Alan Cring Productions in association with the Emergent Light Studio presents
the Illinois State Collegiate Compendium, Academic Lectures in Business and Economics.
This is Business Finance, FIL 240 for spring semester 2024.
Today, the capital asset pricing model and just as a heads up, I will have a surprise quiz for you on Wednesday.
So please be surprised. Make sure you have that Excel template for bond yields and bond prices.
That will make that go a lot more efficiently for you if you have it and you know how to use it.
But on a happier note, for today, let's have a look at the numbers.
And as you can see, this is a very quiet bear day.
And it's kind of an unusual one because the least risky of the portfolios, the Dow 30 is down the most, more than a third of a percent.
The S&P 500 is down about 0.2 percent and the NASDAQ is down barely, just 0.06 percent.
It's just one of those days, it's kind of hard to explain. This day started out on a drop.
The opening was down and then it's tried to find its way back except for the Dow.
The Dow just keeps sliding. But as you can see, with both the NASDAQ and the S&P 500, they came up off the opening low.
But they've just never gotten a lot of steam in their whistle.
So it's kind of hard to say what's going to happen, although it looks like there's not a whole lot to move the markets around right now.
Again, just kind of a wait and see attitude.
Crude, it's in a trading range from about 81 to something like about 89, 88.
But it came down off, it broke down below 81 a barrel, but it kind of got excited and pushed it back up.
But it's on the low side of that new trading range. But of course that means higher gas prices because overall the price of the oil is higher.
So that's why you're seeing, as I said would happen, the 379 a gallon along that line.
Now gold, the gold bugs are excited about something.
It's got a new neckline up there at about $2,200 an ounce.
And it's trying to get up there, but it doesn't have really a lot of will to punch through it.
So it's just kind of floating up there at 21.75. Nothing big about that.
At least it's not. It swooped up earlier in the day, but then it's kind of quieted down from there.
Now the bond yields. The bond yields popped up and they're still up, but they lost their speed upward and sort of leveled off.
So we're now at about 3.1 basis points up.
Which of course that means that if the yields are up, the prices are down, that means that there's a mild sell-off of bonds, just like there's a mild sell-off of equities.
And the beneficiary seems to be a little bit of gold is being bought. Kind of worrisome there, but other than that not really much to write home about.
Tokyo, it dropped and then it leveled off and right at the closing, in the last 20 minutes before the closing, it started to fall off a cliff.
And fortunately the bell rang and that ended the bear attack, but it was down 1.16% for the day.
London started out plowing downward, but it has recovered somewhat.
And we're still trading over, London I think is still open. It's in the last hour or so.
But as you can see it's beginning to lose a little bit of speed here again. Right now it's down just 0.17%, so that's nothing much to write home about.
But anyway, overall there's a kind of a little bit of a sour mood right now.
Nothing horrible, but probably I would hope that they're just taking a breather before we have our next upsurge.
One way or the other though, let me take this off the board here for a while.
Now there is some math in what I'm about to do, and it's not tragically hard math.
How did I get a marker that is not a good marker?
Okay, good. There's definitions and terminology in here, and the math is not robust. It's not calculus or anything like that.
It's just knowing what is what, what this term means, what this term means, that term means and all that.
Start off just a little bit with the idea of risk.
Now some of this I've already said, say it again, just to get a running start here.
Now risk, remember, is the spread of possible outcomes.
If there's only one possible outcome, then there's no risk. More than one? Yeah, there's risk.
How much risk depends upon first how many different outcomes there could be and how widely they are distributed.
The more wide the distribution of risks, the greater the risk, of outcomes I should say, the greater the risk.
Now our favorite measure for risk in most subjects is the standard deviation.
And for the sample, that's just 1 over n minus 1 times the sum from i equals 1 to n of each data point minus the mean squared.
And then you take the square root of that mass right there to get your standard deviation of the sample.
If it were a population, you would use an n, but we hardly ever have a population of data, so this is good for us.
Now one quick side mention. We square it and then take the square root. Well, why would we do that?
The reason is rather simple. It's because you can have data points below the average and above the average.
