Final answer:
An equity security with a market beta equal to one should expect to earn the same rate of return as the average stock in the market, which is option 'a. This is based on the principle that higher risk is compensated with higher expected returns according to the CAPM.
Step-by-step explanation:
The question revolves around the concept of systematic risk and the relationship between risk and return in the financial markets. An equity security with systematic risk equal to the average amount of systematic risk of all equity securities in the market is generally expected to have a market beta of one. Beta is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Therefore, the correct answer to the student's question is that such a security should expect to earn the same rate of return as the average stock in the market portfolio, which corresponds to the option 'a.
This understanding is based on the capital asset pricing model (CAPM), which predicts that the expected return on a security is equal to the risk-free rate plus beta times the market risk premium. A beta of one indicates that the security's price will move with the market. A beta greater than one indicates greater volatility than the market, and a beta less than one indicates less volatility than the market. The concept of risk is crucial in understanding investment decisions, as investors expect to be compensated for taking higher risks through higher expected returns.