Question

What function does the CAPM fulfill? What is the role of Beta? Explain the role that Beta plays in determining the return on a stock? If the market is up 10 percent and the Beta of the stock is 2, what is suggested regarding the expected return on that stock? What if the market is down 10 percent; what then is the expected return on that stock?

Answer 1

CAPM

The capital asset pricing model (CAPM) is a model that describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for the pricing of risky securities, generating expected returns for assets given the risk of those assets and calculating costs of capital.

The formula for calculating the expected return of an asset given its risk is as follows:

Ra = rf + Beta (Rm - rf)

Ra = Expected Return of Asset A

rf = Risk free rate

Rm = Expected Market return

The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk. The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time. The risk-free rate is customarily the yield on government bonds like U.S. Treasuries.

The other half of the CAPM formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf): the return of the market in excess of the risk-free rate. Beta reflects how risky an asset is compared to overall market risk and is a function of the volatility of the asset and the market as well as the correlation between the two. For stocks, the market is usually represented as the S&P 500 but can be represented by more robust indexes as well.

The CAPM model says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken. The security market line plots the results of the CAPM for all different risks (betas).

Beta

Beta is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta is used in the capital asset pricing model (CAPM), which calculates the expected return of an asset based on its beta and expected market returns. Beta is also known as the beta coefficient.

Beta is calculated using regression analysis. Beta represents the tendency of a security's returns to respond to swings in the market. A security's beta is calculated by dividing the covariance the security's returns and the benchmark's returns by the variance of the benchmark's returns over a specified period.

If a stock's beta is 2, it's theoretically 100% more volatile than the market. Thus, if market moves up by 10%, it is likely to move up by 20% and conversely, wehn market is down 10%, it is likely to down by 20%.