Question

8. Consider the following information:
                          Standard Deviation      Beta

Security X                 29%                    1.22
Security Y             37%                          0.75
a) Which security has higher total risk? Explain.
b) Which security has higher systematic risk? Explain.
c) Which security should have a higher level of expected return? Explain

Answer 1

Before we get into the questions, let's revisit the following concepts:

1. Standard deviation of the returns of a security is the measure of the total risk of a security.
2. The total risk is made up of systematic risk and unsystematic risk. Diversification helps reduce unsystematic risk.
3. Beta is a measure of systematic risk of a security.
4. Risk premium on a security is a function of the systematic risk of the security. Risk premium is proportional to the systematic risk of the security.

Let's now get into the question one by one.

a) Which security has higher total risk? Explain.

Standard deviation of the return of a security is a measure of total risk of the security. Hence, a security with higher standard deviation should have higher total risk. Here, standard deviation of the returns of the security Y = 37% > 29% = standard deviation of the returns of the security X. Hence, security Y has higher total risk.

b) Which security has higher systematic risk? Explain.

Beta is a measure of the systematic risk of a security. Higher the beta, higher will be the systematic risk of the security. In this case, beta of security X = 1.22 > 0.75 = beta of security Y. Hence security X has higher systematic risk.

c) Which security should have a higher level of expected return? Explain

Risk premium of a security is directly proportional to the systematic risk. Hence, the expected return will be higher in case of a security with higher systematic risk. Higher beta implies a higher systematic risk. In this case, beta of security X = 1.22 > 0.75 = beta of security Y. Hence security X has higher systematic risk. And hence, security X should have a higher level of expected return.