Eva is risk-averse. Currently she has 50,000 to invest. She...

Eva is risk-averse. Currently she has $\$ 50,000$ to invest. She faces the following choice: she can invest in the stock of a dot-com company, or she can invest in IBM stock. If she invests in the dot-com company, then with probability 0.5 she will lose $\$ 30,000$, but with probability 0.5 she will gain $\$ 50,000$. If she invests in IBM stock, then with probability 0.5 she will lose only $\$ 10,000,$ but with probability 0.5 she will gain only $\$ 30,000$. Can you tell which investment she will prefer to make?

Key Concepts

Expected Utility Theory

Expected utility theory is a framework used in economics to explain how individuals make choices under uncertainty by assigning a utility value to each outcome rather than simply considering the monetary value. This theory accommodates risk preferences by using a concave utility function for risk-averse agents, which captures the diminishing marginal utility of wealth. Consequently, even if two investments have the same expected monetary value, a risk-averse investor will choose the one with the higher expected utility, which typically involves a smaller variance in outcomes.

Variance

Variance measures the dispersion of outcomes around the expected value, serving as an indication of the risk or uncertainty associated with an investment. A higher variance indicates that the outcomes are more spread out from the expected value, implying greater risk. For a risk-averse investor, an option with a lower variance is typically more attractive because it provides more predictable returns, even if the expected value is the same.

Risk Aversion

Risk aversion is a characteristic of decision-makers who prefer a certain outcome over a gamble with a higher or equal expected value. This concept reflects the idea that individuals experience diminishing marginal utility of wealth; in other words, the pain of losing a given amount is usually greater than the pleasure of gaining the same amount. Risk-averse individuals opt for investments or choices that reduce uncertainty even if the expected monetary outcomes are the same.

Expected Value

The expected value is a central concept in probability and decision theory that represents the average outcome of a probabilistic event, weighted by the probabilities of the various outcomes. In investment decisions, comparing the expected values of different options helps in assessing which option, on average, yields a higher return, although risk-averse individuals might not simply pick the option with the highest expected value.

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