Stock XYZ has an expected return of 12%, and beta = 1. Stock ABC has an expected return of13%, and beta = 1.5. The market's expected return is 11% and rf = 5%. What is the alpha coefficient
Question
Stock XYZ has an expected return of 12%, and beta = 1. Stock ABC has an expected return of13%, and beta = 1.5. The market's expected return is 11% and rf = 5%. What is the alpha coefficient
Solution
The alpha coefficient is a measure of the performance of an investment relative to a benchmark index. It is the intercept of the Security Market Line (SML) which shows the expected return of a security for different levels of systematic, or market, risk. The SML is derived from the Capital Asset Pricing Model (CAPM), which is expressed as:
E(Ri) = Rf + βi[E(Rm) - Rf] + αi
Where: E(Ri) = Expected return on the security Rf = Risk-free rate βi = Beta of the security E(Rm) = Expected return on the market αi = Alpha of the security
Rearranging the formula to solve for alpha gives:
αi = E(Ri) - [Rf + βi[E(Rm) - Rf]]
Let's calculate the alpha for each stock:
For stock XYZ: αXYZ = 0.12 - [0
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