The expected return for a share calculated using the CAPM is 18%. Themarket return is 10% and the beta of the share is 2. Calculate the impliedrisk-free rate (as a percentage)
Question
The expected return for a share calculated using the CAPM is 18%. Themarket return is 10% and the beta of the share is 2. Calculate the impliedrisk-free rate (as a percentage)
Solution
The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between systematic risk and expected return for assets, particularly stocks. The formula for CAPM is:
Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)
We can rearrange this formula to solve for the risk-free rate:
Risk-Free Rate = Expected Return - Beta * (Market Return - Risk-Free Rate)
Given that the expected return is 18%, the market return is 10%, and the beta is 2, we can substitute these values into the formula:
Risk-Free Rate = 0.18 - 2 * (0.10 - Risk-Free Rate)
Solving this equation for the risk-free rate gives:
3 * Risk-Free Rate = 0.18 - 0.20 = -0.02
Risk-Free Rate = -0.02 / 3 = -0.0067 or -0.67%
So, the implied risk-free rate is -0.67%. This negative risk-free rate is unusual and may suggest an error in the input values or assumptions.
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