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. This is a math lecture, but the math is not hard.
It's kind of like arithmetic for the most part.
But it's the conceptual framework behind it that's a little bit more, you've got to take good notes and read back through them, maybe listen to the podcast.
Now on Wednesday I will have a surprise quiz, so please be surprised by that.
And be sure that you have your template for bond pricing and bond yields available to you for that one.
Now the subject of what I'm doing here will also have sort of a template, but it's kind of like a diffuse set of things that I'm doing in this chapter.
So hang on for the ride. But before we do that, a quick look at the numbers.
And this is an odd day, it's a bearish day, but it's a day when the Dow, the safest portfolio, is down the most at about 0.36%.
The S&P 500, a somewhat riskier portfolio, is down less at only, what is that, 0.13%, something like that.
And the NASDAQ, the riskiest of the portfolios, has actually managed to grovel back into positive territory.
It's nothing much, but I mean, it's 0.03%.
It's just an odd day when the risk-return relationship is turned on its head.
But I'll let that go, but looking over here at Crude, as I had said, we are now in a new trading range from about $81 to maybe $88, $87 a barrel.
Now we're at the lower end of that, and it actually crossed back through below this new trading range, but it got right back into the low end of it at $81.96 on light sweet Brent right now.
Which of course, as I said, will translate into somewhat higher gasoline prices. It's nothing catastrophic.
We're seeing about $379 per gallon locally, and it'll probably stay there for a while because oil prices will probably stay in this trading range for a while as well.
Gold is having, it's got a neckline, a new resistance level at about $2,200 an ounce.
But it's chickening out, it gets too close to it, and it backs back down a little bit as you can see in that spark chart there.
It made a run upward, and then it tapped, I think it tapped $21.80 or something like that, and then it backed back down.
So there's money going, seems to be going into gold right now, bonds.
The bond yields are up, and that's always not great news.
It's not much, 3.7 basis points, so the yield is up, the price is down.
The price is down means that there is selling of bonds.
Investors are getting out of bonds, they're getting out of stocks, and a little of that money, unfortunately, is going into gold.
Flight to quality, from stocks to bonds, bonds to gold.
It's nothing really dramatic at all, it's just real lightweight what's going on now.
It's more just an overall kind of grumpy mood the markets have, have had this week.
It's just kind of a sour mood, but it's nothing dramatic at all, nothing to really worry about right now.
But going over to the other side of the world, the Nikkei slid down at the opening, and then it kind of leveled off.
But right before the bell, you can see there was a heavy sell-off.
The bears were really having a rampage, and the only thing that stopped them was the closing bell over in Tokyo yesterday afternoon, last night to us.
So I don't know what that's going to mean for tomorrow.
But London started down, and then it came back, but it never did cross back into positive territory, and it finished the day off about 0.17%, which is pretty trivial.
But still indicating that overall bearish, mildly bearish attitude that seems to be pervading the global markets right now for some reason.
The markets around the world are in a kind of a sour mood.
Whatever. It's just one of those things that's going on right now.
Take good notes. This lecture kind of seems like there's a little bit of here and then here to it, but it all ties together at the end of it.
And it begins with that age-old term risk that I've talked about so often.
How do we measure it? Because we can't really make decisions on something unless, as professionals, unless we have numbers to back up our decisions.
The CYA, cover your ass, the numbers said. And that's how we live in our world.
We rely on laws of the universe to actually work.
And you're going to see a principle of all things applying itself in finance here a little bit later in this lecture.
But to start with risk, the classic measure of risk is the standard deviation.
And the fancy formula 1 over n minus 1 times the square root of the sum from i equals 1 to n of x sub i minus x the average squared.
That's a fancy way of taking each data point minus the average of the data points, squaring it, adding them up, take the square root, and then divide by n minus 1.
And it's the classic measure of risk. In many subjects you would take, standard deviation would be the measure.
They might not call it risk, they might call it variability or something like that, but it's a measure of the risk.
In our world it's a measure of total risk.
Because in finance we break that total risk down into two pieces.
One piece we have to live with, the other piece we can make go away.
But we have to do so in a disciplined fashion.
But risk, that's one of those classics.
Now the next thing that we would probably want to talk about is the coefficient of variation, the CV, which is the standard deviation divided by the average of the data.
Standard deviation of the data divided by the average.
This takes away the scaling problem.
You see I could have one data set that had a standard deviation of a thousand, and another data set that had a standard deviation of ten.
