Which of the following statements regarding risk$-$averse investors is true?

Select one:

a$.$ They only accept risky investments that offer risk premiums over the risk$-$free rate.

b$.$ They have a negative risk aversion coefficient.

c$.$ They will always choose the investment with the lowest risk.

d$.$ They accept investments that have a $50\%$ chance of a positive return.

e$.$ Their utility always decreases when risk increases, even when return increases.