If you just added up those differences, a lot of canceling out would happen.
So we square it so that everything's a positive. Whether the x sub i is below or above, it will be squared to be a positive.
That way we are not getting any canceling of low points and high points.
But anyway, that's kind of our normal one.
And then of course the coefficient of variation is a big one in a lot of subjects, especially, well, in management accounting
or management finance, we look at coefficient variation. I'll explain that in a minute.
But that's a standard deviation over the average.
You will see this. If you were to take one of my higher level courses, and I think they do this in some management courses too,
you might have lines of year by year or month by month or quarter by quarter numbers for your variable costs, your fixed costs, your revenue,
and all those kinds of numbers. And what we like to do is we like to see how those numbers on a given line are varying over time.
But because they would necessarily be of different sizes, fixed costs might be a lot larger than variable costs or vice versa,
it's hard to compare their standard deviations because those are taking the actual numbers.
The coefficient of variation takes out the scale, the size of the numbers, and so we can look at these different lines and compare them.
Now, our variable costs are highly volatile, but our fixed costs seem to be very calm and quiet or something like that.
Our revenues are variable quite a bit, but our net profit doesn't seem to move that much.
So the coefficient of variation does have a lot of good uses to it.
One that I kind of push off to the side sometimes, but it's actually kind of useful.
And I'll tell you why it's not a good idea.
Excuse me.
The Sharpe ratio.
The Sharpe, as a matter of fact, you'll see a template, I'll pull that out on Wednesday.
You'll see a template where you can do all these kinds of calculations, but the Sharpe ratio is one that will...
Yeah, I think I have that in the template.
You take the average returns minus the risk-free rate, and then you divide that by the standard deviation.
The criticism of that one is that it uses the wrong measure of risk, sigma.
The Sharpe ratio, it should be either beta or it should be the coefficient of variation.
Because the Sharpe ratio, I don't know, it's just out there.
It's very popular as a measure of return for mutual funds.
You'll see, as a matter of fact, it's harder to find the beta than it is for the beta of a mutual fund.
The Sharpe ratio is reported very clearly.
I brought it up, so now beta.
Beta is the finance measure of risk.
Beta is the non-diversifiable risk...
The non-diversifiable risk of a security in a well-diversified portfolio.
In other words, beta doesn't mean anything if you're just going to buy a stock.
The total risk is the diversifiable risk plus the non-diversifiable risk.
Make sure you get these down in your notes because I tend on a quiz and an exam to give you a word or term
and then I give you some definitions and you've got to nail the right one for it, risk.
In other words, this whole mass is sigma.
The variation of returns, the total standard deviation of returns is the sum of the diversifiable risk and the non-diversifiable risk.
Something I need to mention here.
Another term for the diversifiable risk is the non-systematic risk.
And the non-diversifiable risk is called the systematic risk.
Now these look kind of backwards.
Diversifiable is non-systematic, non-diversifiable is systematic.
The systematic risk is the risk in the system.
It can't be removed.
The non-systematic risk can be diversified away.
You can make it disappear if you just put more stocks in your portfolio.
There are standalone risk or there risk, internal risk will just cancel each other out.
So those two, there you go, right there.
Okay, now as I said, this is kind of definitions right now.
Another definition.
The return to the market portfolio.
Now when I say the market portfolio, that would be a portfolio of all of the stocks and bonds in the world.
That would be a market portfolio.
It's a theoretical portfolio.
We can't actually buy all of them.
But this is what it would be if we bought all of them.
What's the expected return to the market portfolio is?
We call this the market return over the risk-free rate.
Let me explain this to you.
Let's see if I can do this.
Let's see if it will work.
I got here a $10 bill.
Now, you sir, I shall give you $10 and you have your choice of two things you could do.
You could either walk out the back door here from the first floor and you'd earn a $10.
Or you could go up to the top floor here, and I'll show you how you can get outside from the top, and jump off from there and earn your $10.
Now which one would you rather take?
The first one.
Yeah, I mean, what is the chance, well, okay, yes, you might land on a fat squirrel and survive the drop from that fifth floor here, but most likely not.