But that would be only because the first data set had bigger numbers in it.
The CV, the coefficient of variation, takes away the numbers themselves and turns it into a pure number so that we can compare them.
I should point out that in the standard deviation you may run into that in another course.
You certainly will if you were brave enough to take one of my upper level managerial finance courses.
Because often times we look at accounting data or managerial numbers data.
We'll see by day, by week, month, year, whatever.
We'll see a line of data, let's say for your variable costs.
And we'll see another line of data, let's say for your fixed costs or something like that.
Now we would like to see how variable, how much volatility there is from week to week, month to month, or whatever, in that line of numbers.
Well the standard deviation itself won't help us because your variable costs might be a lot bigger than your fixed costs.
Or we might look at revenue variability versus your net income variability.
And so the numbers would not be on the same size.
And that's when that CV comes through.
We just turn all of those lines of standard deviations into coefficients of variation.
And then they're telling us the variations relative to each other.
It's quite useful that way.
And sometimes I've seen where standard deviations were being used.
And I'm thinking, you should use coefficient of variation because you're comparing numbers from two data sets that are very different in their size of their numbers.
But anyway, that's another one.
Now there's a risk measure, and I kind of dismiss it most of the time.
The book brings it up, it's called the Sharpe Ratio.
Now this one is really popular in some kinds of securities.
As I mentioned before, mutual funds, they, instead of using beta, which is what they should use, they oftentimes will key in on the Sharpe Ratio.
This is the average return to the investment minus the risk-free rate divided by the standard deviation of the data, of the returns.
The Sharpe Ratio is, okay, old timers like me kind of look down our noses at it.
The main reason is that it uses standard deviation instead of beta.
Or at least it should be using the coefficient of variation instead of the standard deviation.
But it goes along, it's popular in some securities to talk about the Sharpe Ratio.
And it's there, and the book brings it up, they give you a problem with it or two.
And I think I have it even in an Excel template where it finds all these numbers and it also calculates the Sharpe for the numbers as well, the returns.
And it's popular, you've got to be careful about it, but you know, there's that.
Now, the 800 pound gorilla is the beta of a stock, the beta.
That's the measure of non-diversifiable risk, that's ours.
And the formula for it is the correlation coefficient of the stock with the market portfolio times the standard deviation of the stock, scaled divided by the standard deviation of the market returns.
It's not hard to calculate.
Now, real quick, if you look at the beta, say what is the beta of the market portfolio?
Well, if I look at the beta, the beta of the market would be the correlation of the market with itself times the standard deviation of the market divided by the standard deviation of the market.
I mean, if I follow the formula, S, S, S, so that's an M, M, M up there.
So I know while the correlation of the market with itself is 1.00, the standard deviation of the market over the standard deviation of the market cancels, so the beta of the market portfolio is a perfect 1.00.
That's what I was talking about all along. Betas above 1 would be riskier than the market portfolio.
Betas below 1 are less risky than the market portfolio.
So that's the explanation why that 1.00 is the fulcrum.
Now, one other one that might be worth talking about, what about the beta of the risk-free portfolio?
Well, that would be the correlation of the risk-free with the market times the standard deviation of the risk-free over the standard deviation of the market.
This one's not quite as obvious, but the correlation of the risk-free rate with the market is zero.
The risk-free doesn't move at any given time.
So the correlation coefficient is zero.
The standard deviation, the risk-free rate, doesn't move around, so it's zero over the standard deviation of the market.
So the beta of the risk-free portfolio is 0.00.
That's important to us, because in other words, we have two points on a line, which we'll graph later.
We've got the beta of the market is 1, the beta of the risk-free is 0.
That will be useful to us a little bit here.
But the next thing to do is to talk about the market premium over the risk-free.
The risk-free rate.
That would be the return to the market minus the risk-free rate.
So in other words, think about it this way.
I've done this one before, but let me try it again here.
You, madam, could have gone right out of high school and gotten a job full-time.
No risk in doing that.
There's a lot of risk going to college.
There's a risk that you will not get a job that's very good.
There's of course the risk that you'll get a professor who is a weird ass and drives you away from college.
Oh, sorry.
So you could have gotten a job right out of college for $12, in your case $8 an hour.
No, $12. We'll give you $12.
Risk-free.
If you make it through the risk of college and you get a good job, you will, let's say, make $50 an hour.
