CFA Level IPortfolio ManagementEasy
Using the Capital Asset Pricing Model, calculate the required rate of return for a stock with a beta of 1.3 if the risk-free rate is 4% and the expected market return is 10%.
- A13.0%
- B11.8%
- C7.8%
- D10.0%
Show answer & explanationAnswer & explanation
Correct answer: B. 11.8%
CAPM: E(R) = Rf + β × [E(Rm) − Rf] = 4% + 1.3 × (10% − 4%) = 4% + 1.3 × 6% = 4% + 7.8% = 11.8%.
Why the other options are wrong
- A. Incorrectly multiplies beta by the full market return instead of the risk premium.
- C. This is only the risk premium component, not the full required return.
- D. This is the market return without adjusting for the stock's beta.
Capital Asset Pricing Model (CAPM)
A model that calculates the expected/required return on an asset based on its systematic risk (beta) relative to the market.
- Formula: E(R) = Rf + β[E(Rm) − Rf]
- Beta measures sensitivity to market movements
- Assumes investors are compensated only for systematic risk
Memory trick: Risk-free base plus beta times the market's extra kick