Understanding Beta in Finance: Calculation, Stability, and Determinants

The Company Beta (β)

β = Cov(R_i, R_M) / Var(R_M)

Problems of Beta:

1. Betas may vary over time.
2. The sample size may be inadequate.
3. Betas are influenced by changing financial leverage and business risk.

Solutions:

1. Problems 1 and 2 can be moderated by more sophisticated statistical techniques.
2. Problem 3 can be lessened by adjusting for changes in business and financial risk.
3. Look at average beta estimates of several comparable firms in the industry.

Stability of Beta

Most analysts argue that betas are generally stable for firms remaining in the same industry, but they can change due to:

• Changes in product line
• Changes in technology
• Deregulation
• Changes in financial leverage

Using an Industry Beta

It is frequently argued that one can better estimate a firm's beta by considering the whole industry. Consider the following:

• If you believe that the operations of the firm are similar to the operations of the rest of the industry: Use the industry beta.
• If you believe that the operations of the firm are different from the operations of the rest of the industry: Use the firm's beta.

Determinants of Beta

We consider three factors: the cyclical nature of revenues, operating leverage, and financial leverage.

Cyclicality of Revenues

The revenues of some firms are quite cyclical. These firms do well in the expansion phase of the business cycle and do poorly in the contraction phase. Empirical evidence suggests that retailers and automotive firms fluctuate with the business cycle. On the other hand, transportation firms and utilities are less dependent on the cycle. As beta measures the responsiveness of a stock's return to the market's return, it is not surprising that highly cyclical stocks have high betas.

Note: Cyclicality is not the same as variability. Stocks with high standard deviations need not have high betas.

Operating Leverage

The degree of operating leverage measures how sensitive a firm is to its fixed costs. It increases as fixed costs rise and variable costs fall. Operating leverage magnifies the effect of cyclicality on beta. That is, a firm with a given sales cyclicality will increase its beta if fixed costs replace variable costs in its production process. DOL is given by:

DOL = ∆EBIT / EBIT ⋅ Sales / ∆Sales

Financial Leverage and Beta

Financial leverage is the sensitivity to a firm's fixed costs of financing. The relationship between the betas of the firm's debt, equity, and assets is given by:

[Formula not included as it requires mathematical symbols and formatting]