So your premium is $50 minus $12, or $38.
That is your extra reward for taking risk instead of no risk.
If you invest in the market and take a market portfolio of all the stocks possible and bonds, you expect to make 16%.
But you don't have to do that.
If you don't want any risk, you can just buy a budget T-bills and get 4%.
So the market premium over risk-free would be the 16% minus the 4% or 12%.
This is the extra you get for taking risk instead of no risk.
Just like the premium for taking the risk of college over just getting a job out of high school was $38.
There's an extra, and that extra is what is important to us in financial modeling.
How much extra do you get?
Okay.
Let me step back from that for just a minute here.
Let's talk about that total risk.
It has two pieces, that's sigma.
It has two pieces.
It has a piece called diversifiable risk.
That is risk that is inherent to the company itself, bobbing up and down.
And then it also has another piece that is the non-diversifiable.
Risk.
That's what beta measures.
You put those together.
Now, usually when we run returns on stocks, we're seeing all of the risk.
You run a beta vector of returns to a stock by month or by year, and you get a standard deviation.
That's the sigma, that's the total risk.
Hidden inside there are the two pieces.
I need to make a note here.
These have another term.
Diversifiable risk is sometimes called non-systematic risk.
It's not really part of the system.
It's part of a company and its variability.
And then the other part, the non-diversifiable risk, is called the systematic risk.
It's kind of backwards, the non's there.
You might have woken up one morning and you look in the mirror and you have a big nodule on your nose.
That's non-systematic, you know, cut it off.
I do it all the time, shaving too fast.
Okay, keeps me from looking like a troll though.
However, suppose I have something inside me like a cancer.
That is system that I can't just get rid of, I can't diversify away.
It's there and it's part of me.
And so, let's talk about these two pieces here.
These two pieces of risk.
I'll show you a Google image here after I've done this.
As a matter of fact, Google, long ago one of my pictures of this was one of the Google images.
But every year there's new images of this too.
But I'll show you what's going on.
Now this graph has been the subject of dissertations, thesis, undergrad research papers for decades.
You take a pile of portfolios.
You can simulate them or you can just take them from actual portfolio data.
And you look at the risk of that portfolio, how much it bounces around with that formula.
And look at how much it returned on an annualized basis.
Okay, that's cool.
Let's do that here.
Let's take on the horizontal axis, we'll take the standard deviation of a portfolio.
And on this axis we'll see what the return to the portfolio was on an annualized basis.
Now these data plots of this, like I said, they've been done countless thousands, maybe tens of thousands of times.
And you'll find, well these low risk portfolios you'll see there.
We plot all these different portfolios, single stocks, a couple of stocks and bonds, all that kind of stuff.
You just keep plotting, going through the data, risk and returns for a portfolio, the risk and the return.
Just keep plotting these.
And you can, I mean some of these, I think the hero was back in my time, someone actually did like 10,000 portfolios.
The risk versus the return.
He did the program in Fortran, how he did that, because we didn't really have the graphics programs that we have now.
Even on your full phone you can do graphs.
We didn't have Excel either.
But I mean they're all over the place, these graphs are.
But there's something that happens.
If you plot a whole lot of points, something is very noticeable.
There's a place where you don't see it, a white space, you don't see any data points there, ever.
In physics and in engineering, they referred, in mathematics, which is where the term came from, they call that an envelope.
In mechanical engineering and in some other types of engineering, it's called a performance envelope.
We see it all through the universe, I mean all through the universe, these envelopes.
So for example, you sir decide that you are going to start lifting weights.
Dude, do you even lift?
And you say, I'm going to be like Rocky, you remember Rocky the fighter, you remember blah blah blah blah.
Now that's an awesome thing.
And you start lifting, get up to 200 pounds.
Deadlift 500, 700.
There's a point you will not get past.
You just won't.
No matter how many grunts, no matter how hard you fart, you will not lift that 900 pounds, let's say.
That's where your envelope is.
You start running, you start running.
There's a point where you can get no faster.
So it's kinesiology, we see envelopes all the time.
You've got a really lame, a nice car, not a lame car, you've got a nice car.
You tweak it, you play with the engine, you can get it up to 120, 122.
But there's a speed you will never get out of it.
Not until you buy that Army surplus jet assisted takeoff and then we never saw you again.
Story's about you landing in Nevada somewhere.
But that's the point. Again, in astronomy, we see stars that are extraordinarily large.
