Question
I have some word problems with Beta involved asking for different premiums or returns. Can I get some help with this concept?
Joe purchased 500 shares of Robotics stock at $4 per share on 1/1/07. Joe sold the shares on 12/31/07 for $5.45. Robotics stock has a beta of 1.4, the risk free rate is 5% and the market risk premium is 9%. The required rate of return on Robotics stock is what?
Emery Inc. has a beta of 1.5 and a required return of 15% based on the CAPM. If the risk free rate of return is 2%, the expected return on the market portfolio is what?
Please help me with step by step means to calculate so that I can relate these to future questions. Thanks
Explanation / Answer
1) According to the given problem, Beta = 1.4 Risk-free rate = 5% Market risk premium [E(Rm) - Rf] = 9% Here we need not figure out the value of market risk premium because the value is directly given. So, no calculation is requierd to compute the market risk premium. According to CAPM, Re = Rf + [ E(Rm) - Rf] Where Re = Required return on stock = ? Rf = Risk-free rate = 5% = risk co-efficient = 1.4 E(Rm) = Expected market return E(Rm) - Rf = Market risk premium = 9% Where Re = Required return on stock = ? Rf = Risk-free rate = 5% = risk co-efficient = 1.4 E(Rm) = Expected market return E(Rm) - Rf = Market risk premium = 9% Substituting the values in the above equation, we get Re = 0.05 + 1.4 [ 0.09] = 0.05 + 0.126 = 0.176 or 17.6% Therefore, the required return on stock is 17.6% 2) According to the given problem, Beta = 1.5 Risk-free rate = 2% Expected Market return E(Rm) = ? Required return (Re) = 15% Here the requried return on stock is given directly, so we have to calculate the value of expected market return using the CAPM equation. By substituting the values in the CAPM equation, we get Re = Rf + [E(Rm) - Rf] 0.15 = 0.02 + 1.5 [E(Rm) - 0.02] 0.15 - 0.02 = 1.5 [ E(Rm) - 0.02] 0.13 = 1.5 [ E(Rm) - 0.02] (0.13 / 1.5) = E(Rm) - 0.02 0.0866 = E(Rm) - 0.02 E(Rm) = 0.0866 + 0.02 = 0.1066 or 10.66% Therefore, the value of expected return on market is 10.66% Beta = 1.5 Risk-free rate = 2% Expected Market return E(Rm) = ? Required return (Re) = 15% Here the requried return on stock is given directly, so we have to calculate the value of expected market return using the CAPM equation. By substituting the values in the CAPM equation, we get Re = Rf + [E(Rm) - Rf] 0.15 = 0.02 + 1.5 [E(Rm) - 0.02] 0.15 - 0.02 = 1.5 [ E(Rm) - 0.02] 0.13 = 1.5 [ E(Rm) - 0.02] (0.13 / 1.5) = E(Rm) - 0.02 0.0866 = E(Rm) - 0.02 E(Rm) = 0.0866 + 0.02 = 0.1066 or 10.66% Therefore, the value of expected return on market is 10.66%