Which of the following statements BEST describes the concept of risk premium?

A$.$ Investors need to be compensated for taking risk. Risk premium suggests that the higher the risk, the higher the required return.

B$.$ Risk premium describes the observation that riskier assets have higher standard deviation in returns than lower risk assets.

C$.$ Risk premium refers to the extra risk associated with a risky asset, such as a stock or bond, compared to the risk on a government treasury bill $($T$-$Bill$).$

D$.$ Risk premium refers to difference between the return on a risky asset, and the return that would otherwise be expected from a risk$-$free asset.