What is a risk-neutral probability measure?

A risk-neutral probability measure is defined as a probability measure under which all investors are indifferent to risk, meaning they value risky and risk-free assets the same way in terms of expected returns. This concept is foundational in financial economics, especially in pricing derivatives and evaluating risky investments.

The correct answer specifies that under a risk-neutral measure, expected returns are equal to the risk-free rate. This reflects the absence of risk preference; investors expect to earn the risk-free rate on average, regardless of the risk associated with individual assets. In a risk-neutral world, every asset is expected to return the risk-free rate, regardless of its inherent risk, simplifying the pricing of risky assets.

In contrast, the other options do not accurately describe a risk-neutral probability measure. The first option incorrectly suggests that risk is accounted for, which is contrary to the concept of risk neutrality. The second option implies that the measure reflects actual market risk preferences, which is not the case in a risk-neutral framework. Lastly, the notion that the measure is specific to real assets is incorrect, as risk-neutral probability measures apply comprehensively to all types of assets, including financial derivatives.