Security A has a standard deviation of 40 and a Beta of 05 S

Security A has a standard deviation of 40% and a Beta of 0.5. Security B has a standard deviation of 20% and a Beta of 1.5. Which of the following statements must be true? a. Security A has more idiosyncratic risk than Security B b. Security A has more unavoidable risk than Security B c. Security A has less total risk than Security B d. Security A will definitely give a lower return next year than Security B e. Security A will likely give a higher return than Security B

Solution

Option \"A\" is correct, i.e., A stock with a high beta might have a higher or lower standard

deviation than a stock with a low beta. The standard deviation is made up of both systematic

and unsystematic risk, whereas beta measures just systematic risk. Stock B has a high beta

and a relatively low sigma, but this might simply reflect that most of stock B’s risk is

systematic. On the other hand, stock A has a higher variance, but if most of this risk is

unsystematic, stock A will have a lower beta.