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.