You see, the walk out the door is risk-free.
You would want something more than the risk-free rate to do it from someplace where you might actually get hurt.
You might be a hero, you know, become the next TikTok sensation.
He jumped off the fifth floor of the State Farm Hall of Business.
You might, but, you know, the point I'm making here is that the risk-free rate would be like what you'd buy.
I got $1,000, I'll put them into treasury bills.
Well, you're not going to lose your money.
So you're going to earn a little bit, but you're not going to earn a lot.
This market premium, and I should put the word premium here.
This is the additional amount that you expect to get above what you would expect to get by taking on the market risk above what you would get by taking on no risk.
So in other words, if we expect the market return for the coming year to be 16% and right now the risk-free rate is 4%,
then the market premium over risk-free is 12%.
This is the additional reward you get for taking a risk.
You, sir, could have graduated from high school and gone out and gotten a job.
$12 an hour, okay, in your case, $8 an hour.
That would have been risk-free.
No risk.
You take college, you go here to college, you're taking an expensive risk.
There's no guarantee you're going to come out with a job because of this degree and all this great learning that you're getting.
You're taking a risk, so you expect an extra return, maybe $50 an hour.
So the premium for taking that risk is 50 minus 12 or $38 per hour.
That's the point of what that market premium over risk-free means.
If you are unwilling to take risk, you get R sub F, the $12.
If you are willing to take an actual risk, then what the extra you get is the 50 minus 12 or the $38.
So that's what that kind of means in a little bit more understandable terms.
Now we're moving kind of forward here.
Let me go back here just for a minute.
When you're building a portfolio, putting more stocks into it, what you are actually trying to do is to narrow,
get this diversifiable risk down because of that risk pooling effect that I was telling you about on Wednesday.
Get the peculiar risks of each stock to cancel each other out.
And the more stocks you put into your portfolio, the more that noise, that diversifiable risk will disappear.
You're probably never going to get rid of all of it unless you had a world portfolio.
Then it's all systematic risk, but you try to get as close as you can.
Now, how many stocks would it take to actually shake out this diversifiable risk?
Well, it works like this. Let me draw you a picture here.
And we've done a lot of simulations on this.
Let's say that on the horizontal axis is the number of stocks, number of stocks, different stocks in your portfolio.
And on this axis is the total risk of the portfolio.
And again, we've done a lot of these simulations and looked at real world data.
At one stock, you've got pure total risk. Pure total risk.
I mean, one stock's got both its diversifiable and its non-diversifiable.
As you put in more and more stocks, it slides off.
You might remember a term from math and algebra, the asymptote.
Actually, in the first five to ten stocks, you squeeze out a lot of that diversifiable noise.
And then it slides off more and more slowly.
The asymptote, not surprisingly, is the non-diversifiable risk, the systematic risk.
In other words, if you get enough stocks in there, all you'll have is non-diversifiable risk.
You will have squeezed out all of that diversifiable non-systematic risk.
How many stocks?
To get rid of 95% of the diversifiable risk, about 35 stocks.
That's actually a lot of stocks in a portfolio.
I mean, you have to buy those. That takes a lot of money.
And then you'd have to manage it to keep the portfolio in balance.
If a stock price goes up a lot, then you shave off so that it comes back into line with the others.
Or if a stock goes down, you put more of it in there to bring its value back up in the portfolio.
But yeah, about 35.
That's why we strongly recommend that you invest in mutual funds and ETFs.
Because they have portfolio managers who have put hundreds of stocks or bonds or both in.
And then they watch them and manage them every hour of every day.
So that's, I mean, for example, let me show you real quick here.
The SPYDR, I've mentioned this one before.
This is the S&P 500.
As a matter of fact, the S&P 500 is so well diversified that we use it oftentimes as a proxy for the market.
It's got, I mean, somewhere between 65% and 70% of the value of the world securities are in the S&P 500.
So it's hugely diversified.
It's managed professionally by the top cats in the industry.
And so it's, you know, I have a fun portfolio too.
