Financial Risk Manager Part 1

Explanation

This question uses the Capital Asset Pricing Model (CAPM) formula:

$E(R_i) = R_f + \beta_i(E(R_m) - R_f)$

Where:

• $E(R_i)$ = Expected return of the stock = 15%
• $R_f$ = Risk-free rate = 3.5%
• $E(R_m)$ = Expected market return = 8%
• $\beta_i$ = Stock beta (what we're solving for)

Step-by-step calculation:

1. Plug in the known values: $15\% = 3.5\% + \beta_i(8\% - 3.5\%)$

2. Calculate the market risk premium: $8\% - 3.5\% = 4.5\%$

3. Rewrite the equation: $15\% = 3.5\% + 4.5\%\beta_i$

4. Subtract the risk-free rate from both sides: $15\% - 3.5\% = 4.5\%\beta_i$ $11.5\% = 4.5\%\beta_i$

5. Solve for beta: $\beta_i = \frac{11.5\%}{4.5\%} = 2.5556$

Interpretation: A beta of 2.5556 means that Company ABC's stock is highly volatile compared to the overall market. For every 1% change in the market return, ABC's stock is expected to change by approximately 2.56%. This high beta is consistent with the stock's high expected return of 15%, as higher risk should be compensated with higher expected returns according to CAPM.