### GIGAMIND

# 3. The Capital Asset Pricing Model

## f. explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML);

## g. calculate and interpret the expected return of an asset using the CAPM;

What does CAPM stand for?

Capital Asset Pricing Model

What is CAPM used for?

The Capital Asset Pricing Model is used to determine the required rate of return for any risky asset.

What are the six assumptions of the Capital Asset Pricing Model (CAPM)?

1. All investors are Markowitz efficient investors

2. Markets are frictionless

3. All investors have the same one-period time horizon (e.g., one year).

4. All investors have homogeneous expectations

5. All investments are infinitely divisible (fractional shares)

6. All investors are price takers. Their trades cannot affect security prices.

What is a Security Market Line (SML)?

The SML represents the required rate of return, given the systematic risk provided by the security. Securities that are efficiently priced should fall directly on the (calculated) SML line.

- If a security is above the line it is deemed undervalued since it is providing more expected return than what is demanded for that risk level.

- Securities falling below the SML line, on the other hand, provides less return than the market demands.

Under CAPM what is the formula for the expected (required) return of a security in a fully diversified portfolio?

$$E(R_{stock}) = R_f + [E(R_M) - R_f] \times \beta_{stock}$$

What is the formula for Market Risk Premium?

$$E(R_M) - R_f$$

What is the formula for risk premium of a security?

$$\beta [E(R_M) - R_f]$$

What is "alpha"?

The difference between the expected and required return is called the alpha (α) or excess rate of return.

Is alpha positive or negative when a stock is undervalued? Where does it lie on the Security Market Line (SML)?

The alpha can be positive when a stock is undervalued (it lies above the SML) or negative when the stock is overvalued (it falls below the SML).

What is a portfolio Beta? How is it measured?

The β of a portfolio is the weighted sum of the individual asset betas. For example, if 40% of the money is in stock A with a β of 2.0 and 60% of the money is in stock B with a β of 0.8, the portfolio β is `0.4 x 2.0 + 0.6 x 0.8 = 1.28`

*Interesting comments on this page:*

**teddajr:** Very Important Topic for review.

**thekapila:** indeed!

**Farina:** Yeah, these premises are the cornerstone of most successful value investing strategy. Rumour has it that the trigger for a Buffet/Berkshire Hathaway purchase is an SML undervaluation of 40%, which would explain why they have such strong long term returns.

##### Source:

- CFA