But we cannot find any star that is larger than a specific volume.
That's an envelope.
Anywhere you look in chemistry, we can use chemicals to create explosions.
But there is a limit to what we can do, refining, purifying the chemicals, mixing them in different ways.
But there is a certain thermal energy level out that we will never cross.
We cannot get it, so we have to go to some other technology to make those ones that go make a bigger boom.
That's the same envelope. It's all through the universe.
And we see it, the data shows it to us.
And now we have a name for this.
This place.
It's called the frontier of efficient investments.
The frontier of efficient investments.
Now I'm going to show you how notable this is.
I put in Google, I said go to images in Google, I said show me some graphs.
I just typed in frontier of efficient investments.
There you go. It's that well known. It is famous.
In a way it's kind of interesting that we have this envelope that has been found over the centuries by physicists, chemists, kinesiologists, I mean you name it, engineers.
And here we have it in finance.
The same phenomenon. Some boundary that is never crossed.
Now the term efficient means that these are portfolios that would be perfectly efficient.
There would be no diversifiable risk.
In other words, on the envelope itself are world portfolios.
Different combinations of all the stocks and bonds of the world in a way.
We'll never achieve a perfectly efficient portfolio.
We can get close to it, but let me show you just an example.
Let me take this point right here. This would be a single stock.
Microsoft would be an example.
So this would be the standard deviation of MSFT.
And that would be associated with this return to MSFT.
It's inefficient because I could get that same return with a portfolio that had much less risk.
Single stocks, even bundles of stocks generally, are well inside of the frontier.
Specifically, let me show you this.
You see from that point horizontally over to the efficient frontier, that is diversifiable risk.
That's what that is. That is a risk that could be taken away.
Only this little piece here is the non-diversifiable.
Taken together, they are the risk, the sigma.
The sum of what is diversifiable and what is not.
So what that means essentially is that the more stocks you put together, the more you're going to shake out, squeeze out that diversifiable risk.
That's one of the big lessons. You have to add stocks.
Now, if you were building your own portfolio, the risk graph, number of stocks, and the total risk of the portfolio.
With one stock, all you've got is the risk of that stock, the total sigma.
You're facing all of the non-diversifiable risk and all of the diversifiable risk with one stock.
However, as you start to add stocks, you're squeezing out the diversifiable risk.
And so, as you add more and more stocks, you are asymptotically approaching the non-diversifiable risk.
You'll never get there. I mean, okay, numbers.
In a portfolio, you're squeezing out about 95% of the risk with 35 different stocks.
That's a real pain in the ass to do, though. I mean, 35 stocks, you'd have to buy all those stocks.
You'd have to keep them in balance so that none of them, price goes up and it's over weighting itself in the portfolio.
It's a real pain in the butt. That's why we recommend portfolios like the ETF like Spyder.
Because Spyder, let me remind you of Spyder here. Spyder is a stock that is actually all of the 500 stocks of the S&P 500, SPY.
You can't get much more diverse than 500 stocks. As a matter of fact, when we say R sub M, the return to the market,
a lot of times we get lazy and we just use the return to the Spyder. Because it is the market portfolio.
As a matter of fact, look here. With the Spyder, it's beta. Well, there you go. Beta is the market.
And that will get you an extraordinarily well diversified portfolio. You've probably squeezed out about 96, 97% of the diversifiable risk.
There's only a very small amount of it left in this.
As a matter of fact, if you were brave enough to take my next course in investments, 242 when I teach it,
you would see there's a trick you can do. I hesitate to call it a trick, but it kind of is a trick.
It's called a super portfolio where you buy maybe three or four of these portfolios that are really efficient,
close to the frontier, and you turn that into a super portfolio. You make that your super portfolio.
And these three working together actually get you closer to the frontier than any one of them individually would.
I did a simulation, and I can't figure out where I put it. I was trying to find it for the last time. I was doing 242.
But there's an ETF for the NASDAQ, an ETF for the Dow, and an ETF for the S&P 500, the Spyder.
If you put those three together and make those just a super portfolio, they had to have been like 99% of the way to the frontier.
They got that close. So, yeah, you can get really close, and it's a lot easier and a lot better if you just let professionals build the diversification.
And then you sit back and enjoy the ride on the diversification that is created for you. That's professional investment.
Now, and I've said this before, a lot of us have a fun portfolio where we throw money at one or two stocks or some options,
and usually get our butts kicked, but that's just the way we are. You have your fun portfolio.
