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A large number of different assets exist into which a saver can invest cash not currently needed, and investors must choose what combination best suits their needs. Because more money is considered to bring more happiness or utility, investors generally seek to maximize the return on their investments.

Although maximizing investor returns and wealth is usually assumed to increase an individual’s happiness or utility, the marginal utility of wealth and consumption is normally found to decline with increases in the level of wealth and consumption. For instance, if an individual has no money, the receipt of one dollar can be used to buy a loaf of bread that might prevent death by starvation. Thus, this first dollar brings a great deal of happiness, although the individual might still be a little hungry. If the individual receives another dollar, she or he could buy a second loaf of bread and eliminate all feelings of hunger. This second dollar also brings happiness but relatively less than the first one (that is, for most individuals, preventing starvation has a higher utility than preventing mere hunger). A similar analysis follows for an individual with $100,000 that can be used to buy one’s first house and which provides more utility than a second $100,000 that could be used to buy an additional house (like a vacation home). As a result, investors tend to be averse to the chance of equal variation above and below a given wealth level (and are therefore averse to the risk of deviations from an expected return level).

Because returns on wealth are not always certain, investors must concern themselves with more than expected return. Investors must also be concerned with the risk that returns from the investments may be different than those expected (especially with the risk that returns may be less than expected).

Risk can be measured as deviations from the expected return. As previously mentioned, since the marginal utility of wealth generally declines with increases in wealth, the possibility of equal deviations from an expected wealth level typically has a net negative expected utility. For instance, assume the poor individual with just one dollar had the opportunity of betting double or nothing on the occurrence of a penny being flipped and landing on its head. With a 50% chance of the penny landing on its head, there exists an equal chance of a one dollar deviation above or below her/his expected ending wealth level of one dollar Because losing a dollar means starvation, whereas winning an additional dollar only means reducing hunger pains, the positive utility of winning the bet has a lower absolute value than the negative utility of losing the bet. As a result, the bet would have a negative expected utility, and the individual would be wise in avoiding the risky investment in the penny flip. Because the possibility of equal deviations from an expected wealth level have negative expected utility, investors try to avoid or minimize such risk.

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