When we employ the Fundamental Theorem of Asset Pricing and the existence of an equivalent probability measure, say $Q$ with respect to the historical probability $P$, we often say the expectation under this risk-neutral probability is "risk-adjusted" payoff or premium.
I often resort to an explanation that the "risk adjustment" occurs, because the actual world we live in, traders are not risk-neutral, so by assuming an arbitrage-free economy and the aforementioned fundamental theorem, we are essentially making use of the existence of the equivalent probability measure where the synthetic construction is uniquely possible (also assuming completeness).
Do you care to share a better and more intuitive way to explain the "risk-adjustment" in this context?
In finance, we often use "risk-adjusted" return on an investment, and some students without math finance background often get confused when these terms are equivocated. How would you relate two concepts on an intuitive level?