Answer: Risk free rate = 1.9%
Explanation:
The Capital Asset Pricing Model allows for the calculation of the required return using the market return, beta and risk free rate.
Required return = Risk free rate + Beta * ( Market return - Risk free rate)
First find the market rate. Stock Y is uniquely positioned to help with that:
12.4% = Risk free rate + 1.0 * (Market return - Risk free rate)
12.4% = rf + Market return - rf
Market return = 12.4%
Apply this to the formula using Stock Z:
8.2% = rf + 0.6 * (12.4% - rf)
8.2% = rf + 7.44% - 0.6rf
rf - 0.6rf = 8.2% - 7.44%
0.4rf = 0.76%
rf = 0.76% / 0.4
Risk free rate = 1.9%
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