So for example, we could consider that a stock index like the SNB

500 is a good representation of what the market actually is.

From that observation, we can say something about the red line.

The characteristic of the red line.

Like any fine functions straight line, it is characterized by it's

intercept where it starts, and here it starts at the level of the risk free rate.

The second element that characterize the equation of a line is the slope.

The slope here is measured by how much you move up when you move to the right.

How much additional return you get by taking additional level of risk.

And for the red line the efficient frontier, we can use the coordinate

of the market portfolio to completely describe the slope of the red line.

The slope is going to be defined by the difference between

the expected return on the market and the risk free rate.

This is the height of the point along the y axis

of the market point minus the height of the risk free rate.

So here it will be a little bit more than 6% minus the 2% of the risk free rate.

And if we look now at how much you move to the right when moving along the red line,

the horizontal movement for the market coordinate is

10% to the right minus the level of the origin which is 0% for the risk free rate.

So the slope is 6% minus 2% divided by 10%.

This is the slope of the red line.

Now, any portfolio which is on the red line can be identified by the intercept,

the origin, the risk-free rate.

The level of risk it is exposed to and the slope of the red line.

This relation between the expected return of an efficient portfolio and

it's level of risk is called the Capital Market Line.

And it's just a reinterpretation of the efficient frontier

including the risk free rate.

I'm going to display now the equation of this capital market line.

And this is precisely what we've just said, right,

the expected return here of one particular efficient portfolio,

which we write E for expectation of Ri, the return

of one particular efficient portfolio, so one portfolio on the red line.

Satisfies the equation of the straight line,

this straight line start at the risk free rate which we write here RF,

and then there is a level of risk for that portfolio which is sigma I which

multiplies the slope of the red line, how is the slope of the red line defined?

It is defined relative to the coordinate of the market portfolio, so

we have expected return on the market portfolio minus RF,

this is E[RM] expected return of the market,

hence the M, divided by the level of risk of the market, sigma M.

So this ratio here E of RM minus RF divided by sigma M.

This is the slope of the red line.

This equation links risk and return, but not for all asset in the market.

It links risk and return only for

those portfolio that are optimally diversified and are on this red line.