Question

Stock A has a standard deviation of returns of 15% and a beta of 1.8. Stock B has a standard deviation of returns of 22% and a beta of 0.46. Which stock has higher levels of unsystematic risk? explain answer please

Answer 1

Standard deviation or total risk comprises of beta (or systematic/market risk) and unsystematic risk.
Unsystematic risk^2=Standard deviation^2-beta*market standard deviation^2

For Stock A:
unsystematic risk^2=(15%)^2-(1.8*m)^2
For Stock B:
unsystematic risk^2=(22%)^2-(0.46*m)^2

We can try for any value of m or market risk and we will see that Stock A has lower unsystematic risk and Stock B has higher unsystematic risk

As Stock A has lower standard deviation and higher beta, it means that Stock A has lower unsystematic risk and Stock B has higher unsystematic risk.