In 1960, Harry Markowitz and Bob Sharpe met,

and Markowitz offered the 26-year-old Sharpe to continue his research on how various stocks

function together. Sharpe wrote his thesis on this subject and

created one of the most important models in finance history. The CAPM setting is not much different than

the one considered by Markowitz. Investors are risk-averse. They prefer earning a higher-return, but are

also cautious about the risks they are facing and want to optimize their portfolios in terms

of both risk and return. Investors are unwilling to buy anything other

than the optimal portfolio that optimizes their expected returns and standard deviation. Sharpe introduces the concept of a market

portfolio that is a bundle of all possible investments in the world (both bonds and stocks),

and the risk-return combination of this portfolio is superior to the one of any other portfolio. The expected return of the market portfolio

coincides with the expected return of the market. And because this is a diversified portfolio,

it makes sense it is optimal in terms of risk – it contains no idiosyncratic risk. The only risk faced by investors, who own

the market portfolio, is systematic risk. And we would expect this portfolio lies somewhere

on the efficient frontier, as it is an efficient portfolio, the most efficient, actually. Great. So far, this looks like a simple extension

of the ideas introduced by Markowitz; however, the CAPM assumes the existence of a risk-free

asset, an investment with no risk (zero standard deviation). It has a positive rate of return, but zero

risk associated with it. And this automatically means there will be

people so risk averse they will prefer to buy the risk-free only. If they want to be 100% certain their investment

contains 0 risk, they’ll be willing to accept a lower expected rate of return. Wait! But why should we assume the risk-free has

a lower expected rate of return? Well, under the CAPM, markets are efficient,

right? Ok. And in an efficient market, investors are

compensated only for additional risk they are willing to bear. Once they own an efficient portfolio, they

can’t arbitrage the system and earn a higher expected return for the same level of risk. In such setting, a higher rate of return means

more risk, and conversely, a lower level of risk means lower return. Zero level of risk translates in the lowest

level of expected return, and that’s why we can expect the risk-free rate will provide

a low level of expected return. All right Excellent! We are almost there. What changes after we introduce a risk-free

asset then? It means the market portfolio isn’t the

only asset rational investors would invest in. The risk-free investment offers something

new to investors – zero-risk. So, rational investors will form their portfolios,

considering both the risk-free rate and the market portfolio. How much are they going to invest in risk-free

and how much are they going to invest in the market portfolio? Well, it depends on how much they want to

earn, right? The line that connects the risk-free rate

and is tangent to the efficient frontier is called the capital market line. Can you guess which is the point where the

capital market line touches the efficient frontier? Yes, precisely! This is the market portfolio. Ok. So, every investor can invest in a combination

between the risk-free asset and the market portfolio according to his risk appetite. If he’s willing to risk more, he’ll hold

a greater portion of the market portfolio, and in the opposite case, if he’s unwilling

to risk, he’ll buy more of the risk-free asset and less of the market portfolio. Investors who are interested in high expected

returns will be able to borrow money and invest it in the market portfolio, going even further

along the capital market line. In our next lesson, we’ll talk about the

relationship between individual securities and the market portfolio, and this will move

us one step closer to learning how to build expectations about the prices of real-world

assets.