It turns out that in a complete market with no arbitrage opportunities there is an alternative way to do this calculation: Instead of first taking the expectation and then adjusting for an investor's risk preference, one can adjust, once and for all, the probabilities of future outcomes such that they incorporate all investors' risk premia, and then take the expectation under this new probability distribution, the "risk-neutral measure". The main benefit stems from the fact that once the risk-neutral probabilities are found, "every" asset can be priced by simply taking the present value of its expected payoff. Note that if we used the actual real-world probabilities, every security would require a different adjustment (as they differ in riskiness).