I just buy and sell a few, take a lot of risk in them and all that.
But the responsible money is in these professionally managed ETFs that you can get.
You just buy a share, you buy a share of this, you've got a perfectly well diversified portfolio.
That's all there is to it.
Now, however, let me take you, there's one more term that is useful for you now.
Well, what the hell is beta?
Beta is the measure of the non-diversifiable risk in a stock.
So you can't really just look at beta and say, well, if I buy this stock, I'll have this much risk.
Because this means something only in a well diversified portfolio.
If you buy a stock on its own, you don't have the beta risk.
You have sigma risk. You have the whole thing.
Like my favorite example, I believe it's Microsoft.
If you buy a share of Microsoft, 60% of its risk is diversifiable.
Only 40%, the part that you will expect a return for, is non-diversifiable.
Now, the actual formula for the beta is the, well, let me find some other place to put this.
Beta of a security, a stock, whatever, it's the correlation coefficient of that stock with the market portfolio
that times the standard deviation of the stock over the standard deviation of the market.
That's the actual formula for beta.
That's about all I just took.
But now, so actually, when we calculate a beta for that standard deviation of the market portfolio,
oftentimes we'll take the standard deviation of the S&P 500 or the standard deviation of that ETF.
That is the standard deviation of the market.
Notice a couple of things.
If I talked about the beta of the market portfolio,
the correlation coefficient of the market with itself times the standard deviation of the market
over the standard deviation of the market.
In other words, that would be the correlation of the market with itself is 1.00
times the standard deviation of the market over the standard deviation of the market.
So the beta of the market portfolio is 1.00.
It's like our anchor.
That's why I kept saying, okay, well, the beta is above 1 or below 1.
That's why if it's above 1, then it's above the market risk.
If it's below 1, then it's below the market risk.
One more.
The beta of the risk-free rate, like a treasury, something like that,
the correlation of the risk-free with the market
times the standard deviation of the risk-free over the standard deviation of the market.
Well, that one's kind of easy.
The correlation of the risk-free rate with anything is 0.
The standard deviation of the risk-free rate is 0
over the standard deviation of the market.
So the standard deviation, the beta of the risk-free rate is 0.
Okay, so we're there.
Now let me step back from this.
I started throwing this kind of algebra and arithmetic,
and it can kind of put you off.
But let me take you on something of a little bit more practical setting.
Suppose that you want to build a portfolio.
I'm going to start.
I know it's 35 stocks, but I've got to start somewhere.
So you put in your first stock.
The next thing that you would want to do,
don't just pick a stock that you like or that someone recommended.
The first thing you want to do is keep that next stock
from being too highly correlated with what you already have,
because the only way that you shake out diversifiable risk
is if the odd whips and saws are canceling each other out.
That means that you want to find stocks that have low correlations
against each other.
You don't want stocks that are highly correlated
because they'll fuel each other.
They'll go in the same direction.
You want stocks that don't run very well together.
They don't play well.
That way they're going to cancel out more of each other's diversifiable risk
and retain the underlying risk of the market.
Let me show you.
There's a site that I...
This has been around for a long, long time.
It's called Portfolio Visualizer,
and I'll put the URL, the address of this,
in your Canvas files folder.
This is a place where you can put in trading symbols of stocks,
and it will show you how correlated they are.
Now, you may remember that the correlation coefficient goes...
If it's 1, then they're perfectly correlated.
Oh, you don't want that.
I'm going to just grab some stocks kind of out of thin air.
Walmart.
Let's take Ford.
Apple.
I don't know. Meta.
I don't know.
What would I want?
Pfizer, let's try.
Rochead Martin.
Anyone got another one?
Trying to...
What? AT&T?
Good.
That's five.
Now, what it's going to do is create a correlation matrix.
Now, remember, correlation matrix is symmetric on the diagonal.
Let's have a look at what these guys do.
Here we go. Correlation matrix.
Now, here's my rule.
Point three, zero, or below.
That's good for a portfolio.
Above point three, and you're getting a little too much feeding.
The stocks are feeding each other too much.
