IBM's common stock has a beta of 0.85. If the expected risk-free return is 4.5% and the market risk premium is 7%.
a) Calculate IBM’s required rate of return (10pts)
b) Assume IBM’s actual realized return is 15%. Calculate its abnormal return (i.e. alpha). (5pts)
a) To calculate IBM's required rate of return, we can use the Capital Asset Pricing Model (CAPM). The CAPM formula is as follows:
Required Rate of Return = Risk-Free Rate + Beta * (Market Risk Premium)
Here, the given risk-free rate is 4.5% and the market risk premium is 7%. The beta for IBM's common stock is given as 0.85. We can substitute these values into the formula to calculate IBM's required rate of return:
Required Rate of Return = 4.5% + 0.85 * 7%
Calculating the multiplication first:
Required Rate of Return = 4.5% + 5.95%
Now, add the percentages together:
Required Rate of Return = 10.45%
Therefore, IBM's required rate of return is 10.45%.
b) To calculate IBM's abnormal return, we need to compare its actual realized return to its expected return (which we calculated in part a).
Abnormal Return (Alpha) = Actual Realized Return - Expected Return
The given actual realized return is 15%, and from part a, we calculated the expected return to be 10.45%. Substituting these values into the formula, we can calculate IBM's abnormal return:
Abnormal Return = 15% - 10.45%
Calculating the subtraction:
Abnormal Return = 4.55%
Therefore, IBM's abnormal return (alpha) is 4.55%.