But let me point out something, though.
If you're trying to diversify your portfolio, the thing you're doing is you're trying to get rid of the peculiar risks that are inherent in a single company.
You put companies together and they do peculiar things at different times, and they kind of cancel out each other's diversifiable risk.
The problem with this is that correlation, which I've erased here, the correlation coefficient.
I did erase it, didn't I? Yes, I did. You don't want stocks in a portfolio that are highly correlated with each other, because they're not helping, they're not canceling each other out very well.
You don't want them to dance too close to each other.
Now, the Pearson correlation coefficient, we would need to have that for each stock that we were looking at to see how it plays with another stock.
You don't want stocks that play well together. You want stocks that don't play well together.
In other words, have low correlation coefficients.
And there is a wonderful site, it's been around for a long, long time, and I'm always using it.
It's called the portfolio visualizers.
You can type in stock symbols, and what will come out is a correlation matrix.
You probably saw those in your stats class.
I'll put in a few.
Let's take General Motors,
Walmart,
let's take
Pfizer,
Meta,
Meet, Meta.
What else? What else can I put in there?
I don't know. Kroger,
and one more, I don't know.
So then, anyone got a suggestion? Kind of blanking. Mr. Lucas, you got one? Huh?
Is that right? Really? Okay.
I don't know if they still have a beta or if their beta has evaporated.
I'll just leave the other ones alone, view the correlations.
There we go.
Now remember, the diagonal, these numbers are symmetric on the diagonal.
Look at General Motors, against itself, of course, 1.1, 1.00, it's correlated perfectly with itself.
Now one thing that I'll tell you, my own preference is to choose stocks that have correlation coefficients below 0.30.
That's just my rule. Some people say 0.20, some people say 0.35, you just want them below.
General Motors is not well correlated with Walmart. That's good.
You'd like those in a portfolio together.
It's not with Pfizer. Meta's getting a little bit scary there.
Kroger is a great one, but what the heck? With Nvidia, why is General Motors correlated so well with Nvidia?
Now sometimes you can tell. Like if I put Kroger together with something that was another grocery store chain,
those would be, that makes sense. But this one, I mean, why, I don't know.
But General Motors and Nvidia in the same portfolio, absolutely not. They're way too correlated.
They're not going to effectively cancel each other's non-systematic or diversifiable risk.
Walmart.
Okay, all of them are good except for Kroger, surprise, surprise.
Grocery stores, they're going to be highly correlated.
That's why sector investing is really stupid, really stupid.
Because if you invest in stocks only of a given sector, you're guaranteeing high correlation coefficients.
So you want to move across sectors.
Now Pfizer, with Meta it's really good. With Kroger it's good. With Nvidia it's good.
As a matter of fact, Pfizer, for this, we would call that a key investment.
Because it seems to play the way we want with a lot of different stocks.
See how I could have Pfizer as the key and then I could choose stocks around it with some confidence that they wouldn't be very well correlated.
Going down to Meta, Meta with GM it's good.
With Nvidia, Meta and Nvidia are correlated too much.
Which I guess kind of makes sense. They're both into computer technologies and all of that.
Kroger, not with Walmart, but look for anything else.
Kroger is actually decent if you know enough not to put it in with Walmart.
Nvidia, GM it's bad with Meta.
You know that's actually Nvidia. That's one that shows that it plays too well with stocks, other stocks.
So that one would be when if you want Nvidia, you would have to watch and look very carefully at other investments to add to it.
To make sure that they weren't correlated with it very much.
As a matter of fact, just out of curiosity, let me take Nvidia.
Nvidia, let me try that with Alphabet.
Let's try it with Moderna, another vaccine company.
Let me try it with US Steel.
Let me do it with Marathon Oil.
And with, I don't know, Mastercard.
Let's see how Meta plays, Nvidia plays.
Not too bad. It's a little bit nasty with the correlation with Mastercard.
And with Google, it's just insane.
If you look at it with Alphabet, wow.
There's no way you could have those in the same portfolio.
With Moderna, it's not bad at all.
With US Steel, United Steel, with Google, why would those be, for heaven's sakes?
And with Marathon Oil, I get it, both use hydrocarbon products.
And with Marathon Oil, US Steel, and Mastercard, why would Mastercard and Marathon Oil be so highly correlated?
And Mastercard, yeah, it has a couple of nasties in there and one that's not very good.