They're correlations. They're too closely moving together
and feeding each other's diversifiable risk.
Now, let's look at Walmart.
Walmart.
Ford and Walmart would be good in a portfolio together.
That correlation coefficient is a low.19.
Apple, it's right on the boundary.
Now, I have no clue.
Sometimes it's obvious why they're highly correlated.
But sometimes you've got to think,
well, why would those be correlated?
But Apple and Walmart are somewhat correlated.
I might...there's plenty of others.
Now, look at Walmart and Meta.
Obviously, they're so different, what they do.
And their correlation is commensurately low,.12.
Walmart and Pfizer are okay together.
Walmart and Lockheed Martin are good together.
And Walmart and AT&T are good together.
Walmart looks from this like what we might call a key stock.
The one that would be in almost any good portfolio
because it doesn't correlate well with others.
In fact, if I build this matrix with a few more stocks,
you'd see that it doesn't like anything very much.
Now, let's look at Ford.
Ford with itself is obviously 1.0.
So Ford with Apple, now that is a little surprising.
You would not want those in the same portfolio.
Just a little too highly correlated for my taste.
It's okay with Meta, and it's okay with Pfizer,
Lockheed Martin, and Ford, and AT&T.
The one that is a little bit disturbing there,
Ford with Apple, and I can't figure that one out at all.
Sometimes it's obvious, like I said,
and sometimes you think,
why would they be so correlated like that?
But Apple, let's get across here.
Apple with Meta, a little bit scary there with.27.
With Pfizer, it's good.
Lockheed Martin, it's okay.
And with AT&T, very good again.
Pfizer, if I go over here, Pfizer with itself,
Pfizer with Lockheed Martin.
Now, why in the heck would those two be correlated?
Unless Pfizer, you know,
Pfizer is a medical supplies, medical stuff kind of company.
Lockheed Martin is a war company.
Maybe something to do with that, I don't know.
But with AT&T, it's okay.
Lockheed Martin.
Now, look over here at AT&T.
It also looks like something of a key stock.
It's nasty with Lockheed Martin,
but with a lot of things, it plays pretty well.
Matter of fact, with Meta,
AT&T and Meta are almost uncorrelated.
So you get a feel for what stocks play well with others,
and what stocks just have everything you put in there
has a.3 or something above or just closely below it.
So this gives you an idea.
This portfolio visualizer, it's something that does not hurt.
If you've got a stock or two,
first of all, look at those two.
Are they highly correlated?
Well, they're not helping you at all
with getting rid of that diversifiable risk.
But when you put in stocks, you just test,
okay, I heard about this stock.
Let me see how it would play with the stocks
that I already have.
You might find that it works very well,
but you also might find that it does not work very well.
Or the stocks that you have in your portfolio,
they don't play well together,
and you might want to consider moving out some of them
and putting other things in
that have less of that correlation with them.
It's something to think about.
Now, let me do something here.
Bring you back a little bit here.
Let me show you something.
Let me show you a graphic.
This graph with actual real-world data,
simulations and all that,
has been done many, many times.
It was sort of like the fuel of PhD dissertations
for a generation or two.
As a matter of fact, Google used to have
one of my graphs of this
when you search for this term that I'm going to show you.
But let me show you this for just a minute.
This is total risk.
And on this axis is the return to a portfolio.
That could be one stock, one bond,
a couple of stocks and bonds, or whatever.
And this has been done many times.
We look at a portfolio and we see its return.
And whenever we do that, whenever we do that,
we'll get data points all over the place.
Just risk, return, plot another portfolio,
risk and its return, plot another,
and all over the place.
We just keep plotting.
And we get some portfolios that have high risk,
very bad return.
Some have low, high risk and high return.
But no matter how many times we plot this,
and believe me, there have been lots and lots of these done,
like I said, there are now even undergrad research papers.
If you're thinking about doing one,
you can't beat this.
You'll find portfolios all over the place
with the risk and the return.
But there's something strange going on.
It's a phenomenon that we see in physics, kinesiology,
astronomy, mechanical engineering,
electrical engineering.
