Chartered Financial Analyst Level 1

Chartered Financial Analyst Level 1

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An analyst gathers the following information about an asset and the market: Risk-free rate: 1% Market risk premium: 5% Asset's expected return: 5% Based on the Capital Asset Pricing Model (CAPM), the asset's beta is closest to:



Explanation:

The correct answer is A (0.80). According to the CAPM, the expected return of an asset is calculated as:

E(Ri)=Rf+Ξ²i(E(Rm)βˆ’Rf)E(R_i) = R_f + \beta_i (E(R_m) - R_f)

Where:

  • E(Ri)E(R_i) is the expected return of the asset (5%).
  • RfR_f is the risk-free rate (1%).
  • E(Rm)βˆ’RfE(R_m) - R_f is the market risk premium (5%).
  • Ξ²i\beta_i is the asset's beta.

Rearranging the formula to solve for Ξ²i\beta_i:

Ξ²i=E(Ri)βˆ’RfE(Rm)βˆ’Rf=5%βˆ’1%5%=4%5%=0.80\beta_i = \frac{E(R_i) - R_f}{E(R_m) - R_f} = \frac{5\% - 1\%}{5\%} = \frac{4\%}{5\%} = 0.80

Option B (1.00) is incorrect because it omits subtracting the risk-free rate in the numerator, leading to Ξ²i=5%5%=1.00\beta_i = \frac{5\%}{5\%} = 1.00.

Option C (1.25) is incorrect because it inverts the formula, resulting in Ξ²i=5%4%=1.25\beta_i = \frac{5\%}{4\%} = 1.25. This error arises from misapplying the CAPM formula.