Video 27 - Security Market Line and the Capital Asset Pricing Model - YouTube

Hi everyone! Today we will be learning how to use the capital asset pricing

model to calculate what a security's market price should be. We can use this

to identify when a security is overvalued or undervalued.

By the end of this video, you will learn about the CAPM formula, the Security Market Line and

its characteristics, and the use of SML and Jensen's alpha in identifying mispriced securities.

CAPM stands for capital asset pricing model, which is an

equation used to estimate the expected rate of return for a stock. The CAPM

formula tells us that the expected rate of return for a stock equals the

risk-free rate, plus the "beta" of the stock, times the difference between the

expected market return rate and the risk-free rate, also known as the "market

premium". Let's go through each of these parts of the equation in more detail.

rf is the risk-free rate. This is the rate of return investors required in the

absence of any risk to compensate them for the time value of money. Beta is

essentially meant to capture the risk of an asset relative to the market. We will

be talking about beta in further detail in its own video.

E(rm) is the expected return of the market. E(rm) minus rf is often called the market

risk premium. In other words, the risk premium represents how much more

investors in the market are being compensated for holding the risky market

portfolio rather than the risk-free asset. The CAPM tells us how much

stockholders, for each individual stock, will earn at the risk-free rate plus the

market risk premium times beta, which is the amount of risk taken. The higher risk

of stock is, relative to the rest of the market, the higher beta is, meaning that

the stock should yield a higher return relative to the market risk premium. Try

solving a few problems using the CAPM formula. Stock A's beta is 1.2. The

risk-free rate is 4%, and the equity risk premium is 8%.

What is Stock A's expected return? Don't forget to use the CAPM formula. Pause

this video for a moment and try this problem yourself.

Let's try it together.

To solve a question, it's a good idea to list out all the given information first.

The risk-rate is 4%, the beta is 1.2, market

risk premium, which is E(rm) minus rf, is 8%. Now we plug those numbers into the

CAPM formula. The expected return equals 4% plus 1.2 times 8%.

Solve that and we get the expected return of Stock A to be

13.6%. In exam questions you will either be given the

expected return on the market or the market risk premium. The risk premium is

the additional return the market can earn above the risk-free rate. It's the

expected return of the market minus the risk-free rate. Don't make the mistake of

subtracting the risk-free rate from the market risk premium, otherwise you'd be

subtracting the risk-free rate twice. Let's try another question that's a

little bit harder. Stock B has an expected return of 10% with a beta of

0.8. Stock C has a beta of 1.3. The risk-free rate is 4%.

What is Stock C's expected return? Pause the video again, try this problem

yourself before watching the solution.

Once again list up the variables.

The risk-free rate is 4%, the expected return of Stock B is 10%, beta of Stock B is 0.8,

beta of Stock C is 1.3. How can we use this information to solve for what is

missing? First, we will want to solve for the market risk premium using the

information given for Stock B, and then use the market risk premium to solve for

the expected return of Stock C. Plug the numbers for Stock B into the CAPM

formula. 10% equals 4% plus 0.8 times the market risk premium. Solve for

the market risk premium to get 7.5%. Now, plug this back into our

equation to solve for Stock C. The expected return equals 4% plus

1.3 times 7.5%. Thus, the expected return for Stock C is 13.75%

The security market line graphs this CAPM equation.

This tells us what the expected return of an asset should be for each possible beta value.

The expected return is on the y-axis, and beta is on the x-axis.

The y-intercept is at the risk-free rate, because risk-free investments have no

risk premium, and therefore have a beta of 0.

The slope is the market risk premium, since it is a constant term multiplied by our

x variable, beta. The SML graphs out the "expected" return of stocks. If all stocks

were to earn a return as expected, then all the stocks should fall on the

security market line. Another way of interpreting the SML, as well as the CAPM

is that it depicts the relationship between required rate of return and risk.

Investors require this amount of return for taking that amount of risk.

This concept is useful for identifying mispriced securities.

If all stocks were to earn an "as expected" return, our graph should look something like this,

where all the points fall on the SML line. But in reality, the graph looks more

like this. These securities are "mispriced" because, compared to the risk associated

with each stock, they are either earning a higher or lower return than expected.

If a stock falls in the part of the graph that is under the SML, we say it is

overvalued. Take this security for example. According to the CAPM formula, it should,

and the investors expected to, earn a return of approximately 9%, but it is

only earning a return of 5%. This means that the price is higher than it should

be, given the returns on the asset. The risk-return trade-off is unsatisfactory

for investors, so we say it's overvalued and we should sell it. But don't worry,

the market will guarantee that stocks will eventually go back up to its

expected returns. If many investors sell this stock, it will increase the supply

of this stock in the market, which will push its price down. If you can now pay less

for the same asset that still pays the same expected return in dollars, this

asset is now a more attractive investment as investors can now get

"more bang for their buck". The lower price has the effect of increasing the percent

return on the price you pay. Investors will continue to sell the stock until

its expected rate of return is back to what investors expect, a return of 9%.

If a stock falls in the part of the graph that is above the SML, we say it as

undervalued. This security is earning a return of 14%, but based on the SML, it

should only earn a return of 7%. You can earn a higher percentage return than if

the security was accurately priced on the SML. The risk-return trade-off is

much more favourable than other stocks, so we say it's undervalued and we

should buy it. But eventually, other investors will realize that this asset

allows you to earn more than if it was accurately priced on the SML, so they

will keep buying this undervalued stock until the demand grows enough to push

the price of the stock up. When you have to pay more to earn the same dollar

return, then the percentage return on your investment to you, as an investor

decreases. As you are now earning less "bang for your buck", lowering the expected

return back down to its predicted level along the SML. A similar method we can

use to identify mispriced securities is by calculating security's Jensen's alpha.

If we want to use our CAPM formula to solve for the realized return rather

than the expected return, we must include another factor to account for the

difference between the expected and realized return, and that factor is

Jensen's alpha. This equation is called the security characteristics line. This

line graphs the excess return, which is the return minus the risk-free rate, of

the security against the excess returns in the market. The discrepancy between

the expected and actual returns is our alpha value. For example, imagine that we

expect for an asset to earn 10%, but it actually paid us 12%, then our realized

rate is 2% higher than what we expected to earn, and this 2% difference is the alpha.

When Jensen's alpha is positive, it means that the security is earning a

higher return than what's expected according to the CAPM, therefore it is undervalued.

When Jensen's alpha is negative, it means that the security is

earning a lower return than expected, therefore is overvalued.

In today's video, we learned how to use the CAPM formula to calculate the expected return of a

risky asset, and identify when a security is mispriced. Comparing the expected

returns to the realized returns can help us

to decide when to buy certain assets, and when to sell.

Thank you for watching!