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>> Hello again. I'm Tucker.

And we're gonna talk a little bit more about the Capital Assets Pricing Model,

and again it's covered in this book.

No, I'm not trying to push this book on you, but I really do like it.

And I'd like to give a shout out to David Lineweber who recommended this to me in

the first place.

Great book.

0:46

And I'm gonna show you, just with a simple example, of

how you can take advantage of this insight to reduce,

or potentially remove market risks from a portfolio.

1:03

Okay so in the last video we talked about the way to

compute expected return for a portfolio using the Capital Assets Pricing Model.

And remember we have this h component which tells us

how much we're investing in each individual equity.

So our overall expected return is a weighted

sum of the individual expected returns.

So the equation there in the middle, r sub p is an expected return for

the portfolio and it's the sum, it's the weighted sum of the expected return for

each component.

Okay, now to illustrate this let's consider a port, I'm sorry.

A situation where there's two stocks.

We're gonna build a portfolio with two stocks.

We believe that stock 1 is gonna go down.

Now we believe that stock 2 is gonna go up.

So eventually we're gonna short stock 1.

We're gonna make a negative bet on stock 1.

And we're gonna make a positive bet on stock 2.

There's an added complication, which is stock 1 has a beta of 2 to the market.

In other words, when a market goes up 1%, stock 1 goes up 2%.

At least, it has historically.

Stock 2 has a beta of just 1 to the market.

So we're gonna take a look at a hypothetical plan

where we'll put 50% of our portfolio on a short bet on

stock 1 and 50% on a long bet on stock 2.

So we're going to bet 50% that stock 1's going to go down and

50% that stock 2 is gonna go up.

So let's explore that a little bit.

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So here's a hypothetical chart.

The markets, what it's done in the past, I show in green here.

That vertical line where I say entry is now, and so

we're looking back at what each stock has done with regard to the market.

So like we said, stock 2 has a beta of 1 with the market,

so it tracks the market pretty closely.

Stock 1 has a beta of 2, so

when the market goes up a little bit it goes up a lot.

When the market goes down, it goes down a lot.

So stock 2 is shown in the blue here and

you can see it's moving with the market but sort of twice as much.

Okay, now let's suppose we put half

our portfolio as a short on stock 1,

and half as a long on stock 2.

And let's assume that the market is just flat.

It doesn't go up or

down, it just goes horizontally, there's no return overall for the market.

What that means is that the beta component of our portfolio.

The part that's due to what the market does.

Your return there is gonna be 0.

And any gains we see is gonna be related to alpha.

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So the green part goes straight flat.

Now as expected, stock 1 goes down,

let's say it goes down 2%, as an example.

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And stock 1 goes, I'm sorry, stock 2 goes up, let's say it goes up 2%.

Okay. Now we've shorted stock 1, and

it went down 2%.

So, on that part of our portfolio, we made 2%.

We longed stock 2, and it went up 2%.

So we made 2% there.

So win win.

5:34

Okay, what if the market goes down and

let's suppose our knowledge, our belief about what's the stocks are gonna

do relative to the market are correct, and our measurements of beta are correct.

All right, so let's suppose the market goes down 10%.

Because stock 1 has a beta of 2, we're gonna see that stock go way down.

So it's gonna go even below 20%.

If it just executes according to its correlation with the market,

it'll go down 20%.

But let's suppose our forecast was right.

That we believed it was gonna even under perform the market by another 2%.

So in this case our stock 1 has gone down 22%,

but we shorted it so we're profiting on that part of our portfolio 22%.

Okay, that's stock 1.

Stock 2, well the market went down.

It's got a beta of 1, so it's gonna go down

to approximately 10%, but we had information.

It panned out, it was correct, that it would outperform the market by 2%.

So stock 2 goes down only 8%.

So overall we have stock 2 at -8%.

Stock 1 with -22, but we shorted it,

so that's a positive 22.

So you add those two together, divide by 2,

that's your total return, so it's 14% divided by 2.

So in this case we win 14% when the market goes down.

All right, we're doing great so far.

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And again let's assume our market relative predictions are correct,

but that beta of the stocks to the market is killing us, and here's why.

Okay we'll assume the market goes up 10%.

Our stock 1, because it's a beta of 2,

is gonna go approximately 20%.

But remember, we believed it was gonna under perform the market by 2%.

So that means it goes up only 18%.

Okay, and we shorted it so we're losing

18% on that side of the portfolio.

Stock 2 went up.

It went up more than the market, so it went up 10%, plus the other two went 12%.

So on part of our portfolio we're making 12%.

In the other part we're losing 18%.

You take the average, it's -3% loss on average.

So what happened?

Why did we lose?

We have skill.

We've made, in all these cases, we've made the correct

predictions about how each stock was gonna perform relative to the market.

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The problem is that we shorted a high beta stock.

And what the market did overwhelmed our skill.

So what can we do about it?

Well we can take advantage of the Capital Assets Pricing Model and here is how.

So let's look at this basic equation again.

That first part is about the return due to the market.

And of course the second part is the residual return,

the part that's due to our skill or what's particular about the individual stocks.

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And assuming that our alpha is correct,

which it was in this case, we'll make money over here.

I'll step through an example here that's not hard to do.

Now as long as we're looking at these components,

I just want to point something out.

If you take the standard deviation of each of these components of return over time,

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The standard deviation of the second part is residual risk.

We'll get into that in a little bit more detail in an upcoming module, but

keep in mind that we can separate these parts of risk.

Our exposure to the market and the risk due to the market, and

our risk with the specific portfolio called residual risk.

We'll return to that later.

Don't worry about that right now.

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of only 1 and half as much on stock 1 which has this high beta.

So putting a little bit into stock 1 that has this high beta,

more into stock 2 that has this lower beta.

I'm not saying this is always what you should do.

I'm just saying this is how it works out for this particular portfolio.

Okay.

Let's carry it forward.

Our overall beta for the portfolio,

we can calculate just by multiplying

the proportion that we put into each equity times its beta.

So it's -0.33 times 2,

cuz the beta for the first stock is 2, plus 0.66 times 1, cuz the beta of

that second stock is 1, that means our beta is 0.

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Stock 1, actually I think I have the alphas mislabeled there, sorry.

Anyways, let's look at stock 1.

It went up 18%, but we shorted it, so we lose 18%.

But remember, we only bet half as much as in stock 1.

So that's really only a relative loss of 9%.

For stock 2, we bet twice as much and

it went up 12%.

So on an equalized basis, on average now we made 2%.

So by weighting our portfolio in such a way to 0 out beta,

we're left with the alpha and we make money in both cases.

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We can reduce market risk by zeroing out beta.

This long short type of investment is core to hedge funds.

It's what they do all the time,

and portfolio optimizers that we talked about in

an earlier session can do this automatically for you.

The deep details of how portfolio optimizers work are for a later course.

But just know that portfolio optimizers can automatically discover

these beta relationships.

And they can take your forecast positive or negative and

weight the holdings appropriately to eliminate market risks and

capture the alpha for you.

Okay that's it for this module.

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Coming up soon is the fundamental law.

The fundamental law of active portfolio

management due to Richard Grinold.

[LAUGH] And Ronald Khan.

It's an important concept that

is based on what we've been talking about in these last two videos.

Anyways, thanks for watching.

I look forward to seeing you again.

Have a great day.

Thank you.

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