We see that systems have a place
where we no longer see any data points above it
or below it, whatever it is.
In mathematics, we call this an envelope.
You decide that you're going to become a weightlifter.
You're going to become one of those beefcakes
with the balloon muscles.
You start talking.
Did you ever see the original movie Rocky?
But you play that music anyway.
You say, da-da-da-da-da-da-da-da-da.
Okay, and I'm going to get my muscles,
and I'm going to lift more and more weight,
more and more weight.
You will find a place where you cannot lift any more.
You will not be able to.
Now, you'll push the envelope,
but you'll never get to that desired, let's say, 900 pounds.
No matter what you do, you try to lift 900 pounds,
but no matter what you do, you fart.
That's right.
Grrr.
I won't make this sound.
We all know what it is.
God knows anyone who's been near you knows what it is.
Okay, but here's the problem.
You're breaking, you're trying to cross into an area
that can't happen.
The same is true with, for example, with astronomy.
You find stars that are absolutely enormous,
but we've never found a star that is larger
than a specific boundary, the envelope.
You can take your car.
You can tweak the hell out of it,
put in everything you need to get speed,
but there's some speed you cannot cross.
That's the envelope.
You've come to the envelope.
No matter what you tweak, it won't get past that.
Your personal best running speed.
There will be a speed you will never cross it
no matter what you do.
Well, I believe in myself.
Try it.
Just keep going and see if there's a speed,
and you can't reach above that speed.
That's the envelope.
Explosives.
There's only so much thermal energy that we can create
from a specific chemical reaction.
We cannot get more.
No matter how efficient, no matter how pure
the elements, the ingredients are,
we can't get past a specific explosive charge on it.
This is the envelope.
It's all through the universe in us,
in everything that we do, and that's the envelope.
We see it in finance.
No matter how hard you try to diversify your portfolio,
you will never get past a specific risk return point.
Well, I want to take this much risk right here.
Dag on it.
I want to get my, I'll take this risk,
and I'll make my portfolio, I want to be up here.
You'll never make it.
It just can't happen.
We've never, we don't see it.
It's just not there.
You'll never get close to this envelope,
but you won't even actually touch the envelope.
We actually know what this envelope is.
Those points on the envelope, those are world portfolios,
different combinations of all the stocks and bonds in the world
and different weights and all that kind of stuff.
We just can't get there.
We have a name for this.
We call this the frontier of efficient investments.
And like I said, this graph can look all kinds of ways
with the axes switched around and all that,
but watch this.
We know about this place.
Let me try, I'll do a Google, Google.
Google.com images frontier of efficient investments.
There it is.
We know about it.
It's the 800-pound gorilla in the world of investments.
Can't get past that envelope.
Now, let me really quickly here just to explain
what we're actually seeing here.
Portfolios could be all over here.
For example, this is a portfolio.
Let's say this is a portfolio only of Microsoft stock.
So it's got this risk level here, sigma some MFST,
and it's got this return right here, R sub MSFT.
What this is telling us is that for that risk level
or it is for that return, I could actually be clear back
here in terms of risk because this piece that's inside
of the frontier, that is the diversifiable risk
that you could get rid of by adding more stocks
to the portfolio.
The part from here to here is the nonsystematic risk
or the non-diversifiable risk.
The beta risk.
This whole thing is the sigma risk.
This little part in here is the beta risk.
So in other words, whenever you buy a single security,
you are sitting inside of the frontier of efficient investments.
You get that same return from a portfolio
that had less total risk.
In the case of Microsoft, if I remember the numbers right,
that part that is diversifiable, if you have Microsoft stock
and only Microsoft stock, it's 60% of the volatility,
of the total volatility.
Only about 40% of the volatility of Microsoft
is rewardable by the markets.
The markets are going to reward you for taking risks
that you did not need to take.
That's the important point about that.
Now, a word about this envelope.
We can't get to it.
It's just a theoretical thing.
It's like the speed of light.
We can get as close as we want.
We get subatomic particles within a fraction of a percent,
but we can't get to it.
But there are some strategies that will get you really close to it.
