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Financial Risk Manager Part 1

Financial Risk Manager Part 1

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Company ABC is expected to return 15% per year to its investors, the market expected return is 8%, and the risk-free rate is 3.5%. What is ABC's stock beta?

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TTanishq

Explanation:

Explanation

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

E(Ri)=Rf+βi(E(Rm)−Rf)E(R_i) = R_f + \beta_i(E(R_m) - R_f)E(Ri​)=Rf​+βi​(E(Rm​)−Rf​)

Where:

  • E(Ri)E(R_i)E(Ri​) = Expected return of the stock = 15%
  • RfR_fRf​ = Risk-free rate = 3.5%
  • E(Rm)E(R_m)E(Rm​) = Expected market return = 8%
  • βi\beta_iβi​ = Stock beta (what we're solving for)

Step-by-step calculation:

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

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

  3. Rewrite the equation: 15%=3.5%+4.5%βi15\% = 3.5\% + 4.5\%\beta_i15%=3.5%+4.5%βi​

  4. Subtract the risk-free rate from both sides: 15%−3.5%=4.5%βi15\% - 3.5\% = 4.5\%\beta_i15%−3.5%=4.5%βi​ 11.5%=4.5%βi11.5\% = 4.5\%\beta_i11.5%=4.5%βi​

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

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