So this gives you an idea. You begin to think about what stocks will get my non-systematic, my diversifiable risk out the best.
And you can use this, you don't have to kill yourself, you just type in symbols whenever you feel like adding a stock to your portfolio and see how well it plays with the other ones.
Okay, enough of that.
Going back here, a couple of little pointers, a couple of minor matters.
And this is kind of obvious, if you think about it enough.
The return to your portfolio is going to be the sum from i equals 1 to n of the weight of each stock in the portfolio times the expected return to that.
In other words, you multiply the weight of the return times the amount of the return for all of them, add them up, and that's your return to the portfolio.
Nothing complicated about that, makes sense.
But also the beta of a portfolio is nothing but the sum of the weights of each stock in the portfolio times the beta of that stock.
In other words, just another weighted average.
Now for the end of this story.
This formula I'm going to give here, it's just a simple arithmetic formula, but it has huge implications.
It's called the capital asset pricing model.
The CAPM.
The capital asset pricing model.
It says, and we've tested this a lot and I'll bring that up here in a minute or two, the expected return to a stock or to a portfolio, whatever you want,
is going to be, first and foremost, every stock or portfolio has to return at least the risk-free rate.
Why would you invest in anything that you didn't expect to return, at least what you can get taking no risk?
I can't remember. Madam, I've got ten dollars here.
I shall give you this ten dollars if you will walk out the door and stand outside for just a minute.
I will also give you this ten dollars if you will go up to the roof of this building and jump off and land there.
I mean, there are fat squirrels that you could land on that would help.
You know, we're in here and we hear, that's a squirrel splattering.
So which one do you want to do?
There you go. You see, in order to jump off the roof, you would then want more than the ten dollars, right?
So the risk list would have to be your starting point for anything that had risk.
That's why the CAPM starts, every expected return starts with an expectation that at least you'll get the risk-free rate.
But then we go on from there and we say, plus the beta of the stock times the return to the market portfolio, there's that risk, that market premium.
The beta is nothing but a magnifier or a demagnifier on the market premium.
So look back here, look back here.
Suppose that I, again, let's say that the return to the market, the expected return to the market is 60 percent, the return, risk-free rate return is 4 percent.
Okay? So let's say we have a beta of 0.5.
In that case, the beta of the stock is 0.5. In that case, we would have the expected return to the stock would be 4 percent plus 0.5 times the market premium, 16 percent minus 4 percent.
4 percent plus 0.05 times 12 percent, so that should be 10 percent.
Do you see how the beta demagnified the market premium? It lowered it because there's not as much risk. It's 0.5 instead of the market.
On the other hand, let's take a beta of 1.5. That's a risky portfolio.
Well then the expected return to that stock would be 4 percent plus 1.5 times the market premium over risk-free, 16 percent minus 4 percent.
And in that case, it would be 4 percent plus 1.5 times 12 percent, so that would be 4 percent plus 18, 22 percent.
There you go. CAPM isn't hard. You just write down the formula and just plug in the numbers.
A couple of kind of useful points.
I'm going to do a couple that are a couple more betas that seem kind of trivial, but they're important because I'm going to draw a graph of the CAPM.
But let me do a beta of 0. What would be the return to a beta stock with a beta of 0?
In other words, a risk-free treasury bill, for example.
Well in that case, the expected return to the stock would be the risk-free rate, 4 percent, plus 0.0 times 16 percent minus 4 percent.
So in this case, it would be 4 percent plus 0.0 times 12 percent.
Oh, the return to a stock with no risk is the risk-free rate. Surprise, surprise.
And one last one. What if the beta of the stock was 1.00?
Well, the expected return to the stock would be 4 percent plus 1.00 times 16 percent minus 4 percent.
So it would be 4 percent plus 1.00 times 12 percent.
Oh, well, duh. The return to the market portfolio is the return to the market portfolio.
Now that looks kind of like trivial. Okay, a beta of 0 gets us the risk-free rate.
A beta of 1 gets us the market rate. Nothing tricky about that at all.
But now, I'm going to draw a graph of the cap M.
The first thing to note is that the expected return to the portfolio on the left side will be the y-axis.
And I'm going to make the beta the x-axis.
This is just a weird version of a linear equation. You know, the y equals Mx plus b. That's all it is.
Notice that at least the b part is the y-interceptors right there.
