Measuring Market Risk

Market Portfolio

The market portfolio is a theoretical portfolio that includes all assets in the economy, weighted by their market values. In practice, a broad stock market index, such as the S&P 500, is used to represent the market portfolio.

• Market Portfolio: Represents the aggregate of all investable assets.

• Stock Market Index: Used as a proxy for the market portfolio in empirical studies.

Beta measures the sensitivity of a stock's return to the return on the market portfolio.

• Beta (β): Indicates how much a stock's price moves relative to the market.

• Beta > 1: Stock is more volatile than the market.

• Beta < 1: Stock is less volatile than the market.

Example: Calculating Beta

Consider Turbot-Charged Seafoods, with the following monthly returns compared to the market:

• When the market was up 1.0%, Turbot's average % change was 0.8%.

• When the market was down 1.0%, Turbot's average % change was -0.8%.

• Average change of 1.6% divided by the 2.0% change in the market gives beta:

Interpretation: Turbot-Charged Seafoods is less volatile than the market.

Portfolio Betas

Portfolio Diversification and Beta

Diversification reduces variability from unique (unsystematic) risk, but not from market (systematic) risk. The portfolio beta equals the weighted average of the betas of the securities in the portfolio.

• Portfolio Beta:

• S&P Composite Index stocks have an average beta of 1.0.

Example: Betas of Major Companies

Betas calculated with price data from January 2015 through December (sample):

Interpretation: Higher beta indicates higher market risk exposure.

Calculating Portfolio Beta

• Portfolio beta is calculated as the sum of the products of each asset's weight and its beta:

• Where is the fraction of the portfolio invested in asset , and is the beta of asset $i$.

Risk and Return

Risk Premium

The risk premium is the difference between the expected market return and the return on risk-free assets (such as Treasury bills). It represents compensation for bearing market risk.

• Market Risk Premium:

• Risk-Free Rate (): Return on government securities.

• Market Return (): Expected return on the market portfolio.

Capital Asset Pricing Model (CAPM)

The CAPM describes the relationship between risk and expected return. It states that the expected risk premium on any security equals its beta times the market risk premium.

• CAPM Formula:

• = risk-free rate

• = expected market return

• = asset's beta

Example: Calculating Expected Return

• Market return (): 10%

• Risk-free rate (): 3%

• Stock X beta (): 0.5

Market risk premium:

Expected return for Stock X: or 6.5%

The CAPM and the Opportunity Cost of Capital

Opportunity Cost of Capital

The opportunity cost of capital is the expected rate of return that is foregone by investing in a project rather than in securities of equivalent risk. For a firm, the company cost of capital is the appropriate discount rate for average-risk investment projects.

• Company cost of capital reflects the risk of the firm as a whole.

• Project cost of capital depends on the risk of the specific project.

Example: Project-Specific Cost of Capital

• Suppose a company has three divisions with different betas:

• Gene therapy:

• Pharmaceuticals:

• Dog food production:

For dog food production, if and :

Project cost of capital: or 10%

Interpretation: Use the project-specific cost of capital for evaluating investments with different risk profiles.

Summary Table: Key Terms and Formulas

Additional info: These notes expand on the original slides by providing definitions, formulas, and context for each concept, ensuring a self-contained study guide for Financial Accounting students.