9.5 Beta

In addition to serving as a measure of market risk, Beta tells us how a particular stock moves in relation to the rest of the stock market as a whole.

[latex]\boxed{9.5}[/latex] Beta

[latex]{\color{red}{\beta_{A}}}[/latex] represents the Beta of Stock A

[latex]{\color{blue}{\sigma_{A}}}[/latex] represents the standard deviation of stock A

[latex]{\color{green}{corr_{A,MKT}}}[/latex] represents the correlation between stock A and the overall market

[latex]{\color{purple}{\sigma_{MKT}}}[/latex] represents the standard deviation of the overall market

What is the Market?

The market refers to a portfolio of all investment assets (stocks, bonds, gold , art, etc.). However, in more practical terms, the market usually refers to the stock market and can be measured by a market index (such as the S&P 500 or Dow Jones Industrial Average).

How do we Interpret Beta?

Most betas range between [latex]0.35[/latex] and [latex]1.8[/latex] (there are many outside this range, but the majority of stocks fall in this range – review Observed Correlations, Returns, Standard Deviations and Betas Table in Appendix B and note that all the stocks other than Wal-Mart fall in this window.)

Go back to our example where we calculated the beta for stock A. By itself, stock A is much riskier than the overall market as determined by its standard deviation. However, when we consider it as part of an overall portfolio its risk is much lower (less than average) due to the fact that it has a relatively low correlation to the overall market. The riskiness of stock A depends on whether we plan to use it as a stand alone investment or as part of a portfolio.

Standard Deviation vs. Beta

At this point, we have introduced two risk measurements. The first is standard deviation and the second is beta. In some cases, these two risk measurements will tell a different story. For instance, stock A may have a standard deviation of [latex]30\%[/latex] and a beta of [latex]0.8[/latex] while stock B may have a standard deviation of [latex]25\%[/latex] and a beta of [latex]1.3[/latex]. Which stock is riskier? The answer is depends on the specific situation. Because each risk measurement is measuring a different type of risk (standard deviation measures total risk while beta measures market risk), we need to think of situations where each is appropriate.

Single Security and/or Poorly Diversified Portfolio

If you are going to place your entire investment into a single security or a poorly diversified portfolio, then standard deviation is the appropriate risk measurement. In this situation, you have not diversified away the majority of the firm-specific risk, so you need to include it in your analysis. Standard deviation does this because it includes both sources (market and firm-specific) of risk.

Adding a Security to a Well-Diversified Portfolio

If you own a well-diversified portfolio and you are planning to add a single security to that portfolio, then the firm-specific risk of the security you are adding is not relevant. The reason it is not relevant is because it will be one of many stocks in the large portfolio and the firm-specific risk will be diversified away. What matters is how that stock moves with the overall market. Since we measure this market risk with beta, our appropriate risk measurement here is beta.

Choosing Between 2 (or more) Well-Diversified Portfolios

If you are choosing between two or more portfolios that are each well-diversified, then you can use either standard deviation or beta as your risk measurement. The reason for this is that at this point, the firm-specific risk is already diversified away so that your total risk and market risk should be essentially the same. Thus, whichever portfolio has the higher standard deviation should also have the higher beta (if not, you know the portfolios are not well-diversified).

Beta and Required Return: Capital Asset Pricing Model (CAPM)

During the mid-1960’s and early-1970’s some finance professors developed the Capital Asset Pricing Model (CAPM). (Sharpe, 1964; Lintner, 1965; Black, 1972) One of the key components of this model is the Security Market Line (SML) which states that the required rate of return for a stock is dependent on the beta of that stock. While technically, the SML is a subset of the larger model (CAPM), in practice the two terms are typically used interchangeably. Thus, think of them as the same basic model.

[latex]\boxed{9.6}[/latex] Required Return (SML)

[latex]{\color{red}{k_{A}}}[/latex] is the required return for stock A

[latex]{\color{blue}{k_\textrm{RF}}}[/latex] is the risk-free rate of interest (often approximated by the yield on [latex]10-[/latex]year Treasury bond)

[latex]{\color{green}{\beta_{A}}}[/latex] is the beta for stock A

[latex]{\color{purple}{\bar{k_{m}}}}[/latex] is the expected return on the market (often approximated by the S&P 500)

Video: “Beta and the SML Part One” by Kevin Bracker [7:43] is licensed under the Standard YouTube License.Transcript and closed captions available on YouTube.

Video: “Beta and the Security Market Line Two” by Kevin Bracker [7:30] is licensed under the Standard YouTube License.Transcript and closed captions available on YouTube.

Attribution

“Chapter 7 – Risk Analysis” from Business Finance Essentials by Dr. Kevin Bracker; Dr. Fang Lin; and Jennifer Pursley is licensed under a Creative Commons Attribution-NonCommercial [latex]4.0[/latex] International License, except where otherwise noted.