Learning outcomes.

After watching this video,

you will be able to describe the market portfolio,

define the capital market line.

The market portfolio and the capital market line.

We have largely ignored the relation between risk and return

other than saying that risky investments would required higher expected returns,

but we haven't talked about what the fair return for an asset should be given its risk.

This is the ambitious goal of asset pricing models,

the first of which is the capital asset pricing model – CAPM in short.

The CAPM is the earliest asset pricing model,

derived back in 1962.

It is a theoretical model derived mathematically

from first principles and not motivated by data.

It is based on the concept of equilibrium,

which is an economic state where no one wants to do anything differently.

In equilibrium, the risk premium per unit of risk is the same for all assets.

However, the CAPM is not supported by data.

Some claim that it is not even testable with the data.

Though it is a very popular asset pricing model among practitioners,

its practical relevance is ambiguous.

Here is a long list of assumptions that were made to mathematically derive the CAPM.

Investors only care about the mean and variance of their portfolios.

All assets are divisible.

All investors plan for one holding period,

which may be one day,

one month, one year, etc.

There are no transaction costs or taxes.

There is perfect competition among all investors.

All investors are rational mean-variance optimizers.

A risk-free asset is available.

Markets are in equilibrium,

that is, they are properly priced given their risk.

Asset pricing models, like the CAPM,

attempt to explain the variation in the returns of different assets.

For example, why is Apple's return different from that of

Alphabet Inc.'s which in turn is different from that of Microsoft,

even though all three companies are in similar lines of business.

The CAPM argues that this is because of the assets' betas.

Let's get to describing the CAPM now.

Remember the three risky and one risk-free asset case we saw earlier?

We are simply going to extend that framework to all assets in the market.

This includes all stocks, all bonds,

currencies, derivatives, commodities, human capital, etc.

With this universe of risky assets and one risk-free asset,

we will still have an efficient frontier,

which maximizes expected return for a given level of

risk and minimizes risk for a given level of return.

Drawing a tangent from the risk-free asset to

the efficient frontier identifies the mean-variance efficient portfolio.

In the CAPM world which includes the universe of risky assets,

this MVE portfolio is called the market portfolio.

The capital allocation line between the risk-free asset and

the market portfolio is called the capital market line, CML in short.

What is the weight of each risky asset in the market portfolio?

The weight is the ratio of the market value of

each risky asset to the market value of all risky assets.

For example, the market value,

also called market capitalization,

of Facebook is a current value of all its shares outstanding.

Facebook has 2.29 billion shares outstanding,

and each share is currently worth $107.

So its market capitalization is 2.29 billion times 107,

which is $245 billion.

The weight of Facebook in the market portfolio will be

245 billion divided by the market value of all risky assets.

Let's go back to our three risky assets.

Remember the weights of the three risky assets X, Y,

and Z in the MVE portfolio are 0.2274,

1.7793, and a -1.0067, respectively.

If we assume that these are the only three risky assets in the entire world,

is this MVE portfolio the market portfolio?

The answer is no.

Why? Remember the weight of each risky asset in

the market portfolio is in proportion to its market capitalization.

Larger its market capitalization,

larger is its weight in the market portfolio.

Here, the weight of Z in the MVE portfolio is, however, negative.

This implies that Z has a negative market capitalization which is not possible.

So the MVE portfolio,

even though correctly identified,

cannot be a market portfolio.

Next time, we will see what the mathematical form of the CAPM is.