4.6. Capital asset pricing model (CAPM). Examples

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來自 Moscow Institute of Physics and Technology 的課程

Principles of Corporate Finance – A Tale of Value

個評分

Moscow Institute of Physics and Technology

Principles of Corporate Finance – A Tale of Value

個評分

課程 2（共 5 門，Specialization Understanding Modern Finance）

The study of Corporate Finance seems to be a very generic part of business education. Still, it either falls in the trap of intimidating formulas or is superficially journalistic. Both extremes preclude the understanding of the core finance ideas, concepts, and models. This Course is an attempt to avoid the above extremes. We discuss the core basis and mechanisms of modern corporate finance in a learner-friendly way. We will analyze the market’s most fundamental problems, realize the intrinsic interests and preferences of investors, reveal the true meaning of specific financial terms, and uncover important issues that are so often ignored in choosing and valuing investment projects. The learners will gain insight into the essence of corporate finance. They will be able to use the obtained knowledge and skills to successfully advance in their career at a financial institution, as well as in the area of financial management at non-financial businesses.

從本節課中

Risk and Return – From Basics to Reality

In Week 4 we study risk and return. We present a stochastic mathematical model of risk and apply it to find the returns and standard deviations of portfolios of assets. We discuss diversification and the role of special portfolios – the riskless portfolio and the market portfolio – in approaching asset risk. We demonstrate how any asset contributes to the market risk and introduce the β coefficient. Then we derive the capital asset pricing model (CAPM) and study how it is used on examples. We discuss the application of the company cost of capital (CCC) rule to choosing investment projects. Then we use CAPM to determine the cost of capital – first, for an equity-financed company and then in the general case with debt and equity. We present the weighted average cost of capital (WACC) formula and discuss it. Finally, on an example we study the steps in applying CAPM.

4.1. Mathematics of risk8:36

4.2. The expected return and the standard deviation for a portfolio of securities. Some empirical evidence9:56

4.3. Diversification. “Special” portfolios6:58

4.4. Contribution to the portfolio risk. β6:22

4.5. Efficient portfolios. The market portfolio’s efficiency7:21

4.6. Capital asset pricing model (CAPM). Examples9:59

4.7. The company cost of capital (CCC) rule10:03

4.8. Applying CAPM – a no debt case4:05

4.9. Applying CAPM – the general case. WACC13:14

4.10. Steps in applying CAPM – an example15:40

4.11. Conclusions. The roadmap to determining WACC. Some objections to using normal distributions7:42

與講師見面

Konstantin Kontor
Director and Professor of Finance and Strategy
American Institute of Business and Economics (AIBEc)

Now we're about to start to look at one of

the most famous formulas in corporate finance

that has a very generic name Capital Asset Pricing Model.

The fact that it's sort of generic,

a test to the idea that it is widespread if you will.

Now I will start with the following chart,

and this is Beta,

and this is the expected return.

And again, there are two special points now.

One is risk-free with the Beta of zero and there is another special point.

If I put Beta1 here.

this is the market portfolio.

Now, I can easily draw a straight line here.

That is a special name that secures the market line,

and now this line is special in the following way.

Well, if we take a look at any portfolio or any security that's let's say is here,

then we can say that this is not a good investment because you can always find a better

one by going up here by the same token if we take B here.

Again you can say, well, this is not a good investment

because for the same level of risk,

we can find a better investment here.

And again, what is this investment?

This is sort of a combination of the market portfolio and borrowing or lending.

For example here, if for this portal A,

Beta is somewhere about 0.6 then,

or you can take a corresponding part of the risk-free portfolio,

and then you will come up here.

Here is Beta is greater,

here you are lending,

so you invest part of your money in the risk-free asset.

Here, you are borrowing because you have to borrow

some money and then invest that in the market portfolio and you come up here.

Now if all these investments that are below this lines are bad,

then on average as we all know these investments lay on this line and therefore,

all of the investments they cannot be

below this line and therefore they

cannot be above this line either because on average they're here.

Then the conclusion goes on all investments should be on this line.

And that leads us to the idea of Capital Asset Pricing Model.

So we can say that for any asset,

there is a linear relations

between the risk Premium and its Beta.

Well, let's proceed. And so,

if this is the case,

we can say that for any asset RI,

it's RF plus sum Lambda

times beta for this asset and this lambda is the same for all assets,

therefore, we can use a special case where I is the market.

And then writing that,

we can see that this Lambda is nothing but RM minus RF.

Because beta for the market is one,

then you can see what Lambda is.

And we, come up with

a famous Capital Asset Pricing Model formula that says, for any asset,

it's expected return is equal to RF plus Beta of this asset times RM minus RF.

Well, strictly speaking, strictly speaking,

these RM and RF are not constants.

But they are quasar constants because we can say that the volatility of

any asset is higher than the volatility of the overall market and the volatility of RF.

Although clearly, every day RF and RM changes,

Both RM changes and RM does so.

But we can say that the general idea that has led us to this formula is the fact that

the market portfolio is efficient.

It can be proven. That's basically the same story.

We just said that the market portfolio

is not efficient as has been proven by empirical evidence,

and looking at this formula we would like to see its pluses

and minuses and study something about that.

Well, first of all some empirical evidence.

As you've seen here,

this is our general approach,

we first start to have some idea,

then we come up with a formula,

then we have to test it by seeing what actually is observed on the market.

Now, there are special challenges to this testing,

and one of the major challenges is the fact that we have to deal with expected variables.

And in reality we can deal only with past or factual variables.

So we can never physically include in our tests, these expectations.

But what has been proven is that with respect to CAPM,

like I said problems.

First of all these are problems in testing.

Well, problem one is this is

expected versus past Rs.

Then another problem is

the composition of the market portfolio and finally measuring Beta.

All these are sort of problems.

Well the good news is that,

it has been shown that CAPM does

provide statistically significant relations between long term returns and Betas.

Well, for small cap stocks and for small betas,

the observed returns proved to be a little bit higher

than those that are predicted by CAPM.

So that's not a perfect explanation,

but the general idea for us is that CAPM is simple,

sort of realistic in terms of empirical evidence,

and, this is a very important point,

that it does take into

account diversification.

So it basically proves the idea that investors require

premier only for non-diversifiable risks.

So then, there are some other ways of pricing assets.

There are plenty of other theories.

But none of them have so far gotten

the basis for being so widespread and widely used and the main reason is,

again, the fact that the formula is generally okay and it

recognizes most important ideas and most important things that happen in the market.

It is not perfectly accurate.

But here you have to step back a little bit and

remember that we talked a lot about this accuracy in this course,

and most often, the inputs that we use in evaluation,

they are not accurate either.

And although we can always say that

inaccuracy here plays a more important role because when you discount,

discount is non-linear and it contributes maybe more severely to that,

but that remains an open question.

So keep it in mind that the famous CAPM is not perfect.

You still have to realize that this is

a widely used instrument and the fact that we recognize challenges to its accuracy,

it does not prevent us from using it in a widespread and widely accepted way.

So here I am wrapping up

the theoretical part and starting for the next episode until the end of this week,

we will see how exactly people use CAPM in order to fix price labels to certain assets.

Well, more accurately speaking,

to fix expected return labels that further on have

to be put intio the NPV formula to come up with these price labels.

So starting the next episode,

we will see how to use CAPM.

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