This type of decision-making based on probable outcomes is used in many different situations: buyers decide how much they are willing to pay for a used car based on the different probabilities that it is in mint condition, that it needs minor repairs, or that it is a useless piece of junk. Students decide how much to study based on their expected performance after different amounts of studying. Art lovers base their decisions on the probabilities that the pieces they are looking at are genuine or forged. In any case where the exact value of a good is unclear, buyers must make their decisions based on probable outcomes and possible worth. After making an estimate of expected value and assessing the risk involved, buyers can then attempt to maximize their utility based on their individual preferences for goods.
Risk usually varies inversely with expected returns. That is, a high risk investment will often yield a much higher potential payoff than a low risk investment. This difference in value can be seen as a "reward" for buyers' willingness to take a higher risk. The "penalty" for taking a higher risk is the possibility of losing a lot of money if the investment fails. We can see this discrepancy in the high yields (and losses) in the stock market, which is relatively high risk, the moderate yields of mutual funds, which are relatively moderate risk, and the low yields of government bonds, which are relatively low risk. When a payoff is guaranteed, as with low risk investments, the payoff is usually small, and when a payoff is uncertain, as with high risk investments, the payoff is usually higher.