So I'm going to draw this. 0.2, 0.4, 0.6, 0.8, 1.0, 0.2, 0.4, 0.6, 0.8, 2.0.
And that would be the beta axis, the x-axis.
And on this one is the expected return axis.
I'm going to use, remember, two points is all I need to draw a line.
So I've got one point right there. At a beta of 0, we get the risk-free rate.
The 4%.
The y-intercept as it were, and the y equals Mx plus b.
With a beta of 1, we get the return to the market portfolio.
Return to the market portfolio. The 16%.
Well, that's enough points. Two points is all I need.
And that is the graph of the capital asset pricing model.
We even have a name for this line. It's called the securities market line.
So look, look at this.
A 0.5 beta takes you up to the 10%, about.
My graphs aren't that great on the board.
A beta of 1.5, which would be about there, takes you up to about 22%.
It's just a graphical representation of CAPM is all it is.
Two important points.
We, again, this is something we do undergrads writing term papers do it,
masters thesis back a long time ago, even dissertations.
They would take the graphical representation of the securities market line,
and they would actually plot portfolios.
A portfolio is beta against its expected return to see how closely they came to the CAPM line.
And these scatter plots, you can Google, if you Google the right term,
you'll see these scatter plots all over the place.
The points are really tightly aligned, for the most part, with the CAPM line.
The data points of actual portfolio betas against the returns of those portfolios,
they're oftentimes very close.
Once in a great while, we see a portfolio that is not close to the line.
These are special.
But one thing I do want to point out before I say that,
all of these contests and these awards given to the portfolio designer that gets the highest return,
that's complete bullshit.
All you have to do is take a high beta and you get a high return.
You expect a high return.
There's nothing heroic about just getting a high return.
Good for you.
You took a massive Hail Mary risk, and there you go.
You got a higher expected return.
You got a high return.
But that's really bad to reward that because you're ignoring the risk of those portfolios.
You can have a fund manager who's getting really high returns on retired people's investments.
He shouldn't be doing that.
If all he's doing is taking high beta stocks and putting them together, that's bad.
In other words, there's no such thing as expected return without talking about the dimension of risk that is involved in it.
However, once in a great while, we'll see a portfolio that is legitimately getting a much higher return than CAPM says it should.
Or it could be getting a much lower return.
You can have them on the other side too.
You took this beta.
You should have been up there and you were clear down there with the return on the portfolio.
Or you took this beta.
How the hell did you get up there with your return?
Once in a great while, we see magic.
There are some investors.
I mean, it's just like if you've ever gone to a casino.
Back in the day, I'd go to these casinos on the strip in Vegas.
There was once in a while someone who was just playing tables against all odds.
He just kept winning.
How the hell are you doing that?
Of course, eventually the bouncers would come along and escort him out unceremoniously.
But it happens.
We are kind of interested in what that magic is that can do that.
We keep an eye on those people.
But there's something important here.
You see, he should have returned this.
What Capem says.
He returned up there.
Something like that.
He should have gotten maybe about 20%.
He pulled 25%.
We have a name for that number, that 5%.
We call it Jensen's Alpha.
It's called Jensen's Alpha.
Now Jensen's Alpha can be positive or like I said, you could have Jensen's Alpha negative.
But it's kind of like, does anyone have...
Now if you've got a Jensen's Alpha of 0.2%, no one cares.
That's just within noise.
But we do see these positive Jensen's Alphas once in a great while.
As a matter of fact, one of the most reputable investment sites on the internet is called Seeking Alpha.
I don't know if any of you have ever run into it.
And of course, the play on it is, if you know this stuff, it's obvious.
They're trying to help you find the positive Alpha for your portfolio.
And they're really great people there too.
They've helped me out understand some really exotic things in a way that my slim mind couldn't do.
But yeah, so Alpha is a thing.
And if you're going to say, I got a high return on my portfolio, I'm going to say, what was your Jensen's Alpha?
Because if all they did was just take a high risk to get a high return, Jensen's Alpha is going to be about 0.
But if they got a Jensen's Alpha, their high return was the result of a positive Jensen's Alpha,
they earned more than the risk the portfolio was indicating by cap M.
Then, that's good stuff.
So that's something to keep in mind.
Ask yourself honestly, what was the risk of my portfolio?
What would cap M have said I should make?
If you make more than cap M says you should have made with that portfolio beta,
then who knows, you might have the magic.
And in which case, I could be your friend.
That's all I have for you today. I thank you.