In other words, almost no diversifiable risk.
Like for example, here's an ETF right here,
sort of like maybe the S&P 500.
It's highly diversified, but it's not perfectly diversified.
Now, and I teach this in the next level, 242.
If you get a couple, maybe three ETFs or things like the ETNs
that are all very efficient, they're all very close to the boundary,
and you get by all of those, what you have is what we call a super portfolio.
And the super portfolio is even closer than any of the individual components.
You can squeeze that down.
First, you let the highly diversified portfolios squeeze out as much as they can,
and then you let the – put them together,
and you can squeeze out even a little more of the diversifiable risk.
Those are called super portfolios.
It's something that I teach in a little more advanced class.
There are other ways that you can squeeze out.
I mean, I don't know how much you're gaining if you go from 99% pure,
non-diversifiable risk to 99.5%,
but you can get awfully close to that boundary, that envelope.
In other words, closer and closer to having, effectively, the world portfolio.
That's the return to the market portfolio.
There. Okay.
So, excuse me.
Next step.
Let me take you over here.
How do we use the beta?
How are we going to – what's that going to – what is it going to buy us, that beta?
This – well, I just erased that.
I'm going to put it up here.
The market premium over the risk-free rate.
It's the extra reward you get for taking the risk of the market
instead of a risk-free treasury bill, as it were.
Now, here's what beta does.
The beta of a stock times the market premium over risk-free.
This tells you what your stock will get of that premium.
So, in other words, let's say you've got a beta of a stock that's 0.5.
Then, by this little formula right here, your stock would get 6% of that extra.
If you had a stock with a beta of 1.50, then you would get 1.50 times 16% minus 4%.
Or you would get 18% on that premium.
Beta is a magnifier or a demagnifier of the premium.
That's all beta does.
Look at this.
Let's take a beta that had a perfectly zero – that was perfectly zero.
Then what you would get is 0.0 times 16% minus 4%.
You would get no extra.
Because you didn't take any risk, why should you participate?
Why should you get any of the market's extra reward?
But if you had a beta of 1.00, then you would get 1.00 times 16% minus 4%.
You would get the whole market premium over risk-free.
You get the whole thing.
Because you took on the market, perfect market risk.
So let's put it all together here.
This is called the capital asset pricing model.
Cap M.
Sort of the triumph of finance.
Discovered or created, as it were, in the 1960s, I believe, it simply says this.
The expected return to a stock or a portfolio of stocks.
It doesn't matter.
It's going to be, first things first, any investment that is risky would have to give you,
at a minimum, the risk-free rate.
At a minimum, it would have to give you the risk-free rate.
So that's the substrate of any investment.
You expect it to at least give you the risk-free rate.
Because otherwise, why wouldn't you just buy treasury bills and get no risk?
Plus that little piece beta sub S times R sub M minus R sub F.
That extra on the premium.
The R sub F sitting by itself is just, you've got to get that.
No investment should have an expectation of getting you less than you could get by taking no risk.
Plus you get the market premium magnified or demagnified by the beta.
So just take one here on that one example where the beta was 1.5.
You would get, what did I say, risk-free rate was 4%.
You'll get that.
Plus you'll get 1.5 times 16% minus 4%.
So what is that?
4% plus 18%.
So your expected return to a stock with a beta of 1.5 should be 22% under the current conditions of R sub M 16% and R sub F 4%.
That's what you should get.
Draw a graph here.
We're almost home, folks.
Draw a graph here.
Okay.
Ouch.
On the horizontal axis, I'm going to mark, I'm going to plot beta.
0.2, 0.4, 0.6, 0.8, 1.0.
1.2, 1.4, 1.6, 1.8, 2.0.
In other words, I'm looking at a range of betas.
And on this axis, the expected return.
If I have a beta of 0.0, I should get the risk-free rate.
No risk, you just get the risk-free rate, whatever it is.
In that case, that would be the 4% for the current example.
If I have a stock that has a beta of 1, look what happens if I do a beta of 1.
I would get the expected return would be 4% plus 1.00 times 16% minus 4%.
So I should get 4% plus 12%.
Surprise, surprise, you get the expected return to the market.
So in other words, at a 1, you would get the return to the market.
And then two points are enough to make a line.
That's the graph of cap M. Don't make it complicated, for God's sake.
All it is is just a graph of that weird equation right there.
So in other words, I could say, well, 1.5 should be up there, about 22%.
A 0.5 should be about there, about what?
What did I figure that to be? 0.56%.
It's just a graph. We have a name for this.
It's called the securities market line.
In test after test that we've done, looking at actual returns versus their betas,
the scatter plots are always very close to the securities market line.
It is so reliable that we can use it very confidently.
It's not perfect. It's not going to give you exactly,
because there is random noise in the system like there is in any system.
But the plots almost always, we take a stock, it's beta, we look at its return,
and we plot the beta against the return.
It's always very close to the securities market line.
This works. And there have been fancier models since then.
Book mentions them, but everyone knows that the cap M has not been overrun by the data.
The data establishes the reliability of cap M.
However, one mention.
First of all, the worst thing in the world that you could believe in is someone
who is said to have way high returns on his or her portfolio.
This is a genius. This person beat the market.
Well, actually all that means is that they just took a high beta.
They didn't beat the cap M. They just got higher than the market return.
Why did they get that? Because they took a beta above one with their portfolio.
There's no hero in that kind of activity.
And yet these contests are done all the time.
The awards are given to the fund managers who get the highest return on their portfolios.
Almost invariably all they did was take giant betas.
They didn't do anything. But what the cap M says to do if you want high returns,
you take high risk. Nothing heroic about that.
However, once in a while we do see someone who's got like a magic.
A fund manager, an amateur investor, and they will get, let me show you.
They'll get a return way above what cap M says they should.
It'll be way above the cap of the securities market line.
We see it. I've seen it myself.
How they do it, God only knows.
And oftentimes they'll do it for a couple of years and then they'll lose their magic.
But we do have a name for this.
See this distance from what they get down to what they should have gotten from the cap M?
We have a name for that. It's called Jensen's Alpha.
Now Jensen's Alpha can be negative too, obviously.
But we do see it.
Now if you've got a Jensen's Alpha of 0.2%, that's nothing.
That's within the data noise range.
But we see some, once in a while we'll see someone who's got a Jensen's Alpha of 3, 4%.
In one case there was some guy who had 12% Jensen's Alpha.
In other words, it was up there in the screen.
Matter of fact, there's even a website.
It's very reliable and I love the people who run it.
It's called Seeking Alpha.
If you get into investments, yeah, it's a play on that.
We're looking for the alpha.
Trying to find a way to do investments so that we get above what the physics of the model say we should.
So Jensen's Alpha, we're all seeking Jensen's Alpha.
Getting a higher reward than we deserve to get based upon the beta of the stock.
And believe me, when you invest, any investment house that is worth its salt is looking for the magician,
looking for the wizard, looking for that person who does trades and is constantly getting better than the CAPM says.
And so once, I mean, if you've got, give 10,000 free accounts, all you have to do is find three or four who have found alpha.
They're not seeking it, they're finding it.
And then we just front run them.
Whenever they put in an order, we put an order in front of them so that we can play on their genius.
This is how it's done. It's illegal, but illegal schmigel.
But there you go.
That's the extent of this.
I should point out one thing here.
And it's almost obvious.
Look, the return to a portfolio would be you take the weight of each stock in the portfolio times its return.
You know, it's just the weighted average.
The portfolio's return will be the weighted average of the component's returns.
And also, the beta of a portfolio is nothing but the same trick from I equals one to N of the beta of each stock times its weight in the entire portfolio.
In other words, just a sum product from Excel.
So you can find the beta of your portfolio.
So if you've got like a high beta stock in your portfolio and you don't want to be that high,
just put in a low beta stock and the weights of them will balance it out.
That's part of what's called portfolio control.
It's just making sure that you always have betas in a range so that they average out to the beta that you desire.
Had enough?
That's all I have for you today.
I thank you.