills would be zero.
They have no volatility.
They just sit there at the risk-free rate.
So you'd have a zero divided by the market portfolio's
standard deviation.
So you'd have a beta of zero.
So in other words, that explains why we use beta,
the risk-free rate, when I start this little diagram right here
of expected returns against beta, a beta of zero would be
whatever the current risk-free rate is.
Now, let's talk about another one.
What if we were talking about the beta of the market portfolio?
Well, the beta of the market portfolio, first of all,
the correlation between the market and itself would be one,
and then the sigma of the market portfolio divided by the
sigma of the market portfolio would be one.
That's why the beta of the market is one, 1.00.
And so that is our expected return to the market portfolio.
And so there's a straight line relationship there.
Beta, and I'm going to show you beta in practice,
how we can use it.
Let me do something here.
Which brings us to the all-time famous capital asset pricing model,
the CAPM.
Little history of it.
It was first published, I believe, in the mid-1960s,
maybe the early 60s.
And it has an elegant simplicity to it.
What it tells us is what we should expect the return to a
stock should be if we know the beta of the stock.
It tells us what to expect.
That's not necessarily what's going to happen,
but it's our best estimate.
Now, the CAPM, at first, in academia,
it was quickly embraced.
Yeah, we get it.
The theory is elegantly simple, kind of that stuff right there.
Really nice, really easy.
But then it was not embraced outside of academia until later.
Corporations didn't embrace it for a long time,
even business courts refused to recognize that this was the way
to determine expected returns to securities until into the 1980s,
I believe it was.
And since then, some other theories that have got equations
so that we can calculate expected returns have come along.
I think the book even brings those up.
One's called APT, the arbitrage pricing theory.
None of them are as clean or as simple as the CAPM,
and none of them do it much better.
Even in graduate level courses, there is currently a really
high-powered mathematical equation that will do the same
thing CAPM does.
I show it, I teach it, but I'm not convinced it's better than CAPM.
Really I'm not convinced of that.
But anyway, here it is.
The expected return to a stock over let's say a year would be
the risk-free rate plus the beta of the stock times expected
return to the market portfolio minus the risk-free rate.
That's CAPM.
Now, if you were thinking of getting a tattoo,
you can't go wrong with this equation.
I mean, I actually knew a fellow who had CAPM.
This was his tat.
Weirdest ass guy I ever met.
But anyway, so what you need for a stock,
you would need the risk-free rate.
You would need the expected return to the market portfolio,
and you would need the beta of the stock,
and then you could tell, you could determine the expected
return to that stock.
Those would be the parameters.
Now, the beta, heck, you can just go to Yahoo Finance or the
Standard & Poor's Global Net Advantage or any one of a
number of other sites.
I think Google has its own finance site.
You can even just type in, what is the beta of TSLA?
It will give it to you.
So that's not hard to get.
Okay, what about the risk-free rate?
We, and this comes from a previous lecture,
the risk-free rate, the best place to get a proxy.
Now, the risk-free rate itself is a theoretical thing,
but it has a very close approximation in real data.
The yield on a one-year T-bill, that's about,
a Treasury bill is riskless, or at least almost as close as you
could get to riskless.
So why don't we just use a one-year T-bill?
And so I brought up the U.S. Department of Treasury par yield
curve rates, and for the latest one,
for a one-year T-bill, is 5.48%.
That's how you do it.
So that's what we'll use today, 5.48%.
Now, the expected return on the market.
This one is the wild card.
What we do, there are services that take a survey of a group
of industry and academic professionals in finance,
and they have the members of the survey give their estimate
what in their judgment will be the expected return to the
world portfolio over the next year.
There are many of these services out there.
I'm in one of them.
It has 70 people, people in the finance industry and in
universities, reputable universities,
and we each give our estimate, and then they take the average
of the data that they get.
And like I said, there's a group that I'm in,
and then there's dozens and dozens of others who do the
same thing.
For the most part, those estimates are usually really
close, in the same, to a tenth of a decimal place away from
each other.
Once in a while you see some deviation,
but you pay your penny and you take your pick.
This is the way it goes.
Right now, here's one.
11.85%.
Now, one thing I would caution, if you try to do something like
a Google, what is the expected return to the market portfolio,
most of the hits you'll get are giving you a little explanation
of what it is instead of giving you a hard number.
The reason is simple.
The hard numbers are done by services that charge you for it,
and so they don't let Google find those numbers and then just
say, oh, well, here it is.
And we know because we charge for that service.
But overall, that's somewhere in the right ballpark right now.
But, okay, you've got all the pieces of it.
Now, let's do the wild thing.
Okay.
Let's go back here to Yee-haw Finance.
Let's take a stock.
Let's go to Flix and Chill.
Beta is 1.26.
Now, I want to point out something.
I'm going to write this here before I forget.
The beta of NFLX is 1.26.
Now, before I go any further, you see this little piece right
here in the cap M, the expected return to the market portfolio
is the highest risk-free rate.
We call that the market premium over risk-free.
Mostly you'll hear me say the market premium.
It's the extra reward for taking the risk of the market
going riskless.
Let me explain.
You.
I'll tell you a story.
One night when I was a teenager, I had all this angst
and thoughts about my life in the future.
So I climbed out on the roof of my house from my bedroom window
and I just yelled to this guy, why am I here?
This old guy across the street leans out his window and says,
because you climbed out there, you moron.
Now I heard his wife say, Harold, come to bed.
And then a dog barked.
That was my first introduction to existentialism.
But anyway, you are here on an expectation that you will get
a degree and you will get a good job and a good salary.
That's one of the reasons that we do this.
We pursue this life.
You could have come out of high school and gotten a $12 an hour job.
But your expectation is that you'll come out of college
and you'll be able to get maybe a $50 an hour job.
50 minus 12 is the market premium over risk-free life.
That's exactly what this is.
It's just what's the extra reward for going long
instead of just playing the safe game.
That's what the expected return of the market portfolio
minus the risk-free rate is.
And I'll show you here.
We're going to look at the expected return to Netflix
over the next year.
The expected return to Netflix, NFLX, is equal to the risk-free rate
5.48% plus the beta of the stock, 1.26,
times 11.85% minus 5.48%.
That's all there is to it.
That's cap M.
Now, I'm going to do something here.
Let me take 11.85 minus-I'm going to do that market premium
to show you something, to point out something.
Let me pull up a calculator here.
11.85 plus 5.48, 6.37.
So I'm going to write this step.
There's a reason why I'm doing this.
I mean, you can just put this into a calculator
and quickly get it.
So we've got 5.48% plus 1.26 times 6.37%.
And this is where you see what beta really is.
Beta is a magnifier.
That's all it is.
It says how much the market premium is magnified by this stock.
Notice the stocks above 1 will expand the market premium.
Stocks that are below 1 will detract from it.
I felt something fall off at my age,
when you start feeling things fall off your belt.
God, was that my spleen?
There, get my recorder back in its pouch.
There we go, good.
That's all beta is.
Beta is just a magnifier or a demagnifier.
So a stock with a beta below 1 would demagnify the market premium.
A stock above 1 will magnify it.
And as you can see, Netflix above 1 magnifies the market premium.
So in this case, finishing this up,
first I'm going to now take the 6.37%
and I'm going to multiply it by the 1.26 beta of Netflix, 8.0262.
Now the thing that I want to bring up here,
where's that risk-free rate sitting out there on its own?
That's pretty easy to explain.
Any investment with risk should at least pay you what you would get with no risk.
That's why you add that 5.48, the risk-free rate on,
because anything you invest in has darn well better pay you
at least what you'd get if you didn't take the risk of a real investment.
So when I add that in there, that 5.48, I get 13.5062%.
That is our best estimate of your expected return for a one-year holding period.
That's our best estimate.
Will that be the holding period return?
Probably not.
I mean, it could be a little above that, a little below that.
But we know from data that we've collected over and over again
that on average, cap M is damn good at it.
Now let me do one more here just to show you.
I'm going to find a stock that would have a beta below one.
Let's take, I wonder if Johnson & Johnson, I can't remember.
Yeah, Johnson & Johnson has a.57 beta.
So let me throw Johnson & Johnson in there.
So the beta of J&J is, what did I say that was?
.57, 0.57.
So this beta will demagnify the market premium.
So I run it again, the expected return for a one-year hold on Johnson & Johnson,
J&J would be risk-free rate, 5.48%, plus the beta of Johnson & Johnson,
0.57 times market premium over risk-free,
which would be the same thing it was before for a given economic regime,
minus the 5.48%.
So we get the 5.48% plus 0.57 times that number I calculated there, 6.37.
See those numbers in there are the same.
And so you see what's happening again in this case,
the beta is demagnifying the market premium.
That's all beta does.
It's not some magical thing.
It's just a multiplier.
And if I crank that one through just very quickly,
5.48 plus 0.57 times, open parenthesis, 6.37, close the parenthesis,
equals 9.1109.
Look at that.
Stocks with betas above one will pay more than the market premium.
Stocks below one will pay less than it.
If I put in a beta of one, surprise, you would get the 11.85.
That's how it works.
Beta is, and I don't know if you see it yet,
but it is actually elegantly self-contained.
It's self-explaining.
And this is actually what we use.
Now we can do little other things.
I'll show you later.
But if you got a beta for a stock, this is the, or a beta for your portfolio,
this is the best way, best practices for a forecast of what you should expect to make.
Take stocks with higher betas, you get a higher expected return.
Take stocks with lower betas, you get a lower expected return.
And the risk level is commensurate with it.
The beta is telling you, you're going to take risk with this,
so you expect a higher return.
Duh.
You don't take as much risk, then you should expect a lower return.
That's all beta does.
Now that graph that I did over there,
that's just the capital asset pricing model graphed out.
We even have a name for that line.
It's called the securities market line.
That's where it is.
So in other words, I could, if I had this graph done really well,
I could say, oh, a beta of 1.26, there would be its,
this would be the 5.48 here on the graph, the R sub F, the Y intercept,
and this would be the 11.85% expected return in the market portfolio.
You tell me 1.26, I could run up to the line and I could say, oh, there it is on the graph.
The 0.57, there that is, take it up to the line, there's that one.
It's just like, it's just plain old high school linear algebra is all it is.
A two-point formula of a line.
And that's the whole story of the capital asset pricing model.
One, okay, two last points here.
I almost forgot there's another measure of risk too, but I'll get to that in a second.
We collect data all the time on stocks, on portfolios,
and see what CAPM says will happen and see what really happens.
For the most part, the data is really nicely clustered right around the securities market line.
It's not going to be perfect because the risk-free rate changes, obviously,
and the expected return to the market portfolio changes and all that kind of stuff.
But it stays very close to the line.
However, once in a blue moon, we find a stock or some investor or fund manager's portfolio
that has a certain beta, and it's way above the securities market line.
In other words, it's temporarily blowing theory.
We actually look for this.
See this portfolio right here, whatever it is, maybe a bay of 1.10,
it should have this return, but instead it has an abnormally higher return.
It happens.
It's not frequent that it happens, but it does happen.
We have a name for that.
Whatever that number is, we call it that unusual extra.
We call it Jensen's alpha.
Believe me, there are algorithms running night and day looking for Jensen's alphas, positive.
Now, you could have a negative one.
Who cares about that?
That's just a bad investor or a bad stock.
Now, if you've got a Jensen's alpha of 0.2%, who cares?
We're looking for those Jensen's alphas that are like a couple percent
because those tell us something is interesting about the stock or about this investor.
In fact, one of the few really reputable websites for investment advice
and really good explanations has the name.
It's called Seeking Alpha.
If you're an insider, which you sort of are now, you get it.
We're always looking for the Jensen's alpha.
Trying to find stocks, portfolios, fund managers that have positive Jensen's alphas in their portfolios.
Now, that's one of those great ridiculous things.
You've got all these awards for, well, this fund manager got the highest return of the year.
Isn't he a great son of a bitch?
Oh, who cares?
You can get any portfolio return you want by taking a high enough beta.
What really matters is you might not have even made that much money,
but did you have a Jensen's alpha that was well, that was decently positive?
That's impressive.
That's when you should get an award, not for just getting the highest return of all the funds.
You can do that, you know, that securities market line goes to betas of 5, 10.
Yeah, who cares?
You took a huge risk and you got a huge return.
Good for you.
Give yourself a cookie.
What we really want to know is did you have magic?
And believe me, the houses all the time, they're looking, you know, you get your,
you get your, well, free stock trades at our brokerage house.
Aren't we wonderful sons of bitches?
Do you think they're not looking for the investors who pulled positive Jensen's alphas?
They're looking for them.
We all are.
And if one of you was, you know, if I found out that one of you had a consistently positive Jensen's alpha,
well, you and I would be buddies.
So that's important.
Just keep that in mind, okay?
What about insider trading?
Is that also like, searching for that as well?
Insider trading, we don't talk about insider trading.
It never happens, ever.
I've never seen a case of insider trading that I would want to talk about because then I'd have to testify in court
and then I'd have someone would pop a cap in my ass.
So it doesn't happen, okay?
It's sort of like aliens.
If I were slurped up by an alien mothership and they, and when I came back, would I tell people?
No, because they'd all think I'm a crazy mofo, which I am, but I don't want people to believe that.
Besides, their captain of that mothership, Zork, he said if I told anyone what had happened in that ship,
he would personally use his phaser on me.
So what happened in that mothership stays in that mothership.
One last thing.
I forgot one measure of risk.
The Sharpe ratio.
Let me show it to you real quick here.
The Sharpe ratio is kind of a low brow measure.
And you can calculate.
All it says is what was the return to the stock minus risk-free rate?
In other words, what was this stock's premium divided by the standard deviation of the stock?
Here's the thing about it, though.
What we hate about it is that it uses standard deviation, which we really don't want to use.
We want to use only the part of the risk that cannot be removed.
All we want, so the question is why would you use sigma instead of beta?
Well, here's the logic of it.
Suppose that you had the risk-free rate, we'll just keep it at 5.48%.
Now let's say we have stock one with a standard deviation of let's say 3.00%, just to make it simple.
Okay?
And the return to stock one is 8.50%.
So Sharpe would be the return to the stock 8.50 less 5.48% divided by 3.00%.
Now watch this.
I'm going to run that one for you and see what happens.
So I would have the return 8.5 minus 5.48 equals and then divided by 3%.
You get 1.0067.
Now suppose that we have another stock which has a return to stock two of let's say some lower amount,
let's say 7.10%.
Standard deviation of stock two is let's say 4.2%.
And the risk-free rate is still 5.48%.
Let me run the Sharpe again and see what happens.
The Sharpe again in this case would be 7.1 minus 5.48 divided by standard deviation of 4.2, 0.3857.
The stock dominates by the Sharpe ratio.
Scaled by the standard deviation, each one scaled by a standard deviation.
That first one is giving you more bang for the buck.
Now here's another part of it.
Why are they using sigma instead of beta?
Because a normal investor doesn't have a well-diversified portfolio of 30, 50 fancy stocks.
They're riding a thin portfolio.
So Sharpe, the whole standard deviation, not just a beta,
is the correct way to judge performance of their portfolios.
And another thing, finding the Sharpe ratio.
You notice with these stocks that I've shown you so far this semester,
you don't see the Sharpe ratio, you see the beta.
If I showed you mutual funds, almost every one of them, they report Sharpe.
Because mutual funds can tend to be thin portfolios.
And so the Sharpe is how you compare the performance of the portfolios.
And the mutual funds report Sharpe ratio is.
And it is actually more useful for funds like mutual funds than the beta is.
There's no cap M or anything like this.
All it does is say what is relatively better than what else.
That's all Sharpe can do for you.
Well, I shouldn't say that. There are people who do really fancy things with it.
But it's out there and I can't criticize it because honestly for a thin portfolio,
beta means nothing because beta is risk in a well-diversified portfolio.
But if you're sitting there with one, two, three stocks,
then probably you're eating the whole sigma.
So you might as well use a metric that uses the whole sigma
instead of that piece of it that's beta.
That's all I have for you today. I thank you.