4.4. Contribution to the portfolio risk. β

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From the course by Moscow Institute of Physics and Technology

Principles of Corporate Finance – A Tale of Value

5 ratings

Moscow Institute of Physics and Technology

Principles of Corporate Finance – A Tale of Value

5 ratings

Course 2 of 5 in the 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.

From the lesson

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

Meet the Instructors

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

Now, in the previous episode,

we talked about the idea of diversification and we basically said that

the total risk of any portfolio consists of two parts.

One part is the individual,

or sometimes it's called idiosyncratic,

but for us, it's important that it's diversifiable risk.

And there is a certain floor,

that's the market risk that cannot be diversified

away by any combination of securities in the portfolio.

Now, this episode contains some fundamental ideas

how this portfolio approach can lead us to very classic,

and I would say usable results.

And I would not spend much time on that.

I will just pronounce them because in order to

study them in detail does require some more attention

to the material and you just have to think about that, let's say, more than once.

I'll just pronounce how this works.

So the whole idea is that we would like to know what

contributes to the portfolio risk.

And here we know that the idea is that's

only the market risk of the portfolio.

And we would like them to find some sensitivity,

with respect to sensitivity of any security,

with respect to the market portfolio.

Well, for the first time I produced this important idea of the market portfolio.

Well, what is it?

In the vast majority of cases,

people use some stock market portfolios like

the S&P 500 in the U.S. as a proxy for the market the portfolio.

Although, this is not perfectly true because

clearly there are all other securities that must be also included in that.

All fixed income securities,

all mortgages, all real estate,

and even all human capital that people do not know how to properly evaluate.

So this whole idea of the composition of the market portfolio remains one of

the few most fundamental questions in

corporate finance that although have been widely studied in the last couple of decades,

but unfortunately, these studies have not produced any final result, if you will.

So people keep thinking about that and

they keep recognizing that this is a huge challenge,

but unfortunately, they have not come up with any mutual except the way to quantify it.

And all that ideally,

is that this sensitivity of insecurity has a special name that all of you heard about,

that's called beta, and for any security I.

And well, you've seen the formulas about that.

The beta, in general,

is equal to covariance between this asset and the market.

And then, divided by variance of

the market which is the same as the correlation coefficient with Rho_I_M,

and then, the ratio of standard deviations.

We now understand why

the market portfolio plays such an important role

because everything else can be diversified away.

Again, the logic here goes that,

if for any reason the people would like to hold

any portfolio of securities that is different from the market portfolio,

it can be shown that they can do a better job

by holding the market portfolio and doing something else.

About that, we will talk in just a few minutes.

But for now, I would just say that this coefficient beta is widely known.

Unfortunately, it's difficult to come up with, in the correct way,

because clearly these betas are not only expected in reality,

they are known only from the pairs,

but also they contain

many series of returns to find them.

And that does create some problem.

Well, for now, I would like to draw your attention to just one thing.

Then, clearly from this formula,

there are two special portfolios.

One portfolio is the market.

Because see what happens with the market if this becomes one,

this is the same, so we can see that beta market is clearly one.

Because, here again, sigma MM is the same as Sigma M squared.

Well, there is another special portfolio that is called beta of the risk-free portfolio.

Well, for risk-free portfolio,

sigma is zero and therefore,

the beta is zero.

So, these two special portfolios will

play a very important role in our further discussion.

And from now on,

we will move ahead and say a few other words about

portfolios that were specified by Markovitz,

and that will lead us to the wrap up of this first,

let's call it a theoretical part of this week and then,

we will move on to some more practical aspects.

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