Chapter 9: Cost of Capital and Risk Concepts
Overview of Cost of Capital
Focus: Understanding the cost of capital as a crucial discount rate in Net Present Value (NPV) calculations, which assess investment profitability.
Goal: Learn how to accurately calculate the cost of capital, identify its components, and understand its importance in financial decision-making.
Review of Chapter 7
Beta and Risk:
Key concept: Beta measures both systematic (market) and unsystematic (specific) risk associated with stocks. It reflects how much a stock's price is expected to move relative to market movements, with values greater than 1 indicating higher sensitivity to market shifts.
Estimating Beta:
Use regression in Excel:
Column 1: Monthly returns of the stock or portfolio (minimum data range: last 5 years).
Column 2: Monthly returns of a chosen market portfolio, often represented by indices like the MSCI World Index or S&P 500.
The regression analysis results in two important outputs: alpha (the intercept) and beta (the slope), where:
Alpha: Represents the stock's return independent of market movements.
Beta: Indicates the stock's market risk exposure, quantified by the slope of the regression line.
Total Risk Composition
Formula Structure:
Total risk equals the sum of market risk and specific risk. It is essential to recognize that market risk affects all investments, while specific risk pertains to individual assets.
Variance Calculation:
Variance can be expressed mathematically as:
ext{Var}(R) = ext{Var}( ext{Market}) + ext{Var}( ext{Error})Math Rule: For any constant in variances, we use the principle:
ext{Var}(C imes X) = C^2 imes ext{Var}(X)
(where C is any constant).
Diversification Effects
Risk Reduction Through Diversification:
Incorporating a diverse range of stocks from different sectors or geographical regions significantly diminishes specific risk, often bringing it to near zero. This practice results in portfolios that primarily shoulder market risk, a risk inherent to the overall economy or market.
Beta of a Portfolio:
The portfolio beta is calculated as the weighted average of the individual betas of each stock held, demonstrating the overall market sensitivity of the portfolio.
Practical Application with Regression
Regression Example with Citigroup:
A visual graph illustrates:
X-axis: Represents market return derived from the MSCI World Index.
Y-axis: Corresponds to Citigroup's monthly returns.
Regression Line:
The slope denotes beta (e.g., Beta = 1.83), indicating that a 1% increase in market return leads to a 1.83% increase in Citigroup’s return.
Alpha (the y-intercept) illustrates additional returns not attributed to market movements, yet may be less critical in some analyses.
R-Squared (R²) Importance
Definition:
R² values provide insight into how well the regression model explains the variability of the dependent variable; in this case, Citigroup returns. R² ranges from 0 to 1, where:
R² = 0.64 indicates that 64% of the variability in Citigroup's returns can be explained by movements in the market.
Higher R² values suggest a stronger relationship between the market and the specific asset being analyzed, highlighting the proportion of total risk attributed to market fluctuations.
Example Comparison
Campbell Stock Analysis:
Campbell's lower Beta (0.33) signifies less volatility relative to market movements, indicating a more stable investment in comparison to Citigroup.
An R² value of 0.22 illustrates that only 22% of Campbell's stock return variability is linked to market changes, suggesting a broader capability of resisting market shocks.
Conclusion and Connections to Risk
Key Takeaway:
From the analysis, bank stocks generally present higher Betas and elevated R² values due to pronounced sensitivity to economic fluctuations and market shocks. In contrast, stocks in the food sector typically exhibit lower Betas and R² values, demonstrating reduced exposure to macroeconomic variances. This information is crucial for investors to gauge risk and make informed investment decisions involving asset returns and market behaviors.