How Changing Capital Structure Affects Beta
Asset beta is the weighted average of debt and equity betas:
\[ \beta_A=\beta_D\frac{D}{V}+\beta_E\frac{E}{V}. \]
Initial structure:
\[ D=33.3,\ E=66.7,\ \beta_D=0.1,\ \beta_E=1.1,\ V=100, \]
so
\[ \beta_A=\frac{33.3}{100}(0.1)+\frac{66.7}{100}(1.1)=0.767. \]
After refinancing:
\[ D=50,\ E=50,\ \beta_D=0.15,\ \beta_E=? \]
and
\[ \frac{50}{100}(0.15)+\frac{50}{100}\beta_E=0.767 \Rightarrow \beta_E=0.767+(0.767-0.15)\frac{50}{50}=1.384. \]
Conclusion: leverage does not change asset risk/return, but it raises common-equity risk.
Notes from the slide:
- Debt betas are often close to zero but may become positive when default risk rises.
- Interest-rate risk can also create positive correlation between bond and stock returns.
- For large firms, debt betas are often in the range \(0